ALBERT

Description: For fully-developed turbulent flow in straight channels of non-circular cross-section, there exists a transverse mean flow superimposed upon the axial mean flow. This transverse flow, commonly known as secondary flow, interacts with the axial mean flow and turbulence structure in a complex manner. In this paper several heretofore unexplored aspects of this type of secondary flow are discussed on the basis of results of an extensive experimental programme which was conducted for steady, incompressible, fully-developed turbulent air flow in both square and rectangular channels. Specifically, the following aspects are examined: (a) the Reynolds-number effect on secondary flow, (b) the directional characteristics of local wall shear stress, (c) the orientation of Reynolds-stress principal planes in a plane normal to the axial flow direction, and (d) the Reynolds equation along a secondary-flow streamline. Within the Reynolds-number range of the investigation, the results indicate that secondary-flow velocities, when non-dimensionalized with either the bulk velocity or the axial mean-flow velocity at the channel centreline, decrease for an increase in Reynolds number. Also, the greatest skewness of local wall shear-stress vectors is shown to occur in the near vicinity of corners where secondary flow is maximum. In addition, it is shown that in planes normal to the axial flow direction, traces of Reynolds stress principal planes are not tangent and normal to lines of constant axial mean-flow velocity. This behaviour is in contrast to that for less complicated turbulent flows, for example, two-dimensional channel flow or circular-pipe flow where such traces are always tangent and normal to lines of constant axial mean-flow velocity in accordance with symmetry considerations. Finally, through experimental evaluation of terms in a momentum balance along a typical secondary-flow streamline, it is shown that secondary flow is the result of small differences in magnitude of opposing forces exerted by the Reynolds stresses and static pressure gradients in planes normal to the axial flow direction. © 1965, Cambridge University Press. All rights reserved.

Description: The response characteristics of a hot wire operated at constant temperature and exposed to a mean-velocity gradient along its length are examined both analytically and experimentally. The shear sensitivity of local wire temperature distributions, as measured with an infrared microscope, are compared with predicted temperature distributions in order to select a convective heat transfer correlation which can be applied locally along a wire in shear flow. On the basis of this correlation, the steady-state and dynamic response behaviour of platinum and tungsten wires in shear flow are examined by means of computer-generated data. Response curves of general applicability are presented which can be used to correct local mean-velocity and turbulence intensity measurements whenever a mean-velocity gradient exists along a wire. © 1971, Cambridge University Press. All rights reserved.

Description: The mechanisms which initiate secondary flow in developing turbulent flow along a corner are examined on the basis of both energy and vorticity considerations. This is done by experimentally evaluating the terms of an energy balance and vorticity balance applied to the mean motion along a corner bisector. The results show that a transverse flow is initiated and directed towards the corner as a direct result of turbulent shear stress gradients normal to the bisector. The results further indicate that anisotropy of the turbulent normal stresses does not play a major role in the generation of secondary flow. Possible extensions of the present results to other related flow situations are ahstrated and discussed. © 1973, Cambridge University Press. All rights reserved.

Description: Development of a pressure-strain model, an algebraic stress model, and wall functions appropriate for flows with spanwise variations in the local wall shear stress are accomplished. Furthermore, a hot-wire measurement technique was also developed for determining the local mean velocity and Reynolds stresses in a complex flow. Experiments were performed on supersonic and subsonic turbulent flow in a square duct, flow about a strut-endwall, flow within a transition duct, and on co-flowing annular jets with swirl. All results are presented in a viewgraph format.

Description: An incompressible, turbulent, swirl-free flow through a circular-to-rectangular transition duct was studied experimentally. The cross-sectional geometry all along the duct was defined using the equation of a superellipse. The three mean velocity components and the six Reynolds stress components were measured at two axial stations downstream from the transition. It is shown that a secondary flow vortex pair which develops along the duct sidewalls significantly distorts the mean and turbulence fields. At the duct exit, the flow is not in local equilibrium, but recovers to local equilibrium conditions in the rectangular extension duct. Analysis demonstrates that conventional wall functions are not applicable at all streamwise locations in the duct.

Description: The nature of supersonic, turbulent, adiabatic-wall flow in a square duct is investigated experimentally over a development length of x/D between 0 and 20 for a uniform flow, Mach 3.9 condition at the duct inlet. Initial discussion centers on the duct configuration itself, which was designed specifically to minimize wave effects and nozzle-induced distortion in the flow. Total pressure contours and local skin friction coefficient distributions are presented which show that the flow develops in a manner similar to that observed for the incompressible case. In particular, undulations exist in total pressure contours within the cross plane and in transverse skin friction coefficient distributions, which are indicative of the presence of a well-defined secondary flow superimposed upon the primary flow. The results are analyzed to show that local law-of-the-wall behavior extends well into the corner region, which implies that wall functions conventionally applied in two-equation type turbulence models, when suitably defined for compressible flow, may also be applied to supersonic streamwise corner flows.

Description: Steady, developing, adiabatic supersonic flow in a square duct is investigated for an inlet Mach number of 3.91 and a unit Reynolds number of 1.8 x 10 to the 6th/m. The numerical results for laminar flow show that two secondary flow cells develop in the near vicinity of the corner which are centered about the corner bisector and distort the primary flow in this region. For turbulent flow, the experimental results indicate that two secondary flow cells also develop about the corner bisector, but are directed in an opposite sense to that observed for the laminar case. Numerical results based on the Baldwin-Lomax model show that this model is incapable of predicting turbulence-generated secondary flow cells. For a suitable choice of constants, the Gessner-Emery model is able to predict the strength of these cells, but is deficient with respect to predicting their positions in the flow and their distorting influence on the primary flow. These observations are based on comparisons made in this paper between predicted and measured total pressure contours, cross flow velocity profiles, and local wall shear stress distributions.

Description: An experimental study was conducted to investigate incompressible flow about a strut-endwall configuration positioned within a constant area duct. The endwal boundary layer was tripped, but natural transition occurred on the strut surface. The results indicate that spanwise varying transition on this surface leads to the formation of a secondary vortex which coexists with the horseshoe vortex generated by endwall flow separation upstream of the strut leading edge. Both vortices are similar in strength downstream of the strut trailing edge, and both distort the primary flow and local turbulence structure in the wake-endwall region. The level of distortion is demonstrated by means of axial mean velocity contours, turbulence kinetic energy contours, and Reynolds shear stress contours measured in the cross plane at two streamwise locations. Analysis of the results shows that conventional eddy viscosity and k-epsilon transport equation models are not wholly adequate for predicting this flow situation.

Description: The mean-flow structure of supersonic, turbulent, adiabatic-wall flow in a square duct is investigated experimentally over a development length x/D = 0-50 for a uniform flow, Mach 3.9 condition at the duct inlet. The results show that a secondary flow cell structure develops which is similar to that for the incompressible case. Development of the primary flow is influenced by the combined effects of the secondary flow and the streamwise adverse pressure gradient. Total pressure, axial mean velocity, and Mach number profiles are presented which show that the outer flow is sensitive primarily to the streamwise pressure gradient, while flow in the near-wall region is dominated by the secondary flow. Axial mean-velocity profiles plotted in terms of van Driest-scaled variables show that a well-defined log-law region exists in the near-wall layer. This region exists in the presence of a secondary flow which continuously modifies spanwise wall shear stress behavior along the length of the duct.

Description: A three-dimensional mixing length model is proposed for modeling local Reynolds stress behavior in rectangular ducts of arbitrary aspect ratio. The model is applicable to both developing and fully-developed flows, and can be applied to other 90-degree corner flows with mild streamwise pressure gradients. Comparisons between theory and experiment show that all components of the Reynolds stress tensor are modeled reasonably well, both in the vicinity of a corner and in two-dimensional regions away from the corner.