Sparrow's theoretical study (1) of laminar flow and Eckert and Irvine's (2) experimental study of transitional flow in isosceles triangular ducts suggest the existence of some rather interesting phenomena in the transitional flow range for such ducts. The purpose of this paper is to present the results of a theoretical analysis and experimental investigation of the transition phenomenon in isosceles triangular ducts and to demonstrate the existence of ;I unique and heretofore theoretically unpredicted phenomenon in this flow region. REVIEW OF PREVIOUS RESEARCHEckert and Irvine ( 2 ) presented data obtained from a flow visualization study of air flow in isosceles triangular ducts which they interpreted as showing the existence of a range of flows for which there occurred simultaneous macroscopically large regions of laminar and turbulent flow in the duct. This is not to be confused with the traditional concept of a laminar sublayer in turbulent flow. Rather, what is implied is a macroscopically large region of the flow field which experiences turbulent flow side by side with a separate macroscopically large region which is in stable laminar flow. Such a duality of mode is furthermore independent of time at a given spatial location.The existence of such a dual flow region implies that the frictional resistance of the duct should be increased over that due to laminar flow because of the turbulence present, but decreased from the turbulent value because of the laminar flow present. However, such a region of frictional flow resistance behavior is not evident in the data of Carlsoii and Irvine ( 3 ) who studied the frictional resistance of air flow in a series of isosceles triangular ducts similar to the ones used by Eckert and Irvine ( 2 ) . Hanks and Brooks ( 4 ) , using a flow birefringence technique, showed that Eckert and Irvine's ( 2 ) interpretation of their flow visualization data was due primarily to the influence of their probe wake.As a result of the above observations, it is unclear just what phenomena are to be expected in transitional flow in triangular ducts. Sparrow's theoretical (1 ) analysis of laminar flow in such ducts makes possible the theoretical analysis of the laminar turbulent transition prablem. That analysis, involving application of Hanks' theory (5, 6) of laminar flow stability, follows. T H E O R E T I C A L ANALYSISIt has been shown (5, 6 ) that the stability* of a rectilinear flow field in a duct of fixed boundaries is determined by the condition that the parameter where the absolute value signs I 1 imply magnitudes of the vectors enclosed thereby. For a rectilinear flow in a duct of isosceles triangular cross section, such as illustrated schematically in Figure 1, Equation (1) can be reduced to * In the presence of strong inlet disturbances, it was shown ( 6 ) that for such a field the necessary and sufficient condition for transition to turbulence is the existence of flow profile instability.
A study of mean velocity distributions and turbulence intensity measurements in ducts having isosceles triangular cross sections has revealed the existence of a range of mean flow Reynolds numbers for which a pronounced nonturbulent secondary flow occurs. The driving mechanism is shown to arise from the threedimensional character of the laminar flow. The secondary flow results in an approximately 6-8% increase in frictional resistance over that observed in rectilinear laminar flows. Transition from rectilinear laminar flow to a three-dimensional laminar flow with secondary circulations occurs at a critical Reynolds number predicted accurately by the momentum stability theory of Hanks. A subsequent transition to a turbulent flow upon which is superimposed a mean secondary flow occurs at a higher Reynolds number.
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