The study and control of wall bounded flows : El estudio y control de flujos de pared

摘要

Turbulent wall-bounded flows are important, because many of the flows found in industry and nature belong to this type of flows. One of the examples is the flow in the low pressure turbine part of an engine. Efficiency can be increased by increasing the curvature of the blades. However, this leads to higher risks of the flow separating, which is undesirable as it can cause vibration and efficiency losses. Another, related, area of interest is the reduction of skin friction on airplane wings. The design of wings or turbine blades is complicated, because the amount of understanding of turbulent wall-bounded and/or separated transitional flows is insufficient to apply daily engineering design methods. The problem is that the physics are not completely understood and the absence of valid models, that can aid in the design process. Wall bounded flows are treated in this thesis from three different points of view. The main interest of the first part of this thesis is the study of Poiseuille channel and Couette flows. These flows, as studied here, are not typically found in real world applications. However their study is necessary to be able to develop models for real world wall-bounded flows. Particularly the near-wall region of wall-bounded flows is known to be difficult to model. The relation between different types of wall-bounded flows is studied. A new code is developed to be able to study boundary layer flows, which is described in the second part. This development is necessary since the code used for the channel simulations cannot simulate boundary layers. The goal was to develop a fourth-order, high resolution numerical scheme to simulate incompressible turbulent flows similar to the ones found on turbine blades. The focus of the third part of this thesis is on the study of separated flow. First the control of separated flow is discussed. Secondly, another important problem is studied, namely the transition and turbulent development in flows that are laminar, separate and reattach after transitioning to turbulence. The information obtained in the second study can be used by modelers to improve or to check the models used in the industrial design of turbines. This part of the thesis has two objectives. The first goal is to give physical mechanisms that control and suppress separation. The second goal is to provide data on the development of the turbulent flow at and after reattachment of the separation bubble. The control of separation is studied by forcing a separation bubble on a flat plate. The forcing is applied at the wall upstream but close to the separation bubble. These simulations are done in two-dimensions using a second-order finite difference code thickness at the inlet of the numerical domain, is relatively low. The newly developed code is used to do three-dimensional simulations on a transitional laminar separated bubble on a flat plate. In addition, and related to control, simulations are done with incoming wakes, mimicking real turbine configurations. Flows with various different adverse pressure gradients are simulated. The highest adverse pressure gradient is chosen similar to the one in a laboratory experiment. No information is available on the spectral content of the velocity perturbations, and therefore only the mean and rms profile are matched. The spectral distribution is chosen according to the most unstable one for a Blasius boundary layer. The frequency with which the wakes pass by the inlet plane is f = 84Hz, which is higher than in the experiment to obtain statistics in a reasonable computational time. At the inlet the Reynolds number is Re_ = 114 in all the three-dimensional cases. The two-dimensional simulations show that three different possibilities exist to control separation. One is related to the instability of the shear layer formed between the separation and the free-stream. The shear layer instability can be triggered with fairly low-amplitude forcing when St ≈ 0.012. The second possibility is to use high-amplitude forcing, which results in large vortices being generated. These are very effective in mixing the low-speed fluid from the separation bubble with the high-speed fluid from the free-stream. The effective frequencies are related with the momentum thickness of the shear layer and the distance between the forcing slot and the separation bubble. The third possibility is to use periodic suction without blowing. The latter two options work with high-amplitudes forcings of around ten percent of the free-stream velocity only. Periodic suction is only effective when applied close to the unforced separation point. The three-dimensional results have provided detailed information on the statistics of the flow. The statistics compare fairly well with the laboratory data, although transition takes place much further downstream compared with the laboratory data. If properly scaled, the data also compares quite well to other data found in the literature. The momentum, Reynolds-stress and energy balances are given. They show the large importance of the turbulent transport term in the Reynolds stress and energy balances. The incoming wakes have a remarkable positive effect as they decrease the bubble length with a factor of at least six. They also cause a decrease in H = δ∗/θ, with a factor of 1.5 in the turbulent part of the domain, compared with the unforced simulation. This newly developed code is second-order, instead of fourth-order accurate. This reduction in order is necessary because the solution of the Pressure-Poisson equation with fourth-order accuracy resulted in a serious penalty in computational speed. However, the convective and viscous terms are all fourth-order accurate using compact finite difference schemes. Overall, this meant that the theoretical resolution of the code is as if fourth-order compact schemes would have been used. The code is second-order accurate in time. The developed code is now used extensively to do other simulations of boundary layers under different types of pressure gradients and with turbulent inflow profiles. on a staggered grid. The Reynolds number Re_ = 30, based on the momentumIt is expected that the new three-dimensional code will be used by the industrial partners to gain insight in the physics that determine the effectiveness of incoming wakes in reducing the risk of open separation. Small modifications would make it possible to study the influence of roughness on separation and reattachment. The three-dimensional simulations, apart from demonstrating the capabilities of the code, have given useful information that can be used to fine-tune the models used in design processes. The two-dimensional simulations provided several control strategies that, after some engineering development, are to be implemented.