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Navier-Stokes Analysis of Turbulent Boundry Layer and Wake for Two-Dimensional Lifting Bodies
Pages 633-644

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From page 633...
... on conformal mapping are combined to develop new 2-D foil sections. Since the turbulent kinetic energy is the dynamic pressure, and the ReynoIcis shear stresses are related to the turbulence production, these quantities are used to develop new 2-D sections with desirable turbulent boundary layer characteristics.
From page 634...
... OUTLINE OF ANALYTICAL METHOD The objective is to maximize the thickness of a 2-D lifting foil and to reduce trailing edge turbulent kinetic energy without incurring significant flow separation. This is achieved by control of the turbulent boundary layer and wake characteristics through careful shaping of the 2-D section.
From page 635...
... Here fk~ and fk2 are convective terms and Ski and 9k2 are viscous diffusion terms. S is a source term added to the equations which moclels the production and dissipation of turbulent kinetic energy.
From page 636...
... measurements of the streamwise and normal velocity components yielded precision within two of the measured free-stream velocity at any position. An(l, the precision of the measured turbulence intensities and Reynolds shear stress was within No of the maximum measured values of a given wake profile.
From page 637...
... As discussed earlier in the previous paragraph for the velocity profiles, this observation could mean that the turbulence models do not work well even for mild flow separation. Also, this observation illustrates the elliptic nature of the N-S simulation, i.e.
From page 638...
... At this design lift for the baseline foil, the N-S analysis indicates some flow separation on the suction side which accounts for the high turbulence activity. And the pressure side of the new section has low turbulence activity because the pressure distribution there is almost flat over the entire surface.
From page 639...
... tI,2~; and 4) concentrate on the development of turbulence models that can calculate more accurately turbulent flows with strong adverse pressure gradient, and even separation.
From page 640...
... and Spalding, D.B., "The Numerical Computation of Turbulent Flows, " Computer Methods in Applied Mechanics and Engineering, Vol.
From page 641...
... -- - - -Cp calculation by DTNS section geometry A\ ,°'\6 opt\ P~ =~\ I I I I ~ 0.0 0.2 0.4 0.6 X/C 0.8 1.0 Figure 2.a) Pressure distribution for the thin section (data from Ref.
From page 642...
... Velocity vector data arid DTNS calculations for the thick section o k data at x/C=1.02 o 0.05 0.03 0.0'1 -0.01 -0.03 -0.05 o x/C= 1 .05 x/C=l .10 -- -- calculation by DTNS 1 ~ 1 ~ 1 ]
From page 643...
... \/elocl~ vector calculations for the new section 0.07 0.05 0.03 0.01 -0.01 -0.03 0 new section calc, x/C=1.02 0 x/C= 1 .05 &- x/C= 1 .09 -- -- baseline section calc it' 5 0 5 0 5 0 5 1000 w/U 2 Figure 8.b) Profiles of Reynolds shear stress for the baseline and the new section
From page 644...
... 2. Preliminary study indicates that the flow solution converges to approximately the same pressure distribution for both the Baldwin-Lomax and the k-e turbulence models.


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