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References                                                            237
















           0.000
               0.0   0.2    0.4    0.6
                                                                              0.8
                            s/c
         Fig.  7.12.  Variation  of  (a)  local skin-friction  coefficient  c/  and  (b)  displacement  thickness
                                                                                6
         6* with  angle  of incidence  on the upper  surface  of the  NACA  0012  airfoil  for  R c  — 3 x  10 .


         References

         [I]  Cebeci,  T.:  Turbulence  Models  and  Their  Application,  Horizons  Pub.,  Long  Beach,
            Calif,  and  Springer,  Heidelberg,  2004.
         [2]  Cebeci,  T.:  Analysis  of  Turbulent  Flows,  Elsevier,  London,  2004.
         [3]  Goldstein,  S.:  "On  Laminar  Boundary  Layer  Flow  near  a Point  of Separation,"  Quart.
            J.  Mech.  & Appl.  Math,  Vol.  1, pp.  43-69,  1948.
         [4]  Cebeci,  T.:  An  Engineering  Approach  to  the  Calculation  of  Aerodynamic  Flows,  Hori-
            zons  Pub.,  Long  Beach,  Calif,  and  Springer,  Heidelberg,  1999.
         [5]  Catherall,  D.  and  Mangier,  K.W.:  "The  Interpretation  of  Two-Dimensional  Laminar
            Boundary  Layer Equations  Past  the Point  of Vanishing  Skin  Friction,"  J.  Fluid  Mech.,
            Vol.  26, p.  163,  1966.
         [6]  Briley,  W. R.:  "A  Numerical  Study  of Laminar  Separation  Bubbles  Using the  Navier-
            Stokes  Equations,"  J.  Fluid  Mech.,  Vol.  47,  no.  4, pp.  713-736,  1971.
         [7]  LeBalleur,  J.C.:  "Couplage  Visqueux-Non  Visqueux:  Methode  Numerique  et  Ap-
            plications  Aux  Ecoulements  Bidimensionnels  Transsoniques  et  Supersoniques,"  La
            Recherche  Aerospatiale,  March-April  1978.
         [8]  Carter,  J.  and  Wornom,  S. F.:  "Solutions  for  Incompressible  Separated  Boundary  Lay-
            ers  Including  Viscous-Inviscid  Interaction,"  In:  Aerodynamic  Analysis  Requiring  Ad-
            vanced  Computers,  NASA  SP-347, p.  125,  1975.
         [9]  Veldman,  A. E. P.:  "A Numerical  Method  for  the  Calculation  of  Laminar  Incompress-
            ible  Boundary  Layers  with  Strong  Inviscid  Interaction,"  NLRTR  79023L,  1979.
         [10] Smith,  A. M. O.:  "Improved  Solutions  of the  Falkner  and  Skan  Boundary-Layer  Equa-
            tions,"  Sherman  M.  Fairchild  Fund  paper  FF-10,  Inst.  Aero.  Sci.,  1954.
         [II]  Iglish,  R.:  "Exact  Calculation  of Laminar  Boundary  Layer  in Longitudinal  Flow  Over
            a  Flat  Plate  with  Homogeneous  Suction,"  NACA  Tech.  Memo.  1205,  1949.



         Problems


         7-1.  Using the  computer  program  of  Section  7.4,  study  the  numerical  accuracy
        of  the  box  method  for  Falkner-Skan  flows  m  =  1  and  0.  Compare  the  wall
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