Unsteady Freestream Research Articles

Semi-similar solution of an unsteady compressible three-dimensional stagnation point boundary layer flow with massive blowing

A semi-similar solution of an unsteady laminar compressible three-dimensional stagnation point boundary layer flow with massive blowing has been obtained when the free stream velocity varies arbitrarily with time. The resulting partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme with a quasi-linearization technique in the nodal point region and an implicit finite-difference scheme with a parametric differentiation technique in the saddle point region. The results have been obtained for two particular unsteady free stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. Results show that the skin-friction and heat-transfer parameters respond significantly to the time dependent arbitrary free stream velocity. Velocity and enthalpy profiles approach their free stream values faster as time increases. There is a reverse flow in the y- wise velocity profile, and overshoot in the x- wise velocity and enthalpy profiles in the saddle point region, which increase as injection and wall temperature increase. Location of the dividing streamline increases as injection increases, but as the wall temperature and time increase, it decreases.

The structure of a separating turbulent boundary layer. Part 5. Frequency effects on periodic unsteady free-stream flows

The results of experimental trials to obtain measurements of the effects of frequency on the sinusoidal variations in the free stream velocity over a separating turbulent boundary layer are reported. An oscillation frequency of 0.596 Hz was examined, in conjunction with a free stream velocity of 10.18 m/sec. Hot-wire anemometers measured the velocity upstream of the separation and the phase-averaged skin friction, while the velocities in the detached flow zone and the downstream velocity were assayed with a laser anemometer. Large amplitude and phase variations developed at the beginning of separation, producing hysteresis in the relationships between flow parameters. Increases in the free stream velocity decreased the detached shear layer thickness, while in the deceleration segment of the cycle the separated shear layer grew thicker. The results are in a frequency range that are significant for axial compressor blades and helicopter blades.

The structure of a separating turbulent boundary layer. Part 4. Effects of periodic free-stream unsteadiness

Unsteady separating turbulent boundary layers are of practical interest because of unsteady aerodynamic phenomena associated with blades in compressors and with helicopter rotors in translating motion during high-loading conditions. Extensive measurements of a steady free-stream, nominally two-dimensional, separating turbulent boundary layer have been reported by Simpson, Chew & Shivaprasad (1981a, b) and Shiloh, Shivaprasad & Simpson (1981). Here measurements are reported that show the effects of sinusoidal unsteadiness of the free-stream velocity on this separating turbulent boundary layer at a practical reduced frequency of 0·61. The ratio of oscillation amplitude to mean velocity is about 0·3.Upstream of flow detachment, single- and cross-wire, hot-wire anemometer measurements were obtained. A surface hot-wire anemometer was used to measure the phase-averaged skin friction. Measurements in the detached-flow zone of phase-averaged velocities and turbulence quantities were obtained with a directionally sensitive laser anemometer. The fraction of time that the flow moves downstream was measured by the LDV and by a thermal flow-direction probe.Upstream of any flow reversal or backflow, the flow behaves in a quasisteady manner, i.e. the phase-averaged flow is described by the steady free-stream flow structure. The semilogarithmic law-of-the-wall velocity profile applies at each phase of the cycle. The Perry & Schofield (1973) velocity-profile correlations fit the mean and ensemble-averaged velocity profiles near detachment.After the beginning of detachment, large amplitude and phase variations develop through the flow. Unsteady effects produce hysteresis in relationships between flow parameters. As the free-stream velocity during a cycle begins to increase, the Reynolds shearing stresses increase, the detached shear layer decreases in thickness, and the fraction of time remains high at the upstream part of the detached flow. After the free-stream velocity begins to decelerate, the detached shear layer grows in thickness and the location where flow reversal begins moves upstream. This cycle is repeated as the free-stream velocity again increases.

A Suggested Mechanism for Nonlinear Wall Roughness Effects on High Reynolds Number Flow Stability

The interactions between an uneven wall and free stream unsteadiness and their resultant nonlinear influence on flow stability are considered by means of a related model problem concerning the nonlinear stability of streaming flow past a moving wavy wall. The particular streaming flows studied are plane Poiseuille flow and attached boundary‐layer flow, and the theory is presented for the high Reynolds number regime in each case. That regime can permit inter alia much more analytical and physical understanding to be obtained than the finite Reynolds number regime; this may be at the expense of some loss of real application, but not necessarily so, as the present study shows. The fundamental differences found between the forced nonlinear stability properties of the two cases are influenced to a large extent by the surprising contrasts existing even in the unforced situations. For the high Reynolds number effects of nonlinearity alone are destabilizing for plane Poiseuille flow, in contrast with both the initial suggestion of earlier numerical work (our prediction is shown to be consistent with these results nevertheless) and the corresponding high Reynolds number effects in boundary‐layer stability. A small amplitude of unevenness at the wall can still have a significant impact on the bifurcation of disturbances to finite‐amplitude periodic solutions, however, producing a destabilizing influence on plane Poiseuille flow but a stabilizing influence on boundary‐layer flow.

Unsteady Stagnation Point Heat Transfer due to Unsteady Free Stream Temperature

Unsteady Stagnation Point Heat Transfer due to Unsteady Free Stream Temperature