On the laminar boundary-layer flow over rotating spheroids

A consolidated method for predicting laminar boundary layers on rotating axi-symmetric bodies

“…Due to the complex relation between r and s for a spheroid we have not verified that equations (8a,b) can be transformed to (23a,b). Nevertheless, velocity profiles calculated by the present method compare well with those generated by Samad and Garrett (2010) in figure 9 for e = 0.3; however, for the higher eccentricity case of e = 0.7, figure 10, the agreement, while good initially, is poor at increased latitude θ. The discrepancy appears to be connected with the different mapping of the η co-ordinates used by Garrett (2010, 2014) and in the present work, as the magnitudes of the peak velocities agree closely.…”

“…The equations for the boundary layer of a rotating prolate spheroid in still air, first investigated by Fadnis (1954), are shown here as formulated by Samad and Garrett (2010), rotating axi-symmetric body to be analysed, both with and without an axial flow. Comparisons with other published shape-specific formulations appear to confirm the validity of both the mathematical formulation and the numerical scheme employed, but there are some isolated discrepancies which remain to be resolved.…”

“…Comparison of the velocity profiles on a rotating sphere (in an axial flow) at θ = 70 • and T s = 0, 0.05, 0.1, 0.15, 0.2 and 0.25 (left to right), obtained using the present approach, with those reported byGarrett (2002) (•); η as defined in equation(13d). Comparison of the velocity profiles on a rotating prolate spheroid (in still air) with eccentricity 0.3 at θ = 10 • → 80 • in 10 • increments (left to right), obtained using the present approach, with those reported bySamad and Garrett (2010) (•); η as defined in equation(13d). Comparison of the velocity profiles on a rotating prolate spheroid (in still air) with eccentricity 0.7 at θ = 10 • → 80 • in 10 • increments (left to right), obtained using the present approach, with those reported bySamad and Garrett (2010) (•); η as defined in equation(13d).…”

“…The discrepancy appears to be connected with the different mapping of the η co-ordinates used by Garrett (2010, 2014) and in the present work, as the magnitudes of the peak velocities agree closely. There is some ambiguity in the definition of η * 0 between Samad and Garrett (2010) and Samad and Garrett (2014) which may explain the discrepancies at higher θ for large eccentricities. In former η * 0 is defined as the wall-normal distance to the surface from the axis of revolution while in the latter it is defined as the length of the semi-major axis.…”

Eggs and milk: Spinning spheres partially immersed in a liquid bath

“…(8) are nondimensional with the Reynolds number, Re = ωR 2 /ν, θ being the tangential location andδ being the normalized boundary layer thickness,δ = δ/R. Equation (8) is solved subject to the condition thatδ = 0 at θ = 0 to yield an expression for the boundary layer …”