Propeller wake impact on transition location

This work has been carried out within ESTRO Clean Sky 2 CfP project, whose goal was to develop an innovative future green regional aircraft configuration based on several new technologies able to match the very demanding and challenging objectives ACARE 2020 in terms of environmental impact. In details, an automatic numerical procedure for the evaluation of the detrimental effect of the propeller on transition location of a laminar turbo-prop wing is proposed here. The evaluation of transition location is based on a well-known procedure, based on the use of eN method implemented in a Linear Stability (LST) solver. The input data for the LST solver are represented by the pressure distribution as derived from high-fidelity Reynolds-Averaged Navier–Stoke (RANS) solutions and the velocity profiles in the boundary layer derived from a conical formulation of the boundary layer equations.


Introduction
Laminar flow technology represents one of the most promising solution to meet environmental requirements in terms of fuel burn because it allows a significant reduction of the aircraft aerodynamic drag.Since the contribution due to the skin friction drag constitutes around 50% of the drag budget for a typical long haul transport aircraft [1] and the skin friction in case of laminar flow is lower than the turbulent skin friction, the design of laminar wing has a great potential in the reduction of aerodynamic drag.The work presented here and performed within ESTRO project [2] is devoted to the description of a numerical approach used for the evaluation of the effect of the propeller on transition location for a laminar wing.The wake produced by the propeller could affect the extension of the laminar flow on the wing: this could result into unpredictable effects regarding the interaction of the wake with the laminar flow and the prediction of friction drag and leading edge separation.The numerical framework proposed here has been already presented in [3,4] and is based on the coupling between Linear Stability Theory and a RANS solution [5].The Linear Stability Theory is based on the use of linearized unsteady Navier-Stokes equations and is typically used for the application of e N method.Boundary layer information regarding the velocity profiles are derived from the solution of the compressible boundary layer equations written in conical form [6].The well-known e N transition prediction approach [7] is used for the prediction of the transition since it is widely used in aircraft industry for design purposes covering transition due to Tollmien--Schlichting (TS) and cross flow (CF) instabilities.

The configuration
The configuration considered in this paper is represented by the clean configuration of a laminar wing equipped with an advanced model of winglet (see Figure 1a).To consider the presence of the propeller, the disk actuator model has been implemented by considering data available in literature of a known model of propeller, whose characteristics are reported in Table 1.Moreover, this model has been implemented by modelling the swirl components (i.e. a radial and a tangential velocity components) of the wake, derived from the distribution of thrust along the span of the propeller.

Numerical approach
The numerical procedure proposed here is fully described in [2].A resume of the main steps is reported below, i.e.
1. Generation of a surface Cp distribution on the model based on RANS solution.The hybrid grid generated on the wing model (see Figure 1b for the surface grid) has both structured (hexahedral) and unstructured (pyramidal and tetrahedral) cells.The first layer thickness is defined to ensure a wall y+ between 0 and 1.The CFD solver used for the numerical simulations is SU2 [8].The presence of the propeller is simulated by considering the disk actuator model in which the tangential and swirl components of the wake are modelled, according to the general momentum theory starting from the knowledge of dC T dr ⁄ and dC P dr ⁄ [9].The pressure coefficient distribution is derived from a RANS solution of the flow field on the wing model considered here.Starting from this distribution, a certain number of sections are extracted: this data represent the position in which the transition location is evaluated.2. Generation of boundary layer profiles (KC-BLC).The in-house numerical code for the generation of boundary layer profiles (KC-BLCode, see [3,4]) is used to achieve the viscous flow solution by solving the compressible boundary layer equations for swept and tapered wings written in the conical formulation [6].The result derived from this step is represented by the velocity profiles in the boundary layer.3. Evaluation of N-factor trend (LISAC).LISACode represents the in-house tool based on the use of the Linear Stability Theory in which the transition onset is obtained through the wellknown e N -method.4. Evaluation of transition locations.The transition location is identified by intersecting the most amplified N-factor curve and N-value of the identified flow condition.5. Analysis and comparison of data.Aerodynamic data will be compared with numerical data derived from the model without propeller.

Results
The flow condition investigated in this section represents the cruise condition whose details are shown in Table 2.The evaluation of transition location through the numerical procedure described in the previous section is performed into 6 sections: the details of their locations are reported in Figure 1c and Table 3 includes the percentage positions in terms of the wing semi-span.If we move in the spanwise direction, S1 represents the first section considered here after the disk actuator, while S6 represents the furthest section.As an example, section S4 has been chosen to give some details about the numerical procedure reported in section 3 ( see Figure 2), i.e.
1. Trend of the pressure coefficient distribution on the upper (see red curve) and lower (see blue curve) surface of the model (in section S4) as derived from a RANS calculation by considering the stagnation point as initial point for both of them (see Figure 2a); 2. Velocity profiles of the streamwise component in the boundary layer for several x/c (see Figure 2b); 3. N-factor scan for 500<fr<15000 Hz at β=0, β=500 and β=1000 (see Figure 2c, d, e): the envelope of N-factor can be simply obtained by analysing the evolution of the N-factor as a function of the streamwise coordinate x/c depicted in all the figures; 4. Most amplified N-factor curve for the definition of the transition location on the upper side of section S4 (see Figure 2f) and estimation of the transition location following N=9.
Figure 3 shows the results of the application of the boundary layer code for S1 section.This figure shows the comparison between the pressure coefficient distribution between the power-off (i.e.without disk) and power-on (with disk) cases (see Figure 3a), the N-factor scan curves and the most amplified N-factor curve (see Figure 3b and Figure 3c respectively for upper and lower sides).
Regarding Figure 3a, it is possible to observe that there is a big discrepancy between p-off and p-on cases, in details the Cp distribution in the p-on case on the upper side is not characterized by the classical smooth distribution typical of laminar airfoils and that can be observed in the p-off case, while it is characterized by an expansion peak not far from the leading edge.If we refer to Figure 3b, that belongs to the upper side, it is possible to observe that the transition location is located before     4 c respectively for upper and lower sides).It refers to S3 section, Cp assumes a trend very similar to the p-off case, even if the maximum peak is higher and located into a different abscissa closest to the leading edge.For this reason, it is possible to observe that the transition location on the upper side moves, gradually, towards the trailing edge.Regarding the lower side of section S3, the situation is very similar to S2 section because the transition location remains around the same chordwise position.

Conclusions
This report summarizes the main results regarding a numerical procedure for the evaluation of the detrimental effect of the propeller on transition location of a laminar turbo-prop wing based on the coupling between a high-fidelity RANS tool and Linear Stability Equations solver.Figure 5 summarizes the transition locations along the wing semispan for the upper and lower sides: in details blue spots represent the power-off condition (derived from [4]) while the orange spots represent the results of this report.In the sections not far from the disk, transition moves towards the leading edge on the upper side if compared with the power-off condition, while on the lower side, transition moves towards the trailing edge.According to these figures, after S5 section it is possible to confirm that the effect of the disk actuator is negligible because the differences of the transition locations between the p-off and p-on cases are very small.At S6 section, the results obtained in both power-off and poweron conditions are almost coincident thus transition in this section is not affected by the presence of the disk.

Figure 1 .
Figure 1.a. Clean configuration with disk actuator; b.Sketch of the surface hybrid grid, c.Sketch of the sectional planes

Figure 4
Figure4has the same structure of Figure3and refers to S3 section, i.e. the comparison between the pressure coefficient distribution between the power-off (i.e.without disk) and power-on (with disk) cases (see Figure4a), the N-factor scan curves and the most amplified N-factor curve (see Figure4b

Figure 5 .
Figure 5. Transition location along the span for the upper and lower side of the wing model by considering the conditions with (orange spots) and without the disk (blue spots) -NOT IN SCALE.

Table 1 .
Characteristics of the propeller.

Table 3 .
Details of the sectional planes.