Large-eddy simulation and streamline coordinate analysis of flow over an axisymmetric hull

A new perspective on the analysis of turbulent boundary layers on streamlined bodies is provided by deriving the axisymmetric Reynolds-averaged Navier–Stokes equations in an orthogonal coordinate system aligned with streamlines, streamline-normal lines and the plane of symmetry. Wall-resolved large-eddy simulation using an unstructured overset method is performed to study flow about the axisymmetric DARPA SUBOFF hull at a Reynolds number of $Re_L = 1.1 \times 10^{6}$ based on the hull length and free-stream velocity. The streamline-normal coordinate is naturally normal to the wall at the hull surface and perpendicular to the free-stream velocity far from the body, which is critical for studying bodies with concave streamwise curvature. The momentum equations naturally reduce to the differential form of Bernoulli's equation and the $s$ – $n$ Euler equation for curved streamlines outside of the boundary layer. In the curved laminar boundary layer at the front of the hull, the streamline momentum equation represents a balance of the streamwise advection, streamwise pressure gradient and viscous stress, while the streamline-normal equation is a balance between the streamline-normal pressure gradient and centripetal acceleration. In the turbulent boundary layer on the mid-hull, the curvature terms and streamwise pressure gradient are negligible and the results conform to traditional analysis of flat-plate boundary layers. In the thick stern boundary layer, the curvature and streamwise pressure gradient terms reappear to balance the turbulent and viscous stresses. This balance explains the characteristic variation of static pressure observed for thick boundary layers at the tails of axisymmetric bodies.

Accuracy of the Cell-Set Model on a Single Vane-Type Vortex Generator in Negligible Streamwise Pressure Gradient Flow with RANS and LES

Passive flow control devices are included in the design of wind turbine blades in order to obtain better performance and reduce loads without consuming any external energy. Vortex Generators are one of the most popular flow control devices, whose main objective is to delay the flow separation and increase the maximum lift coefficient. Computational Fluid Dynamics (CFD) simulations of a Vortex Generator (VG) on a flat plate in negligible streamwise pressure gradient conditions with the fully-resolved mesh model and the cell-set model using Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) were carried out, with the objective of evaluating the accuracy of the cell-set model taking the fully-resolved mesh model as benchmark. The implementation of the cell-set model entailed a considerable reduction of the number of cells, which entailed saving simulation time and resources. The coherent structures, vortex path, wall shear stress and size, strength and velocity profiles of the primary vortex have been analyzed. The results show good agreements between the fully-resolved mesh model and the cell-set mode with RANS in all the analyzed parameters. With LES, acceptable results were obtained in terms of coherent structures, vortex path and wall shear stress, but slight differences between models are visible in the size, strength and velocity profiles of the primary vortex. As this is considered the first application of the cell-set model on VGs, further research is proposed, since the implementation of the cell-set model can represent an advantage over the fully-resolved mesh model.

Streamwise vortex transportation and loss generation in an intermediate turbine duct

Annular S-shaped intermediate turbine ducts are used in modern turbofan engines with large by-pass ratios. To reduce the weight of an engine, the intermediate turbine ducts should be as short as possible, while keeping the loss at an acceptable level. Understanding the flow physics within the intermediate turbine ducts is the key to improve the intermediate turbine duct design. This paper aims to understand the transportation of the inlet streamwise vortices and loss generation in intermediate turbine ducts. First, cases with isolate incoming streamwise vortices at different spanwise locations and different axial velocities are investigated. The transportation of isolated vortex and loss generation are highly related to the interaction between vortex and boundary layer, which are mainly determined by the streamwise pressure gradient. When the axial velocity of the streamwise vortex is different to the main flow, the radial pressure gradient also has an effect. Then, the inlet condition of the intermediate turbine ducts is setup based on the flow field at the exit of a cascade, which contains the flow structures such as the tip leakage vortex, hub secondary vortex and the wake. The flow physics and the loss mechanism are analysed in detail. The formation mechanism of counter-rotating vortices pair and the influence of inlet vortex on loss generation within the intermediate turbine ducts are also presented.

The Mechanism of the Flow in the Hub Corner and the Control by Tailing Edge Gaps

High-pressure ratio is one of the important characteristics of the sustainable development of the modern aero-engine compressor components. When the fluid flows through the compressor cascade row, it will be influenced by both the streamwise pressure gradient and the transverse pressure gradient, which will cause hub-corner separation or stall. In this paper, different diffusion factors are chosen for the cascades. Each diffusion factor has different turning angles. The formation mechanism of hub-corner separation is studied under the condition of zero angle of attack. Numerical simulation is used to study the influence of pressure gradient on the flow field in the corner. The scale of the concentrated shed vortex forms in the suction surface increases with the increasing of the transverse pressure gradient during the hub-corner separation. When the streamwise pressure gradient increases, the suction surface vortex forms the corner stall. By reasonable design, the two vortexes can cancel out each other. At this time, the loss of cascades is the minimum. Based on the flow mechanism of the corner separation/stall, the trailing gaps are set on three typical turn angle cascades. The results show that the trailing gaps can control the radial development of the suction surface vortex during the stall and improve flow field. The jet cannot blow the suction side boundary layer away during the corner separation, because the gap does not change the static pressure distribution at the root of the cascade. In a word, the trailing edge gaps can not only inhibit the separation in the hub corner but also have the minimum leakage loss at design point. It can be used as an effective and practical compressor design method.

Algebraic disturbance growth by interaction of Orr and lift-up mechanisms

Algebraic disturbance growth in spatially developing boundary-layer flows is investigated using an optimization approach. The methodology builds on the framework of the parabolized stability equations and avoids some of the limitations associated with adjoint-based schemes. In the Blasius boundary layer, non-parallel effects are shown to significantly enhance the energy gain due to algebraic growth mechanisms. In contrast to parallel flow, the most energetic perturbations have finite frequency and are generated by the simultaneous activity of the Orr and lift-up mechanisms. The highest amplification occurs in a limited region of the parameter space that is characterized by a linear relation between the wavenumber and frequency of the disturbances. The frequency of the most highly amplified perturbations decreases with Reynolds number. Adverse streamwise pressure gradient further enhances the amplification of disturbances while preserving the linear trend between the wavenumber and frequency of the most energetic perturbations.

Aerodynamic Analysis of Film Cooling Jet Under Different Main Stream Pressure Gradient

Streamwise pressure gradient is an important characteristic of the turbine flow and compound angle film cooling is a sufficient way to improve cooling performance. Both experimental and numerical studies are carried out to investigate the effect of streamwise pressure gradient and film cooling hole compound angle on aerodynamic loss of film cooling. Stronger mainstream favorable pressure gradient leads to a larger discharge coefficient. The effect of momentum supplement of the coolant jet with large blowing ratios is significant when pressure loss coefficient is investigated. Kinetic loss coefficient considering the kinetic energy of the coolant jet is used to investigate the overall aerodynamic loss of film cooling. The kinetic loss coefficient increases with blowing ratio. Favorable pressure gradient decreases the loss coefficient. The boundary layer is quite thick for adverse and moderate favorable pressure gradient case that the coolant jet remains within the boundary layer which increases the mixing loss. The kinetic loss coefficient of compound angle film cooling is about 40% higher than the axial hole. This is due to the dissipation of the momentum component in the spanwise direction and the stronger shearing between the single large vortex formed by the compound angle injection with the main flow.

Optimal wavepackets in streamwise corner flow

The global non-modal stability of the flow in a right-angled streamwise corner is investigated. Spatially confined linear optimal initial conditions and responses are obtained by use of direct-adjoint looping. Two base states are considered, the classical self-similar solution for a zero streamwise pressure gradient, and a modified solution that mimics leading-edge effects commonly observed in experimental studies. The latter solution is obtained in a reverse engineering fashion from published measurement data. Prior to the global analysis, a classical local linear stability and sensitivity analysis of both base states is conducted. It is found that the base-flow modification drastically reduces the critical Reynolds number through an inviscid mechanism, the so-called corner mode. A survey of the geometry of the two base states confirms that the modification greatly aggravates the inflectional nature of the flow. Global optimals are calculated for subcritical and supercritical Reynolds numbers, and for two finite optimization times. The optimal initial conditions are found to be self-confined in the spanwise directions, and symmetric with respect to the corner bisector. They evolve into streaks or streamwise modulated wavepackets, depending on the base state. Substantial transient growth caused by the Orr mechanism and the lift-up effect is observed.