An experimental investigation of the compressible turbulent boundarylayer with a favorable pressure gradient

Abstract

This paper describes the results of a detailed experimental investigation of a two-dimensional turbulent boundary layer in a favorable pressure gradient where the freestream Mach number varied from 3.8 to 4.6; the ratio of wall to adiabatic wall temperature remained constant at a value of 0.82. Detailed profile measurements were made with pressure and temperature probes; skin friction was measured directly with a shear balance. The velocity and temperature profile results are compared with zero pressure gradient and incompressible results. The skin-friction data are correlated with momentum-thickness Reynolds number and the pressure gradient parameter fie -(6/T w )(,dP/dx).The skin friction increases with decreasing fie for a constant value of momentum-thickness Reynolds number. NomenclatureA = constant in Eq. (4) B = constant in Eq. (4) Cf = skin-friction coefficient H u = incompressible shape factor k = Karman's constant M = Mach number N -velocity profile exponent u/u e = (y/8) llN P = pressure Res = momentum-thickness Reynolds number T = temperature f = (T t -T v )/(T te -T w ) u = velocity U T = shear velocity = (r w /p w ) 112 U + = U/Ur x = distance along plate y = distance normal to flow 2/+ = u r y/v w $ = Clauser's equilibrium parameter = (d*/r w )(dP/dx) (3e = pressure gradient parameter = (6/r w }(dP/dx) 5 = boundary-layer thickness p = density 5* = displacement thickness B = momentum thickness T = shear stress v -kinematic viscosity Presented as Paper 69-685 at Subscripts aw -adiabatic wall e = freestream conditions o = supply conditions w = wall conditions t = total conditions

Investigation of the Structure of a Cooled Wall Turbulent Supersonic Boundary Layer.

“…A plot of this parameter versus Re8 is shown in Figure 41 where it is compared to the results of previous investigations of supersonic boundary layers with zero and favorable pressure gradient . 4 The present data show relatively little effec t due to wall temperature , reflecting the fact that the velocity profiles are essentially independent of T~. Interestingly enough , while the present data correspond to a slightly adverse pressure gradient ~ = +0.04, they are in better agreement with the trend of the favorable pressure gradient results of Reference 4 (3 = -0.1 to -0.2) than the zero pressure gradient results of Reference 3.…”

“…into Equation (3)(4)(5)(6)(7)(8)(9). The l a t t e r can then be integrate~ with respec t to y/6 yielding the following expression for the total shear:…”

“…I~u Thy l u/~y P c ~u /~y (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) from which the normalized mixing length can be expressed as:…”

“…The time-averaged conservation equations for the two-dimensional flat plate boundary layer are : -dp/dx + ~T /~Y (3)(4)(5)(6)(7)(8)(9) where ~ = v + p~v / p and the total shear stress T is the sum of a laminar and a turbulent term :…”

“…4 ) to monitor the streamwise and spanwise uniformi ty of surface properties. The pressure tubes are 0.081 cm in diameter wi th a 0.05 cm diameter opening; the thermocouples , comprised of a twisted pair of 0.025 cm diameter wires , were epoxied in place in holes drilled through the plate .…”