Browsing by Author "Klinksiek, William Frederick"

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    An implicit numerical solution of the turbulent three-dimensional incompressible boundary-layer equations
    Klinksiek, William Frederick (Virginia Tech, 1971-06-05)
    A method of solving the three-dimensional, incompressible turbulent boundary-layer equations was developed using a Crank-Nicholson implicit finite-difference technique, with the turbulent stress terms modeled with an eddy-viscosity model obtained from mixing length theory. The method was applied to two three-dimensional flow geometries for which experimental data exists and a comparison with this data showed excellent agreement. The complete computer program was sufficiently generalized for application to two-dimensional laminar and turbulent flows with arbitrary pressure gradients. The method was applied to several such test cases and the solutions agreed well with both theory and experiment. An analysis was presented to determine the conditions for which the finite difference equations were stable and convergent. The results of this analysis demonstrated that the equations are generally stable and convergent. However, care must be exercised when writing the finite difference approximation to the continuity equation, because certain finite difference formulations of the continuity equation can lead to an instability when the initial values for the distribution of the velocity normal to the bounding surface cannot be accurately specified.
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    An incompressible three-dimensional turbulent boundary layer on the floor of a recurving rectangular channel
    Klinksiek, William Frederick (Virginia Tech, 1967-09-15)
    A brief review of three-dimensional turbulent boundary layer mean velocity profile models was presented, with emphasis on the applicability of these to predict cross flow profiles when skewing existed in any single profile. A recurving or s-shaped rectangular channel was used to experimentally investigate the possible existence of such a turbulent boundary layer flow. The time average velocity profiles along the centerline of this channel were obtained with a hot film anemometer. The resultant profiles indicated that a turbulent boundary layer can exist with cross flow in two lateral directions simultaneously in the same profile and this phenomenon can occur over a relatively long flow distance. Several attempts were made to fit the models of Eichelbrenner and Shanebrook to the measured cross flow profiles, but with only limited success. A test of the three-dimensional wall-wake formulation proposed by Coles was made for each profile. A shear velocity was inferred by a modification of the two-dimensional Ludwieg and Tillman skin friction equation, and by a modified form of the two-dimensional Clauser skin friction chart. A linear semi-logarithmic region was judged distinguishable for profiles with skewing in one lateral direction and with the limiting wall streamline angle less than approximately 30 degrees. Additionally in some instances a linear semi-logarithmic region was judged to exist when when simultaneous lateral skewing occurred in two directions. Generally, the constructed wake profiles did not resemble the universal form tentatively proposed by Coles, but rather resembled the characteristic preasymptotic form as discussed by Pierce.