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4 Validation in Computational Fluid Dynamics (CFD)
Experimental Fluid Dynamics (EFD) and Computational Fluid Dynamics (CFD) are two major research fields for analysis and of flow phenomena. EFD technologies measure pressures, fluid properties, directions and velocities of airflows by using special equipments in wind tunnels. EFD has relatively longer history and therefore many researchers feel it is the most reliable technique; however, it has several limitations including costs and schedules. In CFD, instead, is relatively easier to produce a greater variety of analyses and investigate different designs; nonetheless, because of mathematical models, discretization errors and mesh dependence, the results of CFD has to be validated by comparing with corresponding results of EFD.
Validation is the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model.
Validation deals with the assessment of the comparison between sufficiently accurate computational results and the experimental data.
The fundamental strategy of validation involves identification and quantification of the error and uncertainty in the conceptual and computational models, estimation of the experimental uncertainty, and finally, comparison between the computational results and the experimental data.
The first objective is precisely the CFD validation, used in this thesis, by comparing numerical results with the experimental data performed over the NASA Common Research Model.
4.1 Experimental fluid dynamics (EFD)
The experimental approach to a project involves several items, including:
the facility used;
the model itself (in a scale size respect to the geometric one involved in CFD analysis);
the test conditions where the model is tested;
the corrections that are applied to the data.
A detailed description of each of these items is given in the following chapters.
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4.1.1 Model description
The NASA Common Research Model (CRM) consists of a contemporary supercritical transonic wing plus fuselage that is representative of a wide body commercial transport aircraft. The CRM is designed for a cruise Mach number of M∞ = 0.85 and a corresponding design lift coefficient of CL= 0.5. The wing are represented in the deformed configuration at 1_G cruise. The aircraft employed in the experimental test is a scaled model. The aspect ratio is 9.0, the leading edge sweep angle is 37 degrees, the wing reference area (S) is 3.01 ft2(0,2796 m2), the wing span (b) is 62.46 inches (1,5865 m), and the mean aerodynamic chord (c) is 7.45 inches (0.18923 m).
Pressure distributions are measured on both the left and right wings using 291 pressure orifices located in 9 span-wise wing stations (η = 0.131, 0.201, 0.283, 0.397, 0.502, 0.603, 0.727, 0.846, and 0.950). All pressure measurements were made using Electronically Scanned Pressure (PSP) modules mounted inside the forward portion of the fuselage.
Based on quoted accuracies from the ESP module manufacturer, surface pressure measurements should be in error no more than +/- 0.015 psi. This in turn would correspond to a variation of no more than +/- 0.0026 in terms of Cp. The model is mounted in the wind tunnel using a blade sting arrangement. Five different configurations were tested: the wing/body (WB) alone, wing/body/pylon/nacelle (WBPN), wing/body/tail=0° (WBT0), wing/body/tail=+2° (WBT+2) and wing/body/tail=-2° (WBT-2).
Figure 4-1 CRM wind tunnel model
The EFD were carried out in three different transonic wind tunnel:
Ames 11 Ft Wind Tunnel;
Langley National Transonic Facility;
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European Transonic Wind Tunnel.
For simplicity, in this thesis, only the results obtained in the Langley National Transonic Facility (NTF) are taken into account.
4.1.2 Langley National Transonic Facility test conditions
The world’s largest pressurized cryogenic wind tunnel, the National Transonic Facility (NTF), possesses unique capabilities to duplicate actual flight conditions. The NTF supports advanced aerodynamic concept development and assessment, advanced computational fluid dynamics tool validation, and risk reduction for vehicle development.
Figure 4-2 NTF wind tunnel view with CRM and its support structure
The NTF provides the highest transonic Reynolds number testing capability in the world, and can use either conventional air at ambient temperatures as the test gas, or gaseous nitrogen (expanded from injecting liquid nitrogen) at temperatures as low as -250 ºF (116.5 K) for achieving flight test conditions. With a wide range of customizable instrument and measurement techniques, both full-span and semi-span model testing is supported.
The facility has the unique capability to adjust test conditions to match model size.
Independent control of total temperature, pressure, and fan speed allow isolation and study of pure compressibility (Mach) effects, viscous (Reynolds number) effects, and aeroelastic (dynamic pressure) effects. The interior of the pressure shell is thermally insulated to ensure minimal energy consumption, and responsive Mach-number control is achieved with a variable inlet drive system.
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Figure 4-3 CRM model frontal view
The investigation, conducted over a 6-week period, provided force and moment, surface pressure, model deformation, and surface flow visualization data. Testing was conducted at 5, 19.8 and 30 million Reynolds number. All Reynolds number values presented in this paper are based on mean aerodynamic chord. The 5 and 19.8 million Reynolds number data were collected to provide a comparison to previously calculated CFD results and all of the Reynolds numbers were used to provide an assessment of Reynolds number effects. The data were collected at temperatures ranging from -250ºF (116.5 K) up to 120ºF (322 K).
Data were generally obtained over an angle-of-attack range from -3° to +12° at 5 million Reynolds number and from -3° to +6° at 19.8 and 30 million Reynolds numbers.
The reduced angle-of-attack range at the higher Reynolds number was required such that safe model stress levels would not be exceeded. Flow angularity measurements were made and upflow corrections ranging from 0.092° to 0.173° were applied to the final NTF data.
Classical wall corrections accounting for model blockage, wake blockage, tunnel buoyancy, and lift interference have been applied.
In order to ensure a consistent and repeatable transition from laminar to turbulent flow and to support the goal of the wind tunnel data being used for CFD validation purposes, it was important to apply a proven and reliable method to fix transition on the model.
Evercoat trip dots measuring 0.05 inches in diameter and spaced 0.1 inches apart (center to center) were used for the current investigation. For a chord Reynolds number of 5 million, a trip dot height of 0.0035 inches was used from the SOB (side of body) to the yehudi break, 0.003 inches was used from the yehudi break to the midwing and 0.003 inches was used from the midwing to the wing tip. These trip dots were installed at 10% chord. Vinyl adhesive trip dots with a height of 0.004 inches were applied at the nose of the fuselage and left on for the entire test.
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4.1.3 Wall correction methods
Both the NTF and the Ames 11-ft wind tunnels use the Transonic Wall Interference Correction System (TWICS) to provide blockage and incidence corrections due to the presence of the test section boundary. TWICS is an enhanced version of WICS that handles ventilated boundary conditions, typically seen in transonic wind tunnels. This method was chosen to be implemented at the NTF, in an effort to standardize the wall interference correction methodology across NASA centers. TWICS is based on a linearized potential flow method with a Prandtl-Glauert compressibility model which inherently assumes that there is a portion of flow in the test section between the near-field region of the test article and the near-field region of the wall that is a linear perturbation of the empty test section flow field.
The method uses a tared wall pressure signature, which is the difference between the model installed condition and the empty test section, a database of normalized perturbation velocities using unit singularity solutions computed for a given mathematical representation of the wall boundary condition, and geometric information from the test article. Taring of the wall pressure signature is performed to remove first order effects of the empty tunnel boundary layer and buoyancy, is assumed to contain only the solid and wake blockage, and is also assumed that the additional second order change in the test- section-wall boundary layer displacement thickness due to the presence of the test article is negligible (an assumption that is violated by flow near a Mach number of unity where aspects of the crossflow are more critical). The test article is modeled with an appropriately weighted point doublet chain to represent the fuselage, wake, and support system. Line doublets, typically distributed along the lifting surface quarter-chord, are used to simulate the effect of lift. The strengths of the line doublets are determined using the measured lift from the balance. The resulting wall signature from these singularities is subtracted from the tared wall signature, leaving only the blockage signature. This remaining signature is used to determine the strengths of the solid and wake blockage singularities.
4.1.4 Experimental results
In the table are listed the experimental results (NTF test 197 run 44) taking into account for the CFD model validation.
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TEST
AWALL TWICS corrected
alpha
MWALL TWICS corrected Mach
number
CLWALL TWICS corrected lift
coefficient
CDWALL TWICS corrected drag
coefficient
ALPHA MACH
197 -2,83116 0,848792 -0,202898 0,021356 -2,8151 0,849824
197 -1,796652 0,8482626 -0,075555 0,0156166 -1,79069 0,849152 197 -1,315258 0,8492665 -0,0158023 0,0147243 -1,3141 0,850119 197 -0,837648 0,8494133 0,0444843 0,0144084 -0,841323 0,850215 197 -0,297533 0,8490496 0,108481 0,0145457 -0,306372 0,849836
197 0,23375 0,849319 0,172512 0,015144 0,219731 0,850125
197 0,68889 0,8493481 0,229189 0,0159571 0,670284 0,850147
197 1,21194 0,8495326 0,291217 0,0172422 1,18831 0,850353
197 1,70402 0,8494845 0,352194 0,018814 1,6754 0,850329
197 1,95245 0,8500681 0,384026 0,0198492 1,92132 0,850905
197 2,20909 0,8495831 0,419271 0,0210568 2,17504 0,850451
197 2,50374 0,8492768 0,457373 0,0227583 2,4665201 0,850168
197 2,70096 0,8483829 0,48673 0,0240962 2,6612101 0,849295
197 2,93253 0,849668 0,521095 0,0261842 2,89008 0,850643
197 3,21294 0,849895 0,559254 0,0292447 3,1673501 0,850945
197 3,45029 0,849942 0,585643 0,0321999 3,4026301 0,851016
197 3,7219 0,848542 0,609597 0,0356863 3,67205 0,849705
197 3,94714 0,849623 0,623537 0,0394364 3,89625 0,850759
197 4,19734 0,849687 0,640092 0,0437293 4,14505 0,850938
197 4,70112 0,847942 0,672038 0,0521897 4,6459398 0,849353
197 5,15745 0,847927 0,701183 0,0601858 5,0997701 0,849469
197 5,6518 0,84895 0,723458 0,0679954 5,5925002 0,850601
197 6,18855 0,849296 0,742724 0,0766306 6,1277199 0,851091
197 6,69123 0,847213 0,762869 0,0852757 6,6282802 0,849125
197 7,2147 0,848024 0,782156 0,0954355 7,15031 0,850151
197 7,65603 0,848084 0,802058 0,104415 7,5899501 0,850331
197 8,12823 0,847769 0,806623 0,113567 8,0618296 0,850109
197 8,684851 0,847568 0,816959 0,126088 8,6174803 0,850138
197 9,23637 0,846749 0,820943 0,137294 9,1684599 0,849534
197 9,622741 0,845551 0,823531 0,146975 9,5544205 0,848496
197 10,26756 0,846698 0,829882 0,161881 10,1986 0,84985
Table 4-1 NTF test 197 run 44
4.2 CFD approach
Computational Fluid Dynamics (CFD) is a set of numerical methods applied to obtain approximate solutions of problems of fluid dynamics and heat transfer. CFD is not a science by itself, it is a way to apply the methods of one discipline (numerical analysis) to
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another (fluid flow/mass transfer and heat transfer). Exploiting a numerical approach, CFD solve flow fluid problems by the application of continuity equation, momentum equation (widely knows as Navier-Stokes equation) and the energy equation.
There are many types of commercial codes designed for CFD solving. In this work ANSYS FLUENT CFD Solver was chosen. ANSYS FLUENT is based on the finite volume method (domain is discretized into a finite number of control volumes), where general conservation (transport) equations for mass, momentum, energy, species, etc. are solved, allowing an accurate CFD analysis for a wide range of fluids problems.
To solve Engineering problems using ANSYS FLUENT the necessary steps are
Pre-analysis;
Geometry;
Mesh;
Physical setup;
Numerical solution;
Validation.
The first three points have already been addressed in previous chapters, in this one the physical set up numerical solution and validation are faced.
4.2.1 Physical setup
In physical setup step, inputs for solution accuracy, boundary condition, physics, materials and properties are given; in a nutshell, here the real situation to simulate is numerically depicted.
The following set up, is designed to better approximate the CRM physical condition.
Starting ANSYS FLUENT, dimension (3D model), double precision solver (uses 32 bit floating points) and 8 parallel process to speed up the simulation are defined. Under the tree window the tabs, that allow to describe the physic problem and control the simulation, are listed. In the general tab section, the case type is defined: steady model and density based solver because of the high Mach numbers handled in this work (M ≥ 0.8).
The governing equations used to solve the problem are defined in the models tab.
Energy equation is turned on in the solver and the one equation Spalart-Allmaras is set for the viscous turbulent model, with vorticity based and curvature correction options selected.
Spalart-Allmaras was chosen for its robustness and the reduced times in calculation convergence respect to higher complexity two equations models.
75 As fluid, air is the material selected with:
Ideal gas law;
Constant cp in accordance to the standard air model;
Constant thermal conductivity derived from standard air model;
Sutherland law for viscosity: μ= μ0∙(T/T0)3/2 (T0+110,56)/(T+110,56);
The operating pressure is set to zero and the operating temperature is derived from the standard air table in according to the altitude. With the solution methods tab it is possible to adress the solution method to be used. Default conditions are chosen, apart for the second order upwind flow and the second order upwind modified turbulent viscosity. The solution control remains the default one.
Before running the simulation, solution initialization is required. There are two options: standard or hybrid initialization. In standard initialization, all cells have the same value reference value as initial condition, while hybrid initialization makes a non-uniform initial guess. The thesis choice is the standard one.
The number of iteration to be performed are set in the run calculation window, with steering and FMG initialization; two procedures that, thanks to the use of very corse grids and the Courant number sweep, speed up the solution convergence. The boundary conditions task allows to set the boundary type of fluid domain: wall for the aircraft surfaces, symmetry for the border face containing the symmetry plane of geometric model, interior for the fluid and pressure far field for the remain region surrounding the domain.
In the pressure far field , the momentum and thermal description of far field flow are needed. In order to do that Gauge pressure, Mach number, xyz componets of flow direction, turbulent viscosity ratio and temperature have to be defined or derived starting from some input parameters selected by the users. X and Z components of flow are obtained by multiplying the undisturbed velocity U for the cosine and sine of the angle of attack α, while the Y component is zero.
The NTF tests here considered were obtained at fixed Mach number and fixed Reynolds number at an estabilished temperature. This is the reason why, in this work, Re, Mach and T (and the corresponding altitude) are set as input parameters. By solving a simple equations system, some secondary quantities and the Gauge pressure are derived.
Obviously some quantities such as the density could be incoerent with the temperature and the respective altitude, but the experimental tests are conducted in this way.
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Input Equations Derived
M μ= μ0*(T/T0)3/2 (T0+110,56)/(T+110,56) μ [Pa∙s]
Re ρ=Re μ/ U L ρ [kg/m3]
T p=ρRT P [Pa]
a=√ (γRT) a [m/s]
U=M∙a U [m/s]
Table 4-2 equation system used for derived values
The reference values are used to compute normalized flow field variables. Some of them are derived from far field properties while others are set up such as the reference area Aref and the mean chord c, extrapolated by the geometric features of aircraft.
Aref= 191,8447776 [m2];
C= 7,00532.
4.2.2 Setup validation
Neither in the Drag Prediction Workshop 4 (DPW4) or among the CRM files there are no specific and complete guidelines or description about the aforementioned setup configuration, hence some uncertainties about the physical setting remains. This is the reason why a validation process is carried out by exploiting the Mark Oswald CFD results.
The simulations are conducted with Ansys Fluent software and a mesh file is implemented on the CRM model. The results and the mesh are both available on the DPW4 documents [17].
The objective is to validate the setup by comparing the results of Oswald to the results performed by CFD simulations. Thus to eliminate uncertainties and confirm the goodness of the setup, the same mesh exploited in Oswald work is initially simulated with the same settings described in the previous paragraph, with the exception of turbulent model.
Oswald used a Menter’s Shear Stress Transport (SST) configuration in place of the SA, so, only in this case, the simulation was carried out with SST (the viscous turbulence model applied in the rest of the thesis numerical computations still remains the Spalart Allmaras, as explained before). By comparing two simulation with same mesh and geometry model, the only source of uncertainties lies in the setup. Therefore if the results of CFD simulation matches the Oswald ones, the set up process can be validated.
The input parameters are:
M=0.85;
Re=5∙106;
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T=223.25 [K] (1∙104 m of altitude).
The inputs and derived parameters are listed in the following table together with material properties and reference values.
Input:
Re 5000000
M 0,85
T [K] 223,25
R [j/kg∙K] 287,05
γ 1,4
c [m] 7,00532
T0 [k] 273,11
μ0 [Pa∙s] 0,00001716
Ref A [m2] 191,84478
cp specific heat coeff 1005
k thermal conductivity 0,02007
turbulent intensity 0,023267
derived:
μ [Pa∙s] 1,45798E-05
ρ [kg/m3] 0,040873
P [Pa] 2619,29855
a [m/s] 299,52876
U [m/s] 254,59944
Table 4-3 Input and derived parameters for Re 5 M and Mach 0.85
The CFD simulation is conducted for a fixed Mach number with an angle of attack variable.
Mach number=0.85, angle of attack
α
=0°,α=1°, α=2°, α=3°, α=4°;
The results of the simulation and the Oswald results are plotted and compared in CLα and in the CDα charts.
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Figure 4-4 CL-α curves for Re 5 M and SST turbulent model
Figure 4-5 CD-α curves for Re 5 M and SST turbulent model 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
CL
α
CL-α Re 5 M SST
ansys dpw4 Oswald Re 5 M SST
ansys cfd Re 5 M SST
0 0.01 0.02 0.03 0.04 0.05 0.06
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
CD
α
Cd α Re 5 M SST
ansys dpw4 Oswald Re 5 M SST
ansys cfd Re 5 M SST
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The two curves have the same trend, and they are almost overlapped along all sections.
In the end it can be said the validation process gives positive match, the setup method is correct and it is used in the next analyses presented in this thesis.
The same simulation is carried out also with the Spalart Allmaras viscous model and the results show a very little gap with the previous one; also this turbulent model is acceptable, taking into account that the curves trend remains the same.
Figure 4-6 CFD simulations with Spalart Allmaras and SST turbulent models
4.3 CFD model validation
Validation is the primary means to assess accuracy and reliability in computational simulations. In validation, the relationship between computation and the real world, i.e.
experimental data, is the issue. The fundamental strategy is to assess how accurately the computational results match the experimental data, with quantified error and uncertainty estimates for both. Errors and uncertainties prevent the exact match of CL-α and CD-α curves between CFD and EFD.
Therefore the goals for a correct validation process are the identification of:
Uncertainties due to EFD and CFD processes;
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
CL α Re 5 M SA/SST
NTF run 44 Re 5 M
ansys cfd Re 5 M SA
ansys dpw4 Oswald Re 5 M SST
ansys cfd Re 5 M SST
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A trend common for experimental, computational results and the achievement of the same or similar maximum for L/D ratio;
A preliminary evaluation of a reasonable gap between CFD and EFD results;
To verify that the numerical values, coming out from the employed CFD model, lie inside the band of gap evaluated.
The issues of uncertainties in EFD and CFD are mainly due to:
Different wing deformation between models. Although the wings are designed with the same initial deformed shape, the experimental model has a finite stiffness which causes an extra-deformation when subjected to the wind tunnel flow, hence a different wing twist distribution;
The CFD models have a fixed wing deformation, while the deformation of the experimental model changes with the angle of attack.
Turbulence transition modeling: in CFD the flux is considered as fully turbulent; in the wind tunnel the flux is laminar until the transition stripes force turbulence.
No free-air stream condition. The wind tunnel doesn’t guarantee the same flow condition simulate on CFD test because of the wall presence that can induce the generation of undesired phenomena like the flow rebound;
Presence of the support system. Its interference causes a remarkable shift of CFD from EFD results because modifies the wet surface of the model.
Manufacturing tolerances. The wet surfaces could be different from the nominal one and consequently the aerodynamic forces developed;
Limited accuracy of the instrumentation;
Numerical errors due to truncation errors.
In this work the CFD validation is carried out between three different grids shaped on the same geometry. In addition to a validation, this is also a comparison between three different cases: CASE 56, CASE 64 and CASE 73. Their features are described in chapter 3. The aforementioned set up procedure is the same for each case except for the boundary faces. In the case 73 there’s only one semispherical face instead of six of the 56 and 64, but they have all the same pressure far field boundary conditions.
The experimental results performed by Langley national transonic facility are available at three different Reynolds number: 5, 19.8 and 30 millions. In order to have a validation process with physical quantities as close as possible to the cruise conditions, the
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Reynolds number of simulations is set up to 30 millions. The Mach number is equal to the cruise one of 0.85 and the temperature is put to 223.5 [K].
Input:
Re 30000000
M 0,85
T [K] 223,25
R [j/kg∙K] 287,05
γ 1,4
c [m] 7,00532
T0 [k] 273,11
μ0 [Pa∙s] 0,00001716
Ref A [m2] 191,84478
cp specific heat coeff 1005
k thermal conductivity 0,02007
turbulent intensity 0,018598
derived:
μ [Pa∙s] 1,45798E-05
ρ [kg/m3] 0,24524
P [Pa] 15715,79133
a [m/s] 299,528756
U [m/s] 254,59944
Table 4-4 Setup parameters for Re 30 M and T 223.25 K
The CFD simulations are conducted for each case at a fixed Mach number with a variable angle of attack.
CASE 56, Mach number=0.85, angle of attack
α
=0°,α=1°, α=2°, α=3°, α=4°;
CASE 64, Mach number=0.85, angle of attack
α
=0°,α=1°, α=2°, α=3°, α=4°;
CASE 73, Mach number=0.85, angle of attack
α
=0°,α=1°, α=2°, α=3°, α=4°.
The global drag coefficient (CD) and global lift coefficient (CL) are obtained from the CFD simulation for varying angles of attack, each case and fixed Mach number. The values are an average of the last 100 convergence iteration results. Once CD and CL are
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obtained, it’s carried out a numerical comparison between the three different cases, Ansys Fluent results (available in DPW4), and NTF experimental results.
CL-α for CASE 56, CASE 64, CASE 73, ANSYS DPW4 and NTF experimental results;
CD-α for CASE 56, CASE 64, CASE 73, ANSYS DPW4 and NTF experimental results;
CL-CD for CASE 56, CASE 64, CASE 73, ANSYS DPW4 and NTF experimental results;
CL/CD for CASE 56, CASE 64, CASE 73, ANSYS DPW4 and NTF experimental results.
CASE 56 swept wing
Re Mach alpha CL CD CL/CD
30M 0,85 0 0,22701 0,0144 15,763
30M 0,85 1 0,36155 0,01741 20,7616
30M 0,85 2 0,5059 0,0225 22,4844
30M 0,85 2,5 0,58106 0,02713 21,4155
30M 0,85 3 0,64327 0,03383 19,0156
30M 0,85 4 0,65726 0,04436 14,8153
Table 4-5 CASE 56 aerodynamic coefficient results
CASE 64 swept wing
Re Mach alpha CL CD CL/CD
30M 0,85 0 0,22766 0,01435 15,8687
30M 0,85 1 0,36224 0,01737 20,8521
30M 0,85 2 0,50675 0,02246 22,5596
30M 0,85 2,5 0,58172 0,02711 21,4571
30M 0,85 3 0,64378 0,03383 19,0304
30M 0,85 4 0,66326 0,04495 14,7564
Table 4-6 CASE 64 aerodynamic coefficient results
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CASE 73 swept wing
Re Mach alpha CL CD CL/CD
30M 0,85 0 0,22782 0,01415 16,101
30M 0,85 1 0,36257 0,01717 21,120
30M 0,85 2 0,50757 0,02226 22,805
30M 0,85 2,5 0,58255 0,02694 21,623
30M 0,85 3 0,64413 0,03369 19,120
30M 0,85 4 0,66207 0,04467 14,820
Table 4-7 CASE 73 aerodynamic coefficients results
ANSYS FLUENT
Re Mach alpha Cl CD CL/CD
30M 0,85 0 0,23679 0,01456 16,2629
30M 0,85 1 0,36931 0,0175 21,1016
30M 0,85 2 0,51853 0,02296 22,5881
30M 0,85 2,5 0,58803 0,02746 21,4142
30M 0,85 3 0,64283 0,03401 18,9005
30M 0,85 4 0,64173 0,04331 14,8162
Table 4-8 ANSYS FLUENT aerodynamic coefficient results
Figure 4-7 CL-α chart for M 0.85, Re 30 M, different meshes and experimental data 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
CL
Axis Title
CL-α
ansys
swept wing vers 56 swept wing vers 64 swept wing vers 73 experimental
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Figure 4-8 CD-α chart for M 0.85, Re 30 M, different meshes and experimental data
Figure 4-9 CL/CD-α for M 0.85, Re 30 M, different CFD and experimental data 0
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
CD
Axis Title
CD-α
ansys
swept wing vers 56 swept wing vers 64 swept wing vers 73 experimental
0 2 4 6 8 10 12 14 16 18 20 22 24
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
CL/CD
Axis Title
CL/CD-α
ansys
swept wing vers56 swept wing vers 64 swept wing vers 73 experimental
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Figure 4-10 CL-CD chart for Re 30 M, different meshes and experimental data
Recalling the three goals to pursue in order to assert the validation of the model, it can be said the first point is achieved. From a preliminary analysis of the charts, it is easy to see a common trend in CL-α, CD-α and CL-CD curves especially in the linear trait and the maximum L/D ratios are achieved for angles very close among them and the values almost coincide. In order to reinforce the goodness of the trend, it’s useful to analyzed the CL-α charts carried out by the participants to Drag Prediction Workshop IV.
Figure 4-11 Resume of DPW 4 simulations in terms of CL alpha chart 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
CL
Axis Title
CL-CD
ansys
swept wing vers 56 swept wing vers 64 swept wing vers 73 experimental
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 1 2 3 4 5
CL
α
CL-α Re 5 M workshop
Boeing SA Boeing SST indian bangolore JAXA
Indian Bangalore ANSYS DPW4 NTF run 44 NASA uns
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The Reynolds number used in these simulation is equal to 5 million, but it is interesting to note that the slopes of the curves and the relative gap to the experimental data are very similar to the situation depicted in Figure 4.7.
The three studied cases has almost the same behavior and the CL and CD values are very close among them, therefore it’s not necessary to carry out a triple validation process because they are almost equivalent. The model chosen for proceeding in the validation is the CASE 73 because of the better quality of the mesh employed (as seen in chapter 3).
Moreover the CASE 56 and 64 sometimes exhibit problems of limited turbulence in the far field cells. This problem disappears in CASE 73 because of the semispherical far field shape. The evaluation of a reasonable gap can be carried out by assessing the contribution of uncertainties listed before in the paragraph. In order to do that, it can be useful to refer to previous investigations conducted at NASA Langley Research Center [18] and to the CFD results obtained for the DPW IV with Re=5 million.
The aims of NASA Langley Research Center was the research on the amount of discrepancies caused by the support system and by the permanent wing twist distribution.
For comparison, a freestream Mach number of 0.85 and a Reynolds number of 5 million based on mean aerodynamic chord were chosen. Solutions were run over a range of angles- of-attack from 0° to 5° for three different models:
CRM body-wing-tail without support system;
CRM body-wing-tail with support system (ss);
CRM body-wing-tail with support system taking into account the different wing twist distributions (ssa).
In the table only the values for 0°,2°,4° are listed. The evaluation of the percentage of error due to the support system and the permanent wing twist distribution is estimated around 16% for 0° and 3% for 4°. Taking into account the other sources of uncertainty, mentioned before in the chapter, and the tail presence, a preliminary estimation of a reasonable gap could be over the 16% at lower angles and over 3% at higher values for CL; over 16% and 14% for CD.
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CFD case α CL CD ΔCL ΔCD ΔCL% ΔCD%
WBT0 0.0 0.1186 0.01813
WBT0ss 0.0 0.0991 0.01553 -0.0195 0.00260 16,44 14,34087 WBT0ssa 0.0 0.0990 0.01523 -0.0196 0.00290 16,526138 15,99559
WBT0 2.0 0.4026 0.02367
WBT0ss 2.0 0.3783 0.02031 -0.0243 0.00336 6,0357675 14,19518 WBT0ssa 2.0 0.3766 0.01997 -0.0260 0.00370 6,4580229 15,6316
WBT0 4.0 0.6579 0.04469
WBT0ss 4.0 0.6387 0.03924 -0.0192 0.00545 2,9183767 12,19512 WBT0ssa 4.0 0.6388 0.03847 -0.0191 0.00622 2,9031768 13,9181
Table 4-9 Effect of system support and fixed twist angle for Re 5 M
By means of the DPW IV results, it can be possible to depict a preliminary idea of the gap between EFD and the several CFD simulation collected in a narrow layout. The 5 million Reynolds ANSYS simulation belongs to the aforementioned layout, hence can be compared with NTF experimental results.
The values listed in the following table are obtained interpolating the CFD results with fourth degree polynomial laws:
𝑦 = −0.0014𝑥4 + 0.0052𝑥3 − 0.0005𝑥2 + 0.1298𝑥 + 0.2083
α CL NTF 44 CL ΔCL ΔCL%
0.68889 0.229189 0.298865 0.069676 23.31363 1.21194 0.291217 0.371112 0.079895 21.52846 1.70402 0.352194 0.441955 0.089761 20.31004 1.95245 0.384026 0.47818 0.094154 19.69013 2.20909 0.419271 0.515317 0.096046 18.6383 2.50374 0.457373 0.556751 0.099378 17.8496
2.70096 0.48673 0.58319 0.09646 16.5401
2.93253 0.521095 0.612244 0.091149 14.88764 3.21294 0.559254 0.643458 0.084204 13.08611 3.45029 0.585643 0.665376 0.079733 11.98316
Table 4-10 Percentage CL error between DPW4 and NTF results, Re 5 M
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The percentage CL gap respect the constrains derived from the previous analysis and provides an estimation for a maximum ΔCL%.
Finally in order to achieve the validation, it is necessary to ensure the CFD results, found in the thesis, lie in the gap estimated before, with proper precautions due to the different Reynolds number and to the tail presence in the NASA Langley Research Center investigation. Recalling the results of NTF, it’s necessary to extrapolate the CL and CD values, resulting from CFD simulations, for the angles employed in EFD. The values listed in the following table are obtained interpolating the CFD results with two different polynomial laws:
𝑦 = −0,0037𝑥4 + 0,0192𝑥3 − 0,0259𝑥2+ 0,1451𝑥 + 0,2278 for CL;
𝑦 = −0,0003𝑥5+ 0,0024𝑥4 − 0,0066𝑥3+ 0,0082𝑥2− 0,0007𝑥 + 0,0141 for CD.
α CL NTF CL ∆CL ∆CL%
0,6526 0,238809 0,316127 0,077318 24,4579 1,1584 0,299537 0,384312 0,084775 22,05885 1,67438 0,363788 0,459188 0,0954 20,77577 2,16606 0,428788 0,534254 0,105466 19,74074 2,67968 0,499861 0,609307 0,109446 17,96234 3,17364 0,568938 0,66581 0,096872 14,54945 3,44421 0,602229 0,684106 0,081877 11,9684
Table 4-11 Percentage CL error between NTF and CASE 73
α CD NTF CD ∆CD ∆CD%
0,6526 0,013675 0,015701 0,002026 12,90111 1,1584 0,015046 0,017729 0,002684 15,13678 1,67438 0,016853 0,019851 0,002998 15,10093 2,16606 0,019057 0,022509 0,003453 15,33828 2,67968 0,02249 0,026407 0,003917 14,83387 3,17364 0,027189 0,030384 0,003195 10,51435 3,44421 0,030248 0,031633 0,001385 4,379465
Table 4-12 Percentage CD error between NTF and CASE 73
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As visible in the table, the percentage of error in CASE 73, compared to NTF experimental results, is included in the reasonable gap estimated before.
In light of trend and gap considerations, the final goal of model validation is reached and the values obtained in the following chapter using the CFD model 73, can be considered reliable results.
