A Boundary Layer Transition Model

Abstract

A new boundary layer transition model is presented which relates the velocity fluctuations near the wall to the formation of turbulent spots. A relationship for the near wall velocity frequency spectra is also established, which indicates an increasing bias towards low frequencies as the skin friction coefficient for the boundary layer decreases. This result suggests that the dependence of transition on the turbulent length scale is greatest at low freestream turbulence levels. This transition model is incorporated in a conventional boundary layer integral technique and is used to predict eight of the ERCOFTAC test cases. Three of these test cases are for nominally zero pressure gradient and the remaining five are for a pressure distribution typical of an aft loaded turbine blade. The model is demonstrated to predict the development of the boundary layer through transition reasonably accurately for all the test cases. The sensitivity of start of transition to the turbulent length scale at low freestream turbulence levels is also demonstrated.

Discussion: “The Path to Predicting Bypass Transition” (Mayle, R. E., and Schulz, A., 1997, ASME J. Turbomach., 119, pp. 405–411)

“…A similar model to that presented here, but using empirical correlations rather than analytical theory for the induction of the velocity fluctuations through the unsteady pressure field, has been used to predict transition previously (Savill, 1993(Savill, , 1994(Savill, , 1995aJohnson, 1994;Johnson and Ercan, 1996). In this work it was found that the model could be extended to adverse/favorable streamwise pressure gradients using the same unsteady pressure field model, as it is the effect of the streamwise pressure gradient on the time mean laminar boundary layer profile that results in an increase or decrease in the velocity fluctuation levels in an adverse or favorable pressure gradient, respectively.…”

On ‘spot’ evolution under an adverse pressure gradient

“…See also Seifert & Wygnanski (1995), Seifert (1997), Gostelow et al (1997), van Hest (1997) and Howell (1998). Computationally, direct simulations have yielded relatively little on adverse gradient effects, especially concerning their physical understanding, but empirically based modelling has been performed by Johnson (1997Johnson ( , 1998, Solomon, Walker & Gostelow (1996), Johnson & Ercan (1996) and Steelant & Dick (1996). Little basic theoretical nonlinear study without empiricism has been made for 'spots' until quite recently: see references later in this section.…”

“…Here, the term 'spot' is used to denote a spot-like disturbance or, in two dimensions, a strip. 'Spot' propagation models are used in turbomachinery transition predictions (as described by Abu Ghannam & Shaw 1980;Gostelow et al 1993;Clarke, Jones & LaGraff 1994;Narasimha 1997;Johnson 1997; for instance) but are also relevant to other contexts with deep-transition physics (for example Smith & Bowles 1992;Li et al 1998;Savin, Smith & Allen 1999). Most of the many 'spot' experiments are for basic boundary layers under nominally zero pressure gradient, as discussed in the reviews in the references above.…”

The Origin of Turbulent Spots

“…Johnson (1994) considered the effect of the fluctuating pressure field resulting from freestream turbulence on the near wall velocity profile within the laminar boundary layer. Experimental observations (Johnson and Ercan[1996]) of the near wall velocity fluctuations within laminar boundary layers show that the dominant wavelengths are much greater than the boundary layer thickness. Similar results have since been obtained theoretically by Mayle and Schultz [1997].…”