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The effects of different axisymmetric forebody shapes have been studied on the non-axisymmetric (helical) global modes of the boundary layer developed on a circular cylinder. Sharp cone, ellipsoid and paraboloid shapes have been considered with the fineness ratio (FR) of 2.5, 5.0 and 7.5. The base flow is in line with the cylinder’s axis at the inflow boundary, and hence the base flow is axisymmetric. The boundary layer has developed from the tip of the forebody where a highly favourable pressure gradient exists, and it depends on the sharp edge of the forebody’s geometric shape. However, the pressure gradient then remains constant on the cylindrical surface of the main body. Thus, the boundary layer developed on the forebody and main body (cylinder) is non-parallel, non-similar and axisymmetric. The governing equations for the stability analysis of the small disturbances have been derived in the cylindrical polar coordinates. The spectral collocation method with Chebyshev polynomials has been used to discretise the stability equations. An eigenvalue problem has been formulated from the discretised stability equations along with the appropriate boundary conditions. The numerical solution of the eigenvalue problem was done using Arnoldi’s iterative algorithm. The global temporal modes have been computed for helical modes $$N = 1$$ , 2, 3, 4 and 5 for Reynolds number $$Re = 2000$$ , 4000 and 10000. The spatial and temporal structures of the least stable global modes have been studied for different Reynolds numbers and helical modes. The global modes with ellipsoid were found the least stable while that of the sharp cone were found the most stable.

This paper presents the effect of axisymmetric forebody shapes on the global stability characteristics of axisymmetric boundary layer developed on a circular cylinder. Axisymmetric forebodies like sharp-cone, ellipsoid, and paraboloid with a fineness ratio (FR) of 2.5, 5.0 and 7.5 are considered. The boundary layer starts to develop at a stagnation point on the forebody geometry and grows in spatial directions. The inflow velocity component is parallel to the axis of the cylinder, and hence the angle of attack is zero. The base flow is axisymmetric, non-parallel and non-similar. The linearised Navier�Stokes equations are derived in the cylindrical polar coordinates for the disturbance flow components. The discretised linearised Navier�Stokes equations along with appropriate boundary conditions form a general eigenvalue problem and it has been solved using Arnoldi�s algorithm. The global temporal modes have been computed by solving the two-dimensional eigenvalue problem. The extent of a favourable pressure gradient developed in streamwise direction depends on the shape of axisymmetric forebody. The temporal and spatial growth of the disturbances has been computed for axisymmetric ( N = 0) mode for different Reynolds numbers (Re). The forebody shapes have a significant effect on the base flow and stability characteristics at low Re., by Ramesh Bhoraniya and Vinod Narayanan

The drag coefficients of freestream-aligned circular cylinders of fineness ratios of 0.75–2.0 were investigated with a magnetic suspension and balance system (MSBS). The objective was to find the critical geometry, that is, the fineness ratio at which the drag coefficient becomes the local maximum within this ratio range. The experiments were conducted using the 1-m MSBS at the low turbulence wind tunnel at the Institute of Fluid Science, Tohoku University. The drag and base pressure coefficients of various cylinders were measured. The freestream velocity was varied to produce flows with Reynolds numbers ranging from $$0.6\times 10^5$$ to $$1.0\times 10^5$$ . The drag coefficient monotonically decreases as the fineness ratio increases and no critical geometry or local maximum of the drag coefficient is found in the range we investigated. The base pressure coefficient decreases as the fineness ratio increases. The temporal fluctuations of the base pressure of the models with fineness ratios of 0.75, 1.0, and 1.2 are approximately twice as large as that of the model with a ratio of 2.0. The relationship between the fineness ratio and the drag coefficient is similar to that between the fineness ratio and the base pressure coefficient, similar to the findings of previous studies of two-dimensional bodies.

In this work, a simple and efficient numerical approach to determine the shape of the minimum-drag axisymmetric forebody in inviscid supersonic flow with an attached shock constraint has been described. Taylor–Maccoll equation in conjunction with the tangent cone method is employed to estimate the pressure drag coefficient which is also chosen as the cost function. The forebody geometry is parameterized using a Non-Uniform Rational B-Splines (NURBS) curve whose control points are the design variables for optimisation using the steepest descent algorithm. Numerical studies demonstrate that the optimal forebody geometry for a given length and base radius has as much as 15 % lesser drag, depending on the Mach number than a cone of the same fineness ratio and that the convergence to the optimal solution exhibits a relatively weak Mach-number dependence.

The possibility of controlling the aerodynamic characteristics of wing airfoils in transonic regimes of flight using one-sided pulse-periodic energy supply has been studied. The flow structure near the symmetric airfoil at different angles of attack and its aerodynamic characteristics as functions of the value of energy in its nonsymmetric (about the airfoil) supply have been determined by numerical solution of two-dimensional nonstationary gasdynamic equations. A comparison of the obtained results and the data of calculation of flow past the airfoil at different angles of attack without energy supply has been made. It has been established that a prescribed lift can be obtained, using energy supply, with a much higher fineness ratio of the airfoil than that in the case of flow past it at an angle of attack.

An experimental study was done to quantify the effects of a variety of background particulates on the delayed laminar-turbulent transition of a thermally stabilized boundary layer in water. A Laser-Doppler Velocimeter system was used to measure the location of boundary layer transition on a 50 mm diameter, 9:1 fineness ratio ellipsoid. The ellipsoid had a 0.15 μm RMS surface finish. Boundary layer transition locations were determined for length Reynolds numbers ranging from 3.0 × 106 to 7.5 × 106. The ellipsoid was tested in three different heating conditions in water seeded with particles of four distinct size ranges. For each level of boundary layer heating, measurements of transition were made for “clean” water and subsequently, water seeded with 12.5 μm, 38.9 μm, 85.5 μm and 123.2 μm particles, alternately. The three surface heating conditions tested were no heating, ΔT = 10°C and ΔT = 15°C where ΔT is the difference between the inlet model heating water temperature, Ti, and free stream water temperature, T∞. The effects of particle concentration were studied for 85.5 μm and 123.2 μm particulates.

This study considers the numerical results for the airflow pattern to obtain droplet trajectories around and into a leading edge hole of a cloud droplet sampling probe. The probe was initially conceived at MIT and developed into a practical airborne system in the Cloud Physics Program at the National Center for Atmospheric Research. The probe is designed to be an ellipsoid of revolution with a circular sampling hole at the forward stagnation point. The external flow field is assumed to be steady, axisymmetric, irrotational and incompressible and depends on four parameters: the hole radius, axial speed in the hole, free stream velocity and the fineness ratio of the ellipsoid. The trajectory calculations are based on a three-dimensional gravity field with a fluid resistance computed from experimental drag coefficients on spheres. Both numerical and theoretical solutions for the flow field have been obtained for various combinations of the above parameters. For these flow fields, trajectories for droplets have been obtained. From the trajectory calculations we have obtained collection efficiencies for the probe and have compared these trajectories with experimental trajectories obtained at NCAR.