# A numerical approach for assessing slotted wall interference using the CRM model at ETW

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## Abstract

This paper is devoted to the assessment of wall interference in the slotted wall test section of the European Transonic Windtunnel (ETW) over a wide range of Reynolds numbers. The experimental part of the investigation was performed in February 2014 by testing the NASA Common Research Model mounted on a fin-sting support. These tests were carried out within the scope of the ESWIRP project funded by the European Commission in the 7th framework program. The numerical research was based on the Electronic WindTunnel (EWT-TsAGI) software with a cryogenic solver. The assessed Mach number influence on the wall signatures revealed a very similar effect to applying the classical Prandtl–Glauert rule over the investigated Mach number range. Practically, no Reynolds number effects on the wall pressure distributions generated by the model and its support system could be identified over the wide range of *Re* numbers investigated. The first attempt of the EWT-TsAGI code application for a simulation of ETW tests featuring the model in the slotted wall tunnel showed a fair coincidence of the pressure coefficient distribution on test section walls in the model region, on the wing-root sections and the drag polar at moderate lift coefficient values.

## Keywords

CFD NASA CRM Cryogenic test conditions ETW ESWIRP Wall interference Slotted wall## List of symbols

*B*Wing span

- BTWT
Boeing Transonic Wind Tunnel

*c*Mean aerodynamic chord

*C*_{D}Drag coefficient

- CDV =
*C*_{D}−*C*_{L}^{2}*/π/λ* Profile drag coefficient

- CEAS
Council of European Aerospace Societies

- CFD
Computational fluid dynamics

*C*_{L}Lift coefficient

*C*pPressure coefficient

- CRM
NASA Common Research Model

- DLR
German Aerospace Center

*E*Young’s modulus

- ETW
European Transonic Wind Tunnel

- ESWIRP
European strategic wind tunnels improved research potential—so-called targeted approach of the Integrating Activities of the FP7 Capacities Work Program

- HTP
Horizontal tail plane of the model

- EWT-TsAGI
Electronic Wind Tunnel, computer code

- ICAS
Institute of Thermomechanics of the Academy of Sciences of the Czech Republic

- JAXA
Japan Aerospace Exploration Agency

*M*Mach number

- NASA
National Aeronautics and Space Administration

- NTF
National Transonic Facility (NASA)

- ONERA
The French aeronautics, space and defense research lab

*P*,*P*_{t}Total pressure

- PETW
Pilot European Transonic Windtunnel

*q*Dynamic pressure

*R*Coefficient in boundary condition

*Re*Reynolds number

*S*Wing reference area

- SPT
Stereo pattern tracking (ETW system for deformation measurements)

*T*_{tot},*T*_{t}Total temperature

- TR-PIV
Time resolved particle image velocimetry

- TsAGI
Central Aerohydrodynamic Institute

*u*Perturbed longitudinal velocity component

- UCAM
University of Cambridge

- VKI
von Karman Institute for Fluid Dynamics, Belgium

- VZLU
Aerospace research and test establishment, Czech Republic

*v*Perturbed normal velocity component

*x*,*y, z*Coordinates (starting from test section inlet, centreline)

*α*Model angle of attack (°)

*Λ*Wing aspect ratio

*η*Dimensionless (

*y*/*b*) span-wise pressure orifices location

## 1 Introduction

A correct assessment of wind tunnel wall interference is still an essential aspect in terms of increasing the accuracy of test results during the aircraft design phase. In recent years, the manufacturers of transport aircraft have been imposing more and more stringent requirements for the accuracy of results from experimental investigations in wind tunnels. This is due to the needs for a more reliable determination of aerodynamic characteristics of the aircraft and, accordingly, its economic effectiveness. Striving towards the most accurate performance measurements in wind tunnels requires comprehensive knowledge on interference effects introduced by the flow boundaries. Considering slotted wall wind tunnels, the subject appears extremely complex due to the presence of strong 3-dimensional slot flow and the non-homogenous boundary conditions.

Nowadays, in most industrial wind tunnels with slotted walls, there are two standard methods of taking the influence of flow boundaries into account.

The first method uses the measured pressure distribution over the walls as some kind of boundary condition. This method (wall signature method) was used in particular at NTF for solid walls [1, 2] in 1993 and it has since been modified for slotted walls [3]. Its further development at NTF can be found in Refs. [4, 5], at the NASA Langley 14 × 22-ft Subsonic Tunnel—in Refs. [6, 7] and at the NASA Ames 11 ft Transonic Wind Tunnel—in Ref. [8]. The results of testing the CRM in the Ames 11 ft wind tunnel with the use of such a correction methodology are outlined in Refs. [9, 10]. Similar methods are used at the ETW [11, 12] and DNW-HST [13, 14].

The second method is based on the use of a uniform boundary condition relating to the velocity components near the walls. Relevant coefficients are often determined by experiments or on the basis of parametric calculations by comparing the experimental and numerical pressure distributions over the walls. A very similar approach to this problem was realized at BTWT (Boeing). Here, the boundary conditions on the walls were initially formulated in a hybrid form: The impermeability condition is defined on the walls, while the *u* + *v*/*R* = 0 [15] condition has been given on the slots, where the *R* coefficient is different for individual slots, depending on the flow direction of the gas.

As a result of using the methods above, corrections to the incoming flow parameters (*M*, *α*) and to the aerodynamic coefficients are obtained by the interpretation of the wall induced flow field near the model. These methods work well if there is no large gradient of perturbed velocity components and a low sensitivity of aerodynamic characteristics to variations of incoming flow parameters.

Nowadays, the direct numerical simulation of flow around the model in a slotted wall test section represents the actual problem. Its solution is necessary to improve the accuracy of the model aerodynamic characteristic determination, especially for take-off and landing regimes and for testing “oversized” models. There are a number of works devoted to the simulation of the flow in wind tunnels with slotted walls using the solution of Navier–Stokes equations. Initially, in Ref. [16] (DNW-HST), a set of geometrically similar simplified DLR-F4 models were used in the calculation without support in order to reduce the size of the grid. Interesting data were obtained for the flow fields in the plenum chamber just near the slotted wall. The level of flow boundary influence on the wing pressure is shown, but (unfortunately) information on a comparison of the calculated and experimental data is limited, as is information on the wall influence on the integral aerodynamic characteristics. One more attempt was made in 2010 by Krynytzky [17], who investigated the flow in a single slot for the empty test section and for the simplified reference model (Wing-Body Check Standard Model) at BTWT. Calculations showed that the boundary conditions on the slotted wall essentially differed from the classic uniform conditions. The distribution of an “effective” *R*(*x*) along the slot length was obtained. It improved significantly the correspondence of calculated and experimental pressure distributions along the walls of the test section. Further development of this work was shown in Ref. [18]. A sufficiently detailed grid was generated including the test section entry region with solid walls, the test section with alternating longitudinal slots and slats, the plenum chamber surrounding the test section (including the constricted plenum volume below the floor due to the balance pit shields) as well as the re-entry region downstream of the test section, including model support strut and pitch pod. This section is the upstream part of the test leg diffuser. In addition, the computational domain length upstream of the test section was appropriately selected in order to obtain the correct boundary layer thickness at the entrance.

Calculations without a model support system and additionally with a static pressure probe along the test section centerline were made. A satisfactory correlation between the numerically and experimentally gathered pressure distributions along the probe confirmed a high quality level of flow simulation in the test section.

## 2 Background

The first attempts in Russia were made at end of the 1940s to overcome the speed of sound at the TsAGI wind tunnels using perforated walls. Since that time TsAGI uses perforated walls in transonic test sections. There is a scientific interest at TsAGI to investigate interference generated by slotted walls, especially over a wide range of Reynolds numbers. First experimental and numerical investigations on the flow in the slots were performed as part of the ISTC projects 1978 and 3085. Experiments were performed at PETW and at the TsAGI T-125 wind tunnel. The main results were published in Ref. [19]. A topic which is still of interest is the influence of Reynolds numbers on the slotted wall interference problem and here, particularly the boundary conditions. As TsAGI has no cryogenic facility, it was a good opportunity to perform such investigations at ETW in the frame of the ESWIRP project.

The experiments were performed in the ETW cryogenic wind tunnel in February 2014 using the NASA Common Research Model (CRM) to investigate slotted wall interference effects and to form a test case for the verification and validation of CFD tools for in-tunnel simulations. These tests were performed in the frame of the ESWIRP Trans National Access (TNA) activity “Time-resolved wake measurements of separated wing flow and wall interference measurements” [20] which was funded by the European Commission in the 7th framework program.

This finally selected TNA proposal regarding the ESWIRP test at ETW was submitted by a consortium of renowned European research institutions and universities; ONERA (Aerospace Research Center) from France (project leader), the University of Stuttgart, DLR (German Aerospace Center) from Germany, TsAGI (Central Aerohydrodynamic Institute) from Russia, ICAS (Institute of Thermomechanics) and VZLU (Aerospace research and test establishment) from the Czech Republic, VKI (von Karman Institute for Fluid Dynamics) from Belgium and UCAM (University of Cambridge). Two main subjects were addressed during the test campaign: the investigation of unsteady wakes downstream of an aircraft wing under stall and buffet conditions and slotted wall interference in the wide range of Reynolds numbers.

## 3 Description of ETW

^{6}at cruise conditions for large transport aircraft. This takes into account the limitations on minimum temperature (condensation effects) and maximum pressure (model loads). The operating range expressed as Reynolds number versus Mach number is presented in Fig. 1.

*q*/

*E*= const, where

*q*—dynamic pressure,

*E*—Young’s modulus of the model material) and, likewise, the investigation of aeroelastic effects at constant Reynolds number.

As the nitrogen environment prevents classical access to the circuit, models may be moved to a variable temperature room applying a model-cart transport concept. Here, the model cart consists of the model itself including its supporting system and the ceiling of the test section linked by a voluminous structure to a sealing flange to be attached to the top of the tunnel shell. A rail-based transporter allows lifting and lowering of the cart in different areas where warm-ups or cool-downs may be applied as well as the transport from or back to the test section.

While along the major part of the circuit, the tunnel shell is directly internally insulated, the settling chamber, the slotted test section and the 2nd throat area are surrounded by a 10 m diameter plenum minimizing wall interference. During tunnel operation pressure, temperature and density in the plenum are close to the static gas conditions of the test section main flow. This generates a drawback for all instrumentation being placed there to either withstand the operational pressure and temperature conditions or to be housed in suitable mostly thermally controlled boxes. Optical access may then be provided by using the circular windows in the test section walls.

## 4 Description of the NASA CRM model

*M*= 0.85 and a corresponding design lift coefficient of

*C*

_{L}= 0.5. The main model dimensions are given in Table 1. Simple through flow nacelles can be mounted on the model.

Main dimensions of the NASA CRM model

Wing aspect ratio, λ | 9.0 |

Wing leading edge sweep angle | 35° |

Wing reference area, S | 0.280 m |

Wing span, b | 1.586 m |

Mean aerodynamic chord, c | 0.189 m |

Model moment reference center with respect to the fuselage nose | 0.909 m |

Model moment reference center is located below the fuselage centerline | 0.0518 m |

*η*= 0.131, 0.201, 0.283, 0.397, 0.502, 0.603, 0.727, 0.846, and 0.950). The wing-root strain is measured using half bridges on both wings. The model was mounted in the wind tunnel using a blade sting arrangement as shown in Fig. 5. Black markers of dia. 16 mm with a white center of dia. 6 mm and a thickness of 4 μm were applied to the lower surface of the left wing and the HTP (as shown in Fig. 5) for assessing the wing deformation with the SPT system during testing. Some marker positions are correctly determined in real

*x-*,

*y-*,

*z*-coordinates for reference purpose while the complete pattern is recorded by a high resolution stereo camera system installed in the top wall. The image under no load condition is defined as the reference. Wing deformations under aero-loads were tracked by the cameras surveying the spatial displacement of each marker. An online conversion of the individual marker shifts allows for the direct assessment of wing bend (±0.1 mm) and twist (±0.1°).

## 5 Description of EWT-TsAGI software

Nowadays, capabilities exist to apply CFD methods for solving the problem of permeable wall interference due to the significant increase of computer operation memory and speed calculation. A special software package named Electronic Wind Tunnel (EWT-TsAGI) was developed at TsAGI to numerically support wind tunnel testing including cryogenic conditions. The new CFD approach for wall interference analysis and prediction requires additional experimental data (for example wing deformation) in comparison with classical methods. Therefore, the necessity appeared to perform wall interference experiments at the ETW at the new level of technology. The main objectives of the fulfilled wall interference investigations were to increase the accuracy and reliability of ETW wall interference corrections, to investigate the Reynolds number influence on wall interference and to create a test case for the verification of CFD tools for wind tunnel simulations.

Calculations of viscous fluid flows over real model configurations are still of major interest in CFD. The problems in simulating these flows are based on the complexity of both the geometry and the flow structure. In practice different flow features may even simultaneously exist like multiple wakes, laminar to turbulent transition, shock interactions, model deformations, cryogenic phenomena, etc. Additionally, many of these phenomena interact with each other. This naturally requires applying only high-fidelity methods based on the application of Navier–Stokes equations. Generally, a solution of the above problem is possible using powerful computers and new technologies. Some results are published in [23, 24], where the “Electronic Wind Tunnel” is described. This code is used in TsAGI since 1996. It permits to solve the stationary (RANS) and non-stationary (URANS) Navier–Stokes equations using Reynolds-averaging. Special boundary conditions, such as “wind tunnel start”, “permeable walls” (perforated and slotted), “runway simulator” and “plenum chamber walls” are discussed in details. It is mentioned that the code effectively uses chimera-type grids based on the original “connect” technology. Practical aspects are developed. Many grid templates with special blocks for model and wind tunnel parts are prepared in advance. It permits to change a model in the “Electronic Wind Tunnel” operatively. An important algorithm for grid rebuilding, in the case of changing the model incidence and slip angles, has also been developed and is working reliably. It can not give perfect answers to all questions as, for example, the prediction of the drag coefficient which is still a big problem up to now. However, the real problems appear at high model incidences when non-stationary separation zones and wakes will make the task unbelievably complicated. On the one hand, this approach uses explicit numerical schemes for unsteady phenomena modeling. Whereas on the other hand, multiscale features create CFL problems which are impossible to be solved without implicit approaches. It is a well-known fact that the time scale for different physical processes may differ essentially (from 10 to 100 times). As a result, a huge CPU time for calculations is the logical result of using explicit based methods applied in such cases. Contrary to this, implicit methods for multiscale situations show good “economics” but low quality results. A possible solution for the described problem is to use zonal approaches, which include implicit numerical schemes for tiny scale physical phenomena (inner part of the boundary layer) and explicit ones for the remaining part of the computational area. Such an approach simultaneously provides a high level of resolution and an acceptable computing time. To speed up the calculations in the inviscid core, a method of “fractional time stepping” may be used. The idea of this method is that the calculation in each cell is performed with an individual time step. The time step value is proportional to 2*k*, where *k* is the maximal value for which the time step satisfies the local stability condition. The numbers of interim time steps is different in different cells but all the cells achieve the same layer of physical time at some time moments. Processes in different cells are synchronized at the interim time steps using a time interpolation. As a result, the non-stationary development of the flow is described correctly. A detailed description of this method is defined in [24]. The calculations are performed using a multiblock structured grid with hexahedral cells allowing an original switch from the implicit to the explicit method [25] resulting in a good acceleration without any visible loss in quality.

It is a well-known fact that ETW operates under cryogenic conditions using nitrogen as a test gas. The equilibrium state of the gas is strictly monitored to avoid condensation. However, the simultaneously required increase in tunnel pressure of up to 450 kPa for generating highest Reynolds numbers affects density and, hence, intermolecular connections might play an essential role. Consequently, the well-known gas state equation would no longer be valid in such cases. At very low temperatures the heat energy for an individual molecule is close to an energy step between its levels and, therefore, the quantum feature of the energy state has to be taken into account. It could be that the heat capacity is not constant depending on the temperature and density. Due to the fact that the molecular viscosity cannot be correctly estimated by the Sutherland law anymore, a more complicated function of temperature and density is applied. Currently, the empirical formula used provides an accuracy of ~0.1% at a temperature of 100 K and pressure levels approx. 108 kPa. The only chance to operate under such severe conditions is to use pure nitrogen [26]. This is realized at ETW.

Codes with implemented 3D cryogenic approaches are working at the limits of computer capacities available. It results in the fact that computer methodology, as a rule, is closely adjusted to the capacity of the computer system for a maximal optimisation of its resources. A major improvement is given today by modern clusters with hundreds of processors. An essential factor is the exponential reduction of costs for such systems. It permits to include computational investigations into a technological cycle of experiment. In this article authors not only calculate the model but additionally the test section at ETW with open walls and the re-entry region. Special attention is paid to the problem of turbulence level modeling at the entrance of the wind tunnel test section. It is clear that the complexity of the task is increasing numerously and essential extra time is required, e.g., for building additional grids. Additional computer resources are used to calculate the flow field in the regions upstream and downstream of the model. The plenum chamber is an essential part the computer model. Otherwise, this approach gives hope to predict phenomena to be investigated prior to the preparation of the experiment itself.

### 5.1 Geometry and grid

*x*= 2.8313 m,

*y*= 0.97 m,

*z*= 0 m (

*x*= 0—test section inlet,

*y*= 0—test section floor,

*z*= 0—test section symmetry plane). When the incidence angle is varied, the rotation takes place around the axis

*y*= 1 passing through point

*x*= 3.677 m,

*z*= 0 m (model reference center). Calculations may be performed for two configurations: with or without any consideration of the wind tunnel elements.

A block-structured hexa grid carefully approximates all of the main elements. It is compressed in domains of high gradients, especially near the slots and the re-entry region. The wing area is covered by an O-type (around the airfoil) grid, the other areas are H-type meshed. The wing deformation is taken into account by means of the direct implementation of experimental data. Bend and twist were measured using SPT markers. The model wing shape deformation due to increased dynamic pressure loads was assessed on the basis of these measurements. The boundary layer is a special zone. It is predicted on the basis of a “flow over a flat plate” approach and meshed by a refined grid reaching a compression of *y* ^{+} = 0.1 near the walls.

*Re*= 5·10

^{6},

*M*= 0.85,

*α*= 2.0°. Drag and lift curves for the nested grids are shown in Fig. 8. The difference between the values obtained with medium and fine grids is about 5 drag counts. This indicates that medium grid could be used only as a preliminary approximation. The orders of convergence evaluated according to the [27] are 2.26 for

*C*

_{D}and 2.1 for

*C*

_{L}, these values are consistent with the 2nd order of the numerical scheme used.

The number of cells in each grid

Grid size | Isolated model | Model in EWT |
---|---|---|

Coarse (mesh 2) | 1.3 M cells | |

Medium (mesh 1) | 10.6 M cells | 12.8 M cells |

Fine (mesh 0) | 85 M cells | 86.8 M cells |

An algorithm was developed for restructuring calculation grids in accordance with variations of the angle of attack and the slip angle. It permits to change an incidence angle by means of cell deformation without a need for rebuilding the total block structure. Such an approach corrugates the grids especially inside the boundary layer but permits a smooth run from one regime to another. It may be used up to angles of ~20°. In the plenum chamber, the grid is rarefied essentially due to the very slow flow there. Different quality grids are connected to each other using the Chimera-type boundary condition. It has been developed on the basis of bilinear interpolation and does not support the conservative law. Nevertheless, in the regions of slow flows it shows a reasonable quality of blocks’ connection and may be used without essential restrictions.

### 5.2 Numerical method

The numerical method used here is well described in [25]. The implicit smoother method is developed to accelerate the stationary numerical solution of viscid flows around an aircraft by an explicit Godunov–Kolgan–Rodionov scheme. The method used is based on the delayed correction procedure [28] and applies the Gauss–Seidel block method with the cell renumbering to solve the system of linear equations. For the approximation of SST turbulence model source terms, the method based on the analysis of eigenvalues of the Jacobi matrix is applied. The local choice of an explicit or implicit scheme and the manner of time step implementation (global or local), depending on the relationship between the specified global time step and the local stability condition of the explicit scheme is the main specific feature of the numerical method.

It was stated above that ETW is a cryogenic wind tunnel operating at low temperatures to obtain flight Reynolds numbers. In order to take the cryogenic effects into account the numerical method was modified. The modifications are described in detail in [29].

## 6 Description of the experiments performed at ETW

### 6.1 Test matrix

The model was tested in an inverted position (upper wing surfaces facing the tunnel floor) due to specific requirements caused by the viewing areas of the TR-PIV cameras. The generated blockage of the model in the test section was 5.8% based on the wing reference area (0.8% based on maximum model frontal area), while the span of the wing with respect to the test section width was 66%. The distance from the test section inlet to the model nose was 2.8313 m. The single model configuration tested only composed of fuselage, wing and horizontal tail plane at zero incidence.

Test matrix for wall interference investigations

Run | | Re × 10 | Angle of attack | Transition | T | P (kPa) | q/E at M = 0.85 | Remarks |
---|---|---|---|---|---|---|---|---|

139 | 0.697 | 5 | Cont | 10% | 300 | 191 | 0.3342 | Mach number derivatives |

143 | 0.703 | – | – | – | – | – | – | |

152 | 0.847 | – | – | – | – | – | – | |

155 | 0.853 | – | – | – | – | – | – | |

141 | 0.70 | 5 | Cont | 10% | 300 | 191 | 0.3342 | Wall interference and comparison with NTF and 11 ft |

153 | 0.85 | – | – | – | – | – | – | |

145 | 0.78 | 5 | Cont | 10% | 300 | 191 | 0.3342 | Mach number effect |

147 | 0.80 | – | – | – | – | – | – | |

149 | 0.83 | – | – | – | – | – | – | |

157 | 0.87 | – | – | – | – | – | – | |

185 | 0.70 | 2.93 | Cont | 10% | 300 | 111 | 0.1933 | Comparison with JAXA TWT |

186 | 0.85 | – | – | – | – | – | – | |

223 | 0.70 | 19.8 | Cont | Off | 115 | 199 | 0.3342 | Wall interference and comparison with NTF |

226 | 0.85 | – | – | – | – | – | – | |

232 | 0.70 | 30 | – | – | – | 303 | 0.5058 | |

283 | 0.85 | – | – | – | – | – | – | |

182 | 0.85 | 5 | Pitch/pause | 10% | 300 | 191 | 0.3342 | Comparison of pitch/pause and continuous modes |

212 | 0.70 | 19.8 | – | Off | 154 | 300 | 0.5058 | |

218 | 0.85 | – | – | Off | – | – | – | |

227 | 0.85 | – | – | Off | 115 | 199 | –0.3342 | |

237 | 0.85 | 30 | – | Off | – | 303 | 0.5058 |

All relevant tests were performed in the Mach number ranges of 0.7–0.85 and a wide range of Reynolds numbers of *Re* = 3–30 × 10^{6}. Four polars at *M* = 0.697, 0.703, 0.847, 0.853 were additionally acquired to define the derivatives of the model aerodynamic characteristics versus Mach number.

Specific combinations of Reynolds and Mach numbers along with corresponding *q*/*E* ratios were chosen to compare ETW experimental results with the data of two NASA wind tunnels—NTF and 11 ft AMES. The minimum *Re* number 2.93 × 10^{6} was very close to the flow condition when testing a scaled down version of the model in JAXA’s Transonic Wind Tunnel.

### 6.2 Wall interference measurements at ETW

*x*= 0 m. The according flow acceleration and subsequent deceleration around

*x*= 1 m are clearly visible. Further downstream an axial pressure gradient can no longer be identified. No lateral non-uniformity of the flow is to be seen either. Hence, visible data scatter is related to natural degradation of the pressure taps.

All slots in the lower and upper wall were opened for that test campaign, while the side walls used a closed configuration (see Figs. 3, 5).

*M*= 0.7 and 0.85 will be required in the future process of application of wall interference corrections–recalculation of corrected data to the required Mach number values.

## 7 Analysis of experimental and CFD results

### 7.1 Repeatability of wall pressure measurements including the comparison of continuous/pitch-pause polar results and comparison of *C* _{p} at symmetrical lines

*C*

_{p}on the test section walls was investigated to estimate random errors for the further analysis. As an example Fig. 11 shows the

*C*

_{p}repeatability along the line TBL0 on the lower wall (facing the upper model surface) at

*M*= 0.85,

*Re*= 30 × 10

^{6}and

*C*

_{L}≈ 0.5 which is about ±0.0005–0.001. It corresponds to the

*ΔM*≈ ± 0.00025–0.0005 at

*M*= 0.85 or

*ΔM*≈ ±0.00019–0.00038 at

*M*= 0.7.

*C*

_{p}measurements for a model movement in pitch/pause and continuous mode is presented in Fig. 12 for

*M*= 0.85,

*Re*= 30 × 10

^{6}and

*C*

_{L}≈ 0.5. The difference between two sets of data does not exceed 0.001. Comparisons were also done for the pressure coefficient measurements on the lines which were symmetrical with respect to the model plane of symmetry. An example of a performed comparison is shown in Fig. 13 for the lower wall at

*M*= 0.85,

*Re*= 30·10

^{6}and

*C*

_{L}≈ 0.5. The scatter of data does not exceed ±0.004, which is quite close to the values of empty test section data (Fig. 9). To exclude the individual peculiarities of the pressure orifice geometry (see Sect. 6.2) the wall

*C*

_{p}data at zero lift coefficients were subtracted from the data at

*C*

_{L}≈ 0.5. A typical result is shown in Fig. 14 for

*M*= 0.85 at different Reynolds numbers for two lower wall sections. The data scatter is about ±0.0005.

### 7.2 Reynolds number effect on wall *C* _{p} measurements

*C*

_{p}distribution along the walls. Two main aspects of wall interference were separated—blockage and wing vortex sheet effects. Blockage interference was studied at an approximately zero lift coefficient value while the lift effect has been defined as the difference between the

*C*

_{p}values at

*C*

_{L}≈ 0.5 and

*C*

_{L}≈ 0. A typical Reynolds number influence on the lower wall

*C*

_{p}due to the blockage effect is shown in Fig. 15. The scatter of the data is of order ±0.002 (note that line TBL3 reveals the largest scatter in tap signatures due to manufacturing imperfections validated in the tunnel calibration exercises). There is no visible effect of the

*Re*number varied from 3 to 30 million on the wall

*C*

_{p}distribution produced by the model and its support regarding blockage effects.

An example of Reynolds number effects on the wing vortex sheet interference with slotted walls is presented in Fig. 14. The difference between *C* _{p} data for various *Re* numbers is within the repeatability of the measurements. It may be assumed that a variation of Reynolds numbers in the range from 3 × 10^{6} to 30 × 10^{6} does not affect wall *C* _{p} distributions and, hence, the slotted wall boundary conditions. One of the possible explanations of this result may be the fact that Reynolds numbers of the wall boundary layer referred to its length are about two orders higher than model’s *Re* number and corresponds to the values of *Re* ~ 3 × 10^{8}–30 × 10^{8}.

### 7.3 Mach number effect on wall *C* _{p} measurements

*C*

_{p}distributions is demonstrated in Fig. 16 for

*M*= 0.85,

*Re*= 5 × 10

^{6}and

*C*

_{L}= 0.53 on the floor centerline facing the upper wing side (model inverted). The amplitude of

*C*

_{p}increases with Mach number which is very similar to the Prandtl–Glauert rule. This is impressively demonstrated by correcting the pressure coefficient

*C*

_{p}by multiplication with \(\beta = \sqrt {1 - M^{2} }\). The resulting

*C*

_{p}distributions are presented in Fig. 17. The remaining scatter of the data with this well-known Prandtl–Glauert correction is close to the

*C*

_{p}repeatability, although, there is still minor residual Mach number effect. First order compressibility effects in the linear solution of wall interference problems [30, 31, 32] may be expressed as follows:

*C*

_{p}follows the Prandtl–Glauert rule. The plenum pressure was compared with the reference one to ensure that a pressure drop through the slotted wall may be interpreted by a commonly defined pressure coefficient. Figure 18 presents the plenum chamber pressure coefficient calculated with respect to the reference tunnel pressure versus Mach number at an angle of attack of about 2°. The resulting absolute value does not exceed 0.002 for Mach numbers less than 0.85.

The amplitude of the normalised disturbed longitudinal velocity \(u/u_{\infty }\) is of a second order of magnitude ~0.01 for the performed tests.

Hence, it may be concluded that the Mach number influence on the wall pressure coefficient shows a very similar effect to the Prandtl–Glauert rule in the investigated Mach number range from 0.7 to 0.87. On this basis, it may be acceptable considering the application of linear methods for assessing the wall interference at ETW in the slotted wall configuration up to a Mach number of 0.87 and possibly higher.

### 7.4 Comparison of CFD and experimental data

The ETW wind tunnel control system is based on the static pressure recorded by a pressure tap at station *x* = 0.646 m on centerline level on the side wall. For simplification the identical location has been selected for defining the reference condition in all CFD calculations.

*M*= 0.85 in the empty test section. The experimental data were acquired during the tunnel calibration with a centerline probe named short axial probe attached to the pitch system (sector). The downstream end of the probe features the same geometry as a straight sting used for model support. The CFD profile reveals more filled near the wall in comparison with the experimental one. The stated difference in local speed is about 9%. Probably, this is due to the selected turbulence model.

*z*= 0.215 m is shown in Figs. 20 and 21, respectively (note the difference between experimental and numerical coordinate system according to Sect. 5.1). The given data correspond to the upright model position at

*M*= 0.85, α = 4°. The flow field is dominated by the inflow into test section on the upper wall and inflow on the lower wall upstream of the model. Further downstream one can see some outflow from the test section. This behavior is in line with available experience for tunnel flows with ventilated walls. Similar normal velocity distributions can be observed for other sections passing through the slots. Figure 21 demonstrates the rapid decrease of longitudinal velocity inside the slots.

*x*= 2.8, 3.7, 4.5 m). In addition, Fig. 23 shows the distribution of the normal velocity component in the same three cross sections. A penetration of perturbations into the test section caused by low energy slot flow is about half of the slat width deep as shown in Ref. [19].

*M*= 0.85 and

*C*

_{L}= 0.63 featuring the model in inverted position. CFD results are given for an isolated model in ETW (green line) and for the tested model with fin-sting support (red line). The pressure signature on the lower wall documents a downstream shift of the suction peak caused by the presence of the supporting system when compared to the free flight configuration (Fig. 24). The shape of the signature calculated by CFD curve is pretty close to the experimental one including the area at test section inlet (see Fig. 9). The difference in

*C*

_{p}at the model position is lower than 0.007.

The side wall signature also demonstrates a good agreement between experimental and computational results around the model position (Fig. 25).

The *C* _{p} distribution (Fig. 26) on the ceiling exhibits a slightly higher calculated pressure gradient in the model position than the experimental one while the discrepancy in *C* _{p} is about 0.004.

Generally, there is a higher positive pressure gradient to be noticed for the CFD results for *x* > 5 m compared to the experimental data. This may be due to the non-perfect simulation of the real geometrical situation in this area. ETW is operating an artificial sonic throat downstream of the re-entry area for an enhanced Mach number stabilization (Δ*M* < 0.001) when pitching the model. As the area re-entry-sector-throat features a highly complex geometry and, consequently, generates more complex 3D-flow it had been simplified for the meshing procedure for saving grid nodes.

*M*=

*0.85*and

*Re*= 5 × 10

^{6}is given in Fig. 27. The numerical calculations were performed taking into account the wing deformation, as measured by the SPT system during the tests. The presented CFD results correspond to two different model configurations: (a) the model in free flight with its fin-sting support system (green markers) and (b) the model in ETW mounted on its fin-sting support (red markers). A “model on sting” configuration was chosen here to represent the “free flight” case. Comparing this configuration to the “model on sting” in the tunnel, the main part of sting interference is excluded from the addressed problem—the wall interference investigation. The experimental data are presented in uncorrected form and with standard ETW corrections applied. There is shift of CFD data of about Δ

*α*= −0.2° with respect to wind tunnel results. This fact is well known and quite common for computational tools. Inviscid Euler solution result in a shift of about Δ

*α*= −0.5° [23]. Probably this is associated with not fully realistic flow simulation near the trailing edge of the wing. Standard ETW corrections slightly increase the lift curve slope (anti clockwise rotation of the lift polar due to the slotted walls). EWT-TsAGI data for both configurations are on the same curve. This may be originated by the fact that the correction to the angle of attack is practically compensated by the Mach number correction to the lift coefficient derivative versus angle of attack.

*C*

_{L}=

*f*(CDV) for

*M*= 0.85 and

*Re*= 5 × 10

^{6}. The presented CFD results correspond again to two model configurations: (a) the model in free flight with support system (green markers) and (b) the model mounted in ETW on its fin sting (red markers). Experimental data are presented in an uncorrected form and with standard ETW corrections. The correction methodology and the experimental wall interference assessment is based on a strategy developed by Prof. P. Ashill (UK) [12]. As an outcome, the model incidence is corrected in a classical form. The lift is not corrected as it is considered a true measurement by a high performance calibrated balance. Further on, the lift dependant drag was assessed to be zero while the blockage buoyancy drag is a weak function of Mach approaching zero at Mach = 0.9 and, hence, the total corrections applied are pretty small, if no sting corrections are applied.

A good agreement of EWT-TsAGI data and ETW results was achieved for moderate lift coefficients (*C* _{L} < 0.6). The drag coefficient in free flow conditions calculated by CFD is about 5–20 counts less than for the wind tunnel case. The difference in drag increases with the rise of the lift coefficient. The standard ETW corrections applied to the drag coefficient are quite small. EWT-TsAGI results show that wall interference effects for the NASA CRM model in ETW do not exceed eight drag counts in the moderate range of lift coefficients (0 < *C* _{L} < 0.4).

*Re*= 5 × 10

^{6}only). The achieved coincidence of CFD

*C*

_{p}distributions for wind tunnel and free flow configurations confirms the statement given above for the lift coefficient, that the correction to angle of attack is practically compensated by the Mach number correction for the chosen case

*M*= 0.85.

The first attempt of applying the EWT-TsAGI code for the simulation of ETW tests reveals an acceptable coincidence of pressure signatures on test section walls and the drag polar at moderate lift coefficients.

## 8 Conclusions and outlook

Results of wall interference investigations at ETW using the NASA CRM model have been presented. The EWT-TsAGI software used for the complementary numerical analysis is described. The distribution of the wall pressure coefficients obtained was analysed. A repeatability in *C* _{p} of about ±0.0005–0.001 was determined. There is practically no effect of Reynolds number on the wall *C* _{p} distributions generated by the model and its corresponding support blockage effects in the investigated range of *Re* = 3 × 10^{6}–30 × 10^{6}. The Mach number influence on the wall pressure coefficients reveals a very similar effect to the Prandtl–Glauert rule over the investigated Mach number range from 0.7 to 0.87. This provides the opportunity to apply linear methods for the ETW wall interference problem with slotted wall configurations up to Mach numbers of 0.87 and possibly higher. The first attempt of the EWT-TsAGI application for the simulation of ETW tests shows good coincidence of the pressure signatures on the test section walls, on the wing-root sections and drag polars at moderate lift coefficients.

For *M* = 0.85 the analysis performed for the NASA CRM model at ETW revealed that the angle of attack correction was practically compensated by the Mach number correction. A generalisation of this finding will require confirmation from the deployment of other Mach numbers, e.g., *M* = 0.7.

The derived experimental database will enable the use of different methods (classical and CFD) to investigate ETW slotted wall interference. The application of different methods should increase the accuracy and reliability of ETW test results and, consequently, the efficiency and safety of future aircraft performance predictions. One more outcome of this test campaign is the use of experimental data as a complex test case for the validation and verification of different existing and upcoming CFD methods including the ones developed to solve the wall interference problem for Transonic Wind Tunnels with slotted walls.

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