In this section, the results of the various simulation approaches are analyzed in terms of the aerodynamic characteristics and performance. Comparisons are made both with the engine cycle model specifications as well as among the differing fan modeling approaches. Figure 5
shows an overview of the station definitions used in the discussion of the simulation results. The three Chimera interfaces are shown in blue, red and orange, and they generally coincide with locations that are relevant for the performance evaluation of the engine. For example, the evaluation of the fan stage performance, i.e., across both the fan and rotor, draws on the total pressure and temperature results computed in the simulations on the Chimera surfaces located at Station 2 and Station 13. The total mass flow rate of air is evaluated using the Chimera surface at Station 2 and the computed bypass mass flow rate is determined at Station 13. The core engine mass flows are evaluated directly on the planar surfaces which correspond to the previously described boundary conditions definitions, as shown in Figure 3
. In general, these latter mass flows are set directly as per the engine cycle model specifications.
The main focus in the discussions is placed on the APP case. This case was chosen as it is one of the more challenging in terms of fan aerodynamics and has relevance for future airframe driven studies, as the interaction of a wing-mounted UHBR engine jet with the high-lift system may be a concern. Results across the full family of mesh densities as well as for the various time steps used are discussed in detail for this case.
illustrates the impact of the very short intake characteristic of current UHBR nacelle designs on the fan inflow conditions. For the approach condition shown here, which features a high angle of attack of the nacelle, Figure 6
a,b highlight, that in a plane just upstream of the fan blade leading edges, a notably perturbed flowfield can be found. The total pressure contours show the effect of the high acceleration of the flow over the short lower lip of the nacelle at the high incidence angle, while the plot of the fan blade effective angle of attack distribution shows that a blade is subject to essentially the nacelle incidence angle across most of its span. For the counter-clockwise fan rotation, this leads to an increasing effective angle of attack for a blade during the downward sweep on the left side and a reduction thereof on the upward sweep on the right side of the nacelle. As a consequence of this, a fan blade is subject to an azimuthally varying inflow, which results in rotor blade loading variations during a rotation. This is shown through the fan rotor disc loading plotted in Figure 6
c, and the impacts are discussed in detail in the following section.
4.1. uRANS Simulation Analysis
shows an instantaneous result of the uRANS simulation of the UHBR configuration at the approach operating point point using the fine density mesh. The lessons-learned from the previous CROR-studies have been applied and result in a good resolution of the unsteady fan-OGV interactions, as shown in the figure for example through the impingement of the fan blade wakes on the OGV blades. Proper resolution of these dominant unsteady aerodynamic effects is key for potential further exploitation of the uRANS simulations in the frame of structural, aeroelastic or aeroacoustic assessments.
The temporal resolution used in the uRANS analysis has a profound impact on the resolution of the aerodynamic interactions between the fan blades and the OGV vanes. Contour plots of instantaneous solutions taken from the uRANS simulations of the APP case using the medium density mesh at selected time step sizes illustrate this in Figure 8
. In each subfigure, total pressure contours are plotted on a cylindrical surface located at a radial position of
to show the resolution of the fan blade wakes, in particular as they pass through the Chimera overlap region between the rotating fan and the stationary OGV mesh domain. For the relatively coarse time step size of 180 per revolution, shown in Figure 8
a, the significant error introduced in the sustainment of this flow feature, which plays an important role for the unsteady aerodynamic loading on the stator and thus also the fan stage noise, is clearly evident. The successive refinement of the temporal resolution, going to an intermediate value of 720 time steps per rotor revolution in Figure 8
b and the to the finest level of 1728 in Figure 8
c, shows that using an appropriately small time step size is vital to capture the fan blade wake adequately and ensure its interaction with the outlet guide vanes is properly simulated.
A more quantitative analysis of the temporal resolution and fan blade wake sustainment across the chimera interface is presented in Figure 9
. The instantaneous total pressure wake profiles are plotted as a downward look at the engine bypass duct flowfield from above, and show three axial positions denoted using their distance from the fan blade trailing edge at this radial position, as marked in Figure 9
The middle plot, Figure 9
b, compares the medium mesh uRANS results for the three selected temporal resolutions at an axial location of
downstream of the fan blade trailing edge, which is just upstream of the Chimera interface between the rotor and stator mesh domains. Representing a quasi-steady solution in the rotating frame of reference of the fan domain—at least when any temporal resolution impact the upstream effects of the outlet guide vanes have on the fan are negligible—they show an essentially perfect match of all three results. Clear differences between the selected solutions are evident in the mid section of Figure 9
b, which plots the wake profiles at an axial position of
just downstream of the Chimera interface. For the coarsest time step size of 180 per rotor revolution, the transfer of the fan blade wake across the overset boundary is strongly degraded due to the large relative mesh motion that occurs for this temporal resolution choice. The wake deficit is significantly lower than both the results at time steps of 720 and 1728 per rotor revolution, with the latter two in relatively close agreement. The highest temporal resolution of 1728 time steps per revolution shows the best preservation of the fan blade wake across the interface. For the final axial position of
, for which the fan blade wakes have propagated the same distance in the stationary OGV mesh block from the mid plot as they did between the first two axial positions shown in Figure 9
b, these trends and observations remain the same. While the coarse time step result shows wake profiles to be strongly dissipated, clear wake deficits are still observable for the two higher temporal resolution results.
c shows fan blade wake total pressure profiles at the same axial positions previously discussed, but compares the APP case results achieved on the three mesh levels at the highest temporal resolution available for each case. For the position closest to the fan blade trailing edge shown on the left in the figure, the fine and medium mesh results show marginal differences, while slightly more notable deviations in the blade wake deficit predictions are seen for the coarse mesh result. After having passed through the Chimera interface, these general observations are still similar. The coarse mesh wake profiles show a slight increase in their differences to the other two cases, while there is a small indication of a more rapid wake decay on the medium mesh than seen on the fine mesh. This can be deduced from the slightly more pronounced widening in an individual fan blades wake deficit, while the amplitudes remain essentially identical. For the aft most located axial profiles plotted on the right in the figure, the coarse mesh results show a clear impact of numerical dissipation in the reduced amplitude and the widening of the blade wake deficits. This is seen to a much lesser degree when comparing the medium and the fine mesh results, which remain in relatively close agreement even at this downstream axial location of
. All of the wake profiles reflect the non-axisymmetric loading of the fan that results due to the short inlet length and the relatively high nacelle incidence angle, as discussed in Figure 6
. Both the mean total pressure values and the magnitude of the wake deficit increase as a fan blade rotates towards the top position, where the effective blade incidence angle due to the non-uniform inflow is increasing.
For the APP operating point, Figure 10
shows the time history of the unsteady axial loading development for a reference fan blade and the top outlet guide vane during one full rotor revolution. Figure 10
a plots the results of the time step study on the highest density mesh for a reference fan blade during one full revolution. A similar analysis is shown in Figure 10
b for a reference outlet guide vane, which, due to the 16-bladed fan, is affected by four fan blade passages during the plotted quarter rotation of the rotor. For the fan, at all temporal resolutions, the once per revolution sinusoidal oscillation of the blade loading due to the angle of attack of the engine is predicted equally well. However, the upstream potential flow impact of the OGV vanes on a fan blade is only well resolved when the time step is sufficiently small. This is evident when looking at the spectral analysis of the fan blade loading development in Figure 11
a. The fundamental interaction occurring at a shaft order of 36 is only beginning to be captured well enough when at least 360 time steps per revolution are used. A convergence of the oscillation amplitudes, both at the fundamental interaction frequency and at higher harmonics thereof, is then evident as the time step is further refined. The unsteady loading of the outlet guide vane is driven fundamentally by the impingement of the fan blade wakes. As discussed above, the resolution of this flow feature is strongly dependent on the time-step size. Very evident already in the time history plotted in Figure 10
b, the need for a temporal resolution of at least 720 time steps per rotor revolution to obtain a reasonable representation of the unsteady loads is more clearly highlighted by the spectral analysis shown in Figure 11
b. Both images show that, as for the fan, the good match between the results at the two highest temporal resolution indicate a convergence in the capture of this unsteady loading is achieved.
To substantiate the claim of an observed convergence of the unsteady loading amplitudes with higher temporal resolutions, the development of the amplitudes of the dominant unsteady loading for a fan blade at shaft orders 1, 36 and 72 is plotted in Figure 12
a versus the number of time steps used to resolve one rotor revolution. The figure includes the results of the uRANS simulations across the various temporal resolutions for the coarse, medium and fine mesh densities.
The black lines, which show the amplitude predicted for the 1P-loading cycle for each mesh density and time step, reveal a negligible influence of both temporal and spatial resolution. For the interactions with the OGVs at shaft orders 36 and 72, however, a clear asymptotic trend is evident as the time step size is reduced. The unsteady loading at the fundamental interaction frequency (shaft order 32) shows that a good approximation of the loading amplitude is obtained for all meshes when at least 720 time steps are used for one fan rotation. For the coarse mesh, a result using 1440 time steps per revolution is also included. This is a temporal resolution that exceeds that for which the mesh was intended, as discussed in the chosen approach to the rotor–stator interface mesh and how it relates to the time step size choice. For the fundamental frequency, the graph shows that no change in amplitude prediction is found for this additional temporal resolution. Generally, it is seen that the amplitude predictions for the selected frequencies at a given temporal resolution show a small dependence on mesh density. At the fundamental interaction frequency, the coarse mesh leads to the lowest amplitudes being resolved, while medium and fine mesh results show very similar predictions as the temporal resolution is increased in each case. An analogous analysis of the unsteady loading amplitude predictions for an outlet guide vane in dependence of mesh density and temporal resolution is shown in Figure 12
b. In this case, the predicted amplitudes at the fundamental interaction frequency (shaft order 16) and the higher harmonics thereof show values close to those at the highest temporal resolution being achieved when using 360 time steps per period. The exception is the result for the loading cycle occurring at shaft order 48 on the coarse mesh. Here, very low values are evident at all time step sizes, indicating that the spatial resolution is not sufficient on this mesh to properly account for this.
a plots the mean uRANS fan stage performance predictions in terms of total mass flow and fan stage pressure ratios for the APP operating point. The mean fan performance metrics are the result of an averaging done for one full rotor revolution at the various temporal resolutions under study. For both metrics, the values are shown as deviations from the engine cycle model specifications and plotted versus the number of time steps used to resolve one full rotor revolution. The figure compares the coarse, medium and fine mesh results for the APP operating point. Both the mass flow rate and the fan stage pressure ratio are in reasonable agreement with the specifications, considering the challenging nature of this test case with a relatively low fan pressure ratio. The predicted fan face mass flow is within
of the specifications on the coarse mesh and improves to matching the engine model data to within in
on the fine mesh. The stage pressure ratio is in agreement with the reference data to within
in all cases. A very small dependence of these mean performance metrics on the temporal resolution used in the uRANS simulations is seen, generally indicating that a temporal resolution of 360 time steps per rotor revolution is sufficient to obtain good mean performance predictions. The mesh density impact is more profound, showing an improved match with the specifications as the mesh is refined.
b plots the discrepancy in air mass flow that is found across the Chimera interfaces—a potential concern due to the non-conservative nature of the overset mesh technique as implemented in TAU. However, the results show that the interpolation losses are very low at less than
of the fan mass flow. These mass flow discrepancies are reduced both through mesh refinement and through improvements in temporal resolution. Of note is that the interpolation losses across the fan-OGV Chimera interface, which, as described above, was designed to feature co-incident nodes on both sides of boundary, shows the lowest values and a very strong asymptotic trend towards a value of 0 as the time step size is reduced. Thus, the non-conservative Chimera approach in TAU is found to not be an issue for the type of applications that DLR plans to be able to handle with the TAU Code using the simulation capabilities developed in the frame of ASPIRE.
lists all the mean aerodynamic performance results achieved in the DLR TAU uRANS simulations. For all studied operating points, the results for the fan mass flow and the fan stage pressure ratio are listed as deviations from the Airbus specifications and in dependence of the grid density and selected time step sizes as available from the simulation results. While the challenging low fan pressure ratio APP case shows an offset of up to 3% versus the targets, the results for other operating points generally only show deviations on the order of about 1%. Both spatial and temporal resolutions have a small impact on the mean performance predictions, with the former being the more important consideration. For all cases, it can generally be stated that good quality predictions of mean performance metrics are possible using coarse time steps. For all cases, including the approach case as the main focus in this paper, the TAU predictions of the mean UHBR engine performance metrics are within the scatter of results found by the various partners in the ASPIRE project [26
lists the results of a grid convergence study for the fan performance metrics of the APP case. It is done using the approach proposed by the Fluids Engineering Division of the ASME [27
], with refinements to the evaluation of the fine grid convergence index
as proposed by Eca and Hoekstra [29
]. The solution values listed for the fan mass flow and the fan pressure ratio are normalized with the corresponding values form the engine operating point specifications. For both performance metrics, a generally very good grid convergence can be accomplished. Larger values of the approximate relative fine grid error
, the extrapolated relative fine grid error
and the fine grid convergence index
are consistently found for the mass flow. This performance metric may show larger errors due to the additional impact of the Chimera interpolation in addition to the spatial resolution of the global mesh refinement. However, in general, and for the fan pressure ration in particular, the errors are low and the extrapolated values are very close to the values of the fine and medium meshes. In line with the observations made based on Figure 13
a, the medium and fine mesh simulations thus allow for good predictions of the mean aerodynamic performance of the engine.
4.2. Engine Boundary Condition Simulation and uRANS Results Comparison
An initial qualitative comparison of the results achievable for the approach operating point case with both the uRANS and the engine BC approach is shown in Figure 14
. The plots compare the mach number distribution on a plane through the engine centerline, showing the inlet flow, the external flow around the nacelle, and most importantly also the engine jet development. In general, a very favorable agreement between the uRANS result in Figure 14
b and the engine BC result in Figure 14
a is seen. A closer comparison of the jet development however shows that, while a perfectly axisymmetric jet is found for the engine boundary condition simulation, an asymmetry is seen in the uRANS results. Figure 14
b shows higher Mach numbers in the bypass flow on the lower side of the engine than on the top. This is related to the angle of attack and the resulting non-uniform inflow to the fan. With the fully geometrically modeled fan and OGV an azimuthal variation in the blade and stator loading is the consequence, which also results in a non-axisymmetric jet development. The engine boundary condition by design neglects any correlation of flow non-uniformity seen by the fan to the engine exhaust boundary condition. The inlet also shows some very small differences relating to the fact that the uRANS simulation allows for a non-uniform mass flow distribution across the fan face that is not accounted for in the steady state RANS simulation with the engine boundary condition. At the lower lip, for example, where the fan loading is higher than at the top due to the angle of attack effect in the uRANS modeling, a slightly higher flow acceleration is seen than in the steady RANS analysis. While for most applications this is not a particular concern, there may be cases where the jet and inflow non-uniformity is important. Such cases could be studies of engine jet and wing or high-lift system interactions or also studies of configurations with a boundary layer ingesting integration of the engines. In particular, at the the low-speed flight conditions strong inflow perturbations occur, making a better understanding and modeling of the jet development—as well as a proper modeling of the non-uniform fan face flow—an important issue for external aerodynamics studies utilizing an engine modeling.
compares the total engine mass flow rates found in the uRANS and the RANS simulations for the approach and sideline operating point cases. The values are normalized with the specified mass flow rates as computed by the engine cycle model. In general, both modeling approaches are relatively close with a deviation of less than
for the total mass flow rate seen versus the engine model specifications. Thus, in terms of mean engine performance predictions, the boundary condition does deliver very good results, but, as stated, the neglect of non-axisymmetry in the physical flowfield may be an issue for some investigations.
shows views of the UHBR engine from the front with total pressure contours added to highlight the engine jet development for the steady RANS simulation and the uRANS cases discussed in detail in the previous section. Here, the axisymmetry of jet that is inherent to the use of the engine boundary condition is clearly evident, with the total pressures essentially representing the mean azimuthal value found in the uRANS simulations. The coarse mesh result in Figure 15
b shows that jet flow features relating to the interaction of blade wakes with the outlet guide vanes are not resolved sufficiently. For the medium mesh results shown in Figure 15
c,d, it can be seen that the higher spatial resolution helps to enable the sustainment of the fan blade and outlet guide vane wakes as the temporal resolution is improved. As expected and plotted in Figure 15
e, both the strong variations of the flow across the azimuth and the unsteady flow resulting from the wakes of the two blade rows are best captured in the uRANS simulations using the fine mesh.
A quantitative evaluation of the jet characteristics at an axial position downstream of the nozzle that is representative for a position at which the flaps of an aircraft’s high lift system may be located is shown in Figure 16
and Figure 17
. Figure 16
plots profiles of both the total pressure as well as the deviations of the angle of attack from the mean flow along rays in a horizontal plane through the engine centerline.
For the total pressure profiles in Figure 16
a, all uRANS results are seen to be in very good agreement. This indicates that both mesh resolution and temporal resolution do not play a major role in capturing at least the mean flow characteristics in this case. The previously discussed discrepancy due to the uniform jet produced by the engine boundary condition model in the steady RANS result with the asymmetry seen in the uRANS results is the biggest difference to be observed. Furthermore, the combined effect of thicker boundary layers in the uRANS results as well as the unsteady nature of the bypass duct flow lead to a more pronounced mixing of the jet boundaries with the surrounding flow in the unsteady simulations. In the uRANS models, the boundary layers develop beginning at the nacelle lip and on the spinner, while in the RANS simulations boundary layer only start forming at the fan outlet boundary condition, they are thicker when they reach the nozzle in the former case. The steady RANS simulations also show a very constant total pressure profile across a large area of the bypass duct. This is again an inherent consequence of the models design, as constant total pressure and total temperatures are set on the entire plane representing the fan outlet. The variation of the loading distribution across the fan blade (and outlet guide vane) lead to a more non-uniform total pressure distribution across the bypass duct, which also reflect in the observable differences in the jet characteristics predicted by the two approaches. The angle of attack distribution in the jet as plotted in Figure 16
b shows some larger differences between the various uRANS results. This relates mostly to the differing densities of the meshes, which allow the fine mesh results to sustain fan blade and outlet guide vane wakes to be sustained to this axial position, for example, leading to more pronounced peaks in the angles across the jet. The most important difference between the full geometric modeling of the fan and the boundary condition approach is again traceable to the lack of non-uniformity in the latter approach. These results thus do not capture the fact that larger angle of attack deviations are seen in the jet on the left side than on the right, which may be of importance for the high lift system of an aircraft with a very closely coupled under-wing mounting of these types of UHBR engines.
The jet characteristics for lines extending radially through the engine axis in the vertical plane at the same axial position are plotted in Figure 17
. In general, the observations both for the total pressure as well as for the angle of attack deviations in the engine jet are comparable to the horizontal plane findings. The main difference is related to a slightly less pronounced asymmetry between the top and bottom half of the jet development than is found when comparing the left and right sides. Naturally, the presence of a wing and high lift system would lead to mutual interactions between the engine, the jet development and the interaction of the engine flowfield with the aircraft components. However, the general characteristics in terms of jet non-uniformity would certainly still apply, making the consideration of their impact at the aircraft level a worthwhile continuation of the present studies in the near future.
To understand the likely impact of the two fan modeling approaches compared in this article on some external aerodynamic aspects, Figure 18
plots a comparison of the nacelle pressure distributions drawn from all the previously discussed RANS and uRANS simulations. For most of the outer nacelle pressure distribution along the top and the bottom of the engine in Figure 18
a,b, respectively, good agreement is seen between all of the uRANS as well as the steady RANS result using the engine boundary condition model. Stagnation points at the lip are also seen to be in good agreement for all cases, indicating that the external aerodynamics for this nacelle are well captured in all approaches. The main source of any differences, seen predominantly in the inlet as well as at the nacelle trailing edge, are again directly related to the capability of predicting the fan loading non-uniformity.
Looking at the trailing edge, it can be seen that for both the top section and the bottom section, the uRANS results—in good agreement amongst the different mesh densities and temporal resolutions presented—show a slightly different pressure than seen in the RANS result. The engine boundary condition approach leads to an azimuthally uniform jet in terms of all relevant flow properties, while there were notable differences in jet velocities for the uRANS modeling approach, as seen for example in Figure 14
. Similarly, a more highly loaded fan at the bottom than at the top nacelle, properly represented when the fan stage is fully modeled in the uRANS approach, leads to a higher acceleration of the flow in the latter simulation results into the fan on the bottom lip. Subtle differences are visible between the uRANS results on the different meshes, with the highest suction peaks observed for the fine mesh case. Conversely, with a relatively low fan loading occurring at the top, the unsteady simulations show smaller suction peaks on the inner lip at the top of the nacelle.
For the external drag of the engine, as evaluated through a nacelle surface integration from the stagnation line on the inlet lip to the trailing edge at the bypass duct nozzle, the variation in the suction peaks visible at the top of the nacelle in Figure 18
a leads to notable differences when comparing the various results. In line with the observed trends on the suction peaks, where lower pressures lead to negative drag values due to the curvature of the lip, the uRANS results show that lower pressure drag values for the nacelle results, with the coarse mesh nacelle drag lowest at
of the RANS approach value, while those of the medium and the fine mesh increase to values of
, respectively. While an increase in pressure drag can thus be observed as the mesh is refined in the uRANS analysis, the trend in viscous drag is the inverse. This reduction in viscous drag at higher spatial resolution is most likely directly linked to the reduced flow acceleration on the nacelle upper lip. Thus, total drag for the nacelle in the uRANS studies is
for the coarse, medium and fine grid cases, respectively—indicating that non-uniform fan inflow effects for more highly integrated engine–airframe configurations can be an important consideration in the thrust–drag bookkeeping at the aircraft level.