A linear system for pipe flow stability analysis allowing for boundary condition modifications

An accurate system to study the stability of pipe flow that ensures regularity is presented. The system produces a spectrum that is as accurate as Meseguer & Trefethen (2000), while providing flexibility to amend the boundary conditions without a need to modify the formulation. The accuracy is achieved by formulating the state variables to behave as analytic functions. We show that the resulting system retains the regular singularity at the pipe centre with a multiplicity of poles such that the wall boundary conditions are complemented with precisely the needed number of regularity conditions for obtaining unique solutions. In the case of axisymmetric and axially constant perturbations the computed eigenvalues match, to double precision accuracy, the values predicted by the analytical characteristic relations. The derived system is used to obtain the optimal inviscid disturbance pattern, which is found to hold similar structure as in plane shear flows

Temporal and spatial transients in turbulent boundary layer flow over an oscillating wall

Direct numerical simulations have been performed to study the effect of an oscillating segment of the wall on a turbulent boundary layer flow. Two different oscillation amplitudes with equal oscillation period have been used, which allows a direct comparison between a relatively weak and strong forcing of the flow. The weaker forcing results in 18% drag reduction while the stronger forcing, with twice the amplitude, yields 29% drag reduction. The downstream development of the drag reduction is compared with earlier simulations and experiments. In addition, a simulation with identical oscillation parameters as in previous numerical and experimental investigations allows for an estimation of the effect of the Reynolds number on the drag reduction. Reductions in the Reynolds stresses and the important role that the edge of the Stokes layer has is explained. An estimation of the idealized power consumption shows that a positive energy budget is only possible for the weaker wall velocity case. Spatial and temporal transients are investigated and a transformation between spatial and temporal coordinates via a convection velocity is shown to facilitate a comparison between the two transients in a consistent manner. The streamwise shear exhibits a similar monotonic behavior in the spatial and temporal transients, while the non-monotinic temporal transient of the longitudinal Reynolds stress has no counterpart in the spatial development. Furthermore, the evolution in time of the spanwise Reynolds stress is very similar to previously reported channel flow data. The instantaneous spanwise velocity profile (only averaged in the homogeneous spanwise direction) will for the first time be presented from a boundary layer over an oscillating wall, and comparisons with the analytical solution to the laminar Navier–Stokes equations show very good agreement.Accepted versio

Simulating plasma actuators in a channel flow configuration by utilizing the modified Suzen–Huang model

Objective: The present investigation is an attempt to simulate a channel flow driven by two plasma actuators placed on top of each other. Methodology: The model utilizes a modified form of the Suzen-Huang plasma actuator which accounts for a 'dielectric shielding' boundary condition for the potential governing the electric field. In addition, the Fokker-Planck (drift-diffusion) characteristics were implemented on the potential governing the surface charge density. Results: The model is able to correctly predict the maximum velocities for channel flow at larger channel heights. However, at lower channel heights, the model underestimates the maximum velocities. Analysis and Discussion: An analysis of the body force profile at the centreline region in the vicinity of the plasma actuators indicated that negative vertical body forces may have contributed to the discrepancies. Following this observation, a hypothetical model which does not account for vertical body force contributions on the fluid domain was simulated. While the results from this hypothetical model show marginally improvements to the maximum induced velocities at larger channel heights in relation to experimental data, the model still underpredicts the velocity magnitude at lower channel heights. This could point to the presence of interactions between the induced body force of the top and bottom actuators, specifically at lower channel heights, that have not been captured in the present model

Simulations of the linear plasma synthetic jet actuator utilizing a modified Suzen-Huang model

The linear plasma synthetic jet actuator (L-PSJA) is a unique form of flow control device which harnesses the interaction of induced flows from two linear plasma actuators to form an upward jet. Since each injection can be manipulated in intensity, the synthetic jet has thrust vectoring properties. Our study simulates the L-PSJA by utilizing a modified Suzen-Huang (S-H) model that accounts for drift and diffusive properties in the surface charge. The results of the present model show that the centreline velocity is closer to the experimental values found in literature as compared to the default form of S-H modelling. Thrust vectoring simulations were also performed to demonstrate the feasibility of flow directional variation in the L-PSJA

Kolmogorov spectrum consistent optimization for multi-scale flow decomposition

Multi-scale analysis is widely adopted in turbulence research for studying flow structures corresponding to specific length scales in the Kolmogorov spectrum. In the present work, a new methodology based on novel optimization techniques for scale decomposition is introduced, which leads to a bandpass filter with prescribed properties. With this filter, we can efficiently perform scale decomposition using Fourier transform directly while adequately suppressing Gibbs ringing artifacts. Both 2D and 3D scale decomposition results are presented, together with qualitative and quantitative analysis. The comparison with existing multi-scale analysis technique is conducted to verify the effectiveness of our method. Validation of this decomposition technique is demonstrated both qualitatively and quantitatively. The advantage of the proposed methodology enables a precise specification of continuous length scales while preserving the original structures. These unique features of the proposed methodology may provide future insights into the evolution of turbulent flow structures.Published versio

Varicose instabilities in turbulent boundary layers

An investigation of a model of turbulence generation in the wall region of a turbulent boundary layer is made through direct numerical simulations. The model is based on the varicose instability of a streak. First, a laminar boundary layer disturbed by a continuous blowing through a slot is simulated in order to reproduce and further investigate the results reported from the experiments of Acarlar and Smith [J. Fluid Mech. 175, 43 (1987)]. An isolated streak with an inflectional profile is generated that becomes unstable, resulting in a train of horseshoe vortices. The frequency of the vortex generation is equal to the experimental results. Comparison of the instability characteristics to those predicted through an Orr–Sommerfeld analysis are in good agreement. Second, a direct numerical simulation of a turbulent boundary layer is performed to point out the similarities between the horseshoe vortices in a turbulent and a laminar boundary layer. The characteristics of streaks and the vortical structures surrounding them in a turbulent boundary layer compare well with the model streak. The results of the present study show that one mechanism for the generation of horseshoe vortices in turbulent boundary layers is related to a normal inflectional instability of the streaks.Published versio

Direct numerical simulation of self-similar turbulent boundary layers in adverse pressure gradients

Direct numerical simulations of the Navier–Stokes equations have been carried out with § the objective of studying turbulent boundary layers in adverse pressure gradients. The boundary layer flows concerned are of the equilibrium type which makes the analysis simpler and the results ¨can be compared with earlier experiments and simulations. This type of turbulent boundary layers © also permits an analysis of the equation of motion to predict separation. The linear analysis based �on the assumption of asymptotically high Reynolds number gives results that are not applicable § to finite Reynolds number flows. A different non-linear approach is presented to obtain a useful relation between the freestream variation and other mean flow parameters. Comparison of turbulent �statistics from the zero pressure gradient case and two adverse pressure gradient cases shows the �development of an outer peak in the turbulent energy in agreement with experiment. The turbulent �flows have also been investigated using a differential Reynolds stress model. Profiles for velocity and § turbulence quantities obtained from the direct numerical simulations were used as initial data. The initial transients in the model predictions vanished rapidly. The model predictions are compared with § the direct simulations and low Reynolds number effects are investigated