Shock-Boundary Layer Interactions in Supersonic Turbine Cascades

The physics of shock-boundary layer interactions in a supersonic turbine cascade is investigated through a wall-resolved large eddy simulation. Special attention is given to the characterization of the low-frequency dynamics of the separation bubbles using flow visualization, spectral analysis, space-time cross correlations, and flow modal decomposition. The mean flowfield shows different shock structures formed on both sides of the airfoil. On the suction side, an oblique shock impinges on the turbulent boundary layer, whereas a Mach reflection interacts with the pressure side boundary layer. Instantaneous flow visualizations illustrate elongated streamwise structures on the incoming boundary layers and their interactions with the shocks and separation bubbles. The passage of high-speed (low-speed) streaks through the recirculation bubbles leads to the downstream (upstream) motion of the separation point on both suction and pressure sides, resulting in spanwise modulation of the bubbles. Space-time cross-correlations reveal that the near-wall streaks drive the suction side separation bubble motion, which in turn promotes the oscillations of the reattachment shock and shear layer flapping. Space-time correlations also indicate the existence of a $\pi$ phase jump in the pressure fluctuations along the separation bubble on the suction side. After this phase jump, a downstream propagating pressure disturbance is observed, while prior to this point, the pressure disturbances dominantly propagate in the upstream direction. Finally, the organized motions in the shock-boundary layer interactions and their corresponding characteristic frequencies are identified using proper orthogonal decomposition.Comment: 40 pages, 19 figures. Submitted to Physical Review Fluid

Acoustic Streaming in Compressible Turbulent Boundary Layers

The growing need to improve the power density of compact thermal systems necessitates developing new techniques to modulate the convective heat transfer efficiently. In the present research, acoustic streaming is evaluated as a potential technology to achieve this objective. Numerical simulations using the linearized and fully non-linear Navier-Stokes equations are employed to characterize the physics underlying this process. The linearized Navier-Stokes equations accurately replicate the low-frequency flow unsteadiness, which is used to find the optimal control parameters. Local and global stability analysis tools were developed to identify the modes with a global and positive heat transfer effect. High-fidelity numerical simulations are performed to evaluate the effect of the excitation at selected frequencies, directed by the linear stability analysis, on the heat and momentum transport in the flow. Results indicate that, under favorable conditions, superimposing an acoustic wave, traveling along with the flow, can resonate within the domain and lead to a significant heat transfer enhancement with minimal skin friction losses. Two main flow configurations are considered; at the fixed Reynolds number Reb “ 3000, in the supersonic case, 10.1% heat transfer enhancement is achieved by an 8.4% skin friction increase; however, in the subsonic case, 10% enhancement in heat transfer only caused a 5.3% increase to the skin friction. The deviation between these two quantities suggests a violation of the Reynolds analogy. This study is extended to include a larger Reynolds number, namely Reb “ 6000 at Mb “ 0.75 and a similar response is observed. The effect of excitation amplitude and frequency on the resonance, limit-cycle oscillations, heat transfer, and skin friction are also investigated here. Applying acoustic waves normal to the flow in the spanwise direction disrupts the near-wall turbulent structures that are primarily responsible for heat and momentum transport near the solid boundary. Direct numerical simulations were employed to investigate this technique in a supersonic channel flow at Mb “ 1.5 and Reb “ 3000. The external excitation is applied through a periodic body force in the spanwise direction, mimicking loudspeakers placed on both walls that are operating with a 180˝ phase shift. By keeping the product of forcing amplitude (Af ) and pulsation period (T ) constant, spanwise velocity perturbations are generated with a similar amplitude at different frequencies. Under this condition, spanwise pulsations at T “ 20 and T “ 10 show up to 8% reduction in Nusselt number as well as the skin friction coefficient. Excitation at higher or lower frequencies fails to achieve such high level of modulations in heat and momentum transport processes near the walls. In configurations involving a spatially-developing boundary layer, a computational setup that includes laminar, transitional, and turbulent regions inside the domain is considered and the impact of acoustic excitation on this flow configuration has been characterized. Large-eddy simulations with dynamic Smagorinsky sub-grid scale modeling has been implemented, due to the excessive computational cost of DNS calculations at high-Reynolds numbers. The optimal excitation frequency that resembles the mode chosen for the fully-developed case has been identified via global stability analysis. Fully non-linear simulations of the spatially-developing boundary layer subjected to the excitation at this frequency reveal an interaction between the pulsations and the perturbations originated from the tripping which creates a re-laminarization zone traveling downstream. Such technique can locally enhance or reduce the heat transfer along the walls

Analytical study of unsteady sedimentation analysis of spherical particle in Newtonian fluid media

Unsteady settling behavior of solid spherical particles falling in water as a Newtonian fluid is investigated in this research. Least square method (LSM), Galerkin method, LSM-Padé, and numerical model are applied to analyze the characteristics of the particles motion. The influence of physical parameters on terminal velocity is discussed and it is showed that LSM and Galerkin method are efficient techniques for solving the governing equation. Among these methods, LSM-Padé demonstrates the best agreement with numerical results. The novelty of this work is to introduce new analytical methods for solving the non-linear equation of sedimentation applicable in many industrial and chemical applications