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Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation
Abstract
A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, ut, with the intermittency factory. Turbulent quantities are predicted by using Menter's two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.
... The first is the use of the low-Reynolds-number (low-Re) turbulence model, where the wall damping functions of the underlying turbulence model trigger the transition onset [12]. However, experience has shown that this approach is not capable of reliably capturing the influence of many factors that affect transition [13][14][15], such as freestream turbulence, separation due to pressure gradients, Mach number effects, turbulent length scale influence, wall roughness, streamline curvatures, etc. Thus, this low-Re modeling approach is not widely used in industrial CFD simulations. ...
... As a result, these models are typically only available in specialized in-house CFD codes for specific applications and geometries. Correlation-based models are frequently linked to an intermittency transport equation, such as that developed by Suzen et al. [15] (or more complex formulations as proposed by Steelant and Dick [19]). Nevertheless, all these models require nonlocal information to trigger the production term in the intermittency equation. ...
... This preserves second-order spatial accuracy and is known to be more accurate than the Green-Gauss cell-based method on skewed and distorted unstructured meshes. Therefore, this method is more appropriate for anisotropic meshes produced by Ansys OptiGrid, which better resolves the secondary flow effects at wing-fuselage junction as shown in Fig. 9. Turbulent closure is achieved using the SST-γ-Re θ transition model [12][13][14][15][16]. ...
This paper presents Ansys Fluent laminar–turbulent transition results using the shear stress transport (SST)-γ-Reθ model applied to the workshop cases of the First American Institute of Aeronautics and Astronautics Computational Fluid Dynamics (CFD) Transition Modeling Prediction Workshop. The key objectives of this workshop were to assess the current state-of-the-art laminar–turbulent transition models in an industrial Computational Fluid Dynamics environment and to determine and document the best practices to simulate laminar–turbulent transition flows. Sensitivity of the shear stress transport (SST)-γ-Reθ model to mesh refinement was established on a zero-pressure-gradient flat plate. Two other cases [a two-dimensional natural laminar flow (NLF) (1)-0416F airfoil, and a scaled Common Research Model (CRM)-NLF aircraft model] were selected as validation cases using a hierarchy of structured and unstructured meshes. Due to the complexity of the geometry and the airflow around the Common Research Model (CRM)- Natural laminar Flow (NLF) aircraft model, mesh adaptation cycles were also conducted to capture the shock, the wake, and the wing-tip vortices produced by the CRM-NLF. The accuracy of the SST-γ-Reθ model is evaluated using transition location measurements obtained with temperature-sensitive paint, pressure coefficient distributions at multiple wingspan stations, and aerodynamic coefficients at numerous angles of attack. The outcome of these comparisons will provide guidelines to conduct laminar–turbulent transition simulations with the SST-γ-Reθ model on simple and complex aerospace designs.
... This parameter was introduced by Spalart [56] as a pressure gradient parameter in studies of flow relaminarization under favorable pressure gradients (K > 0) but it is also used to quantify the flow deceleration associated with an adverse pressure gradient (K < 0) [37,49,57,58] in boundary layer flows. In the ideal scenario of a boundary layer that is unbounded on the wall-normal direction, the free-stream value of the streamwise velocity would be used and Bernoulli's equation would relate it directly to the streamwise pressure gradient. ...
The separated flow over a wall-mounted bump geometry under harmonic oscillations of the inflow stream is investigated with direct numerical simulations. The bump geometry gives rise to streamwise pressure gradients similar to those encountered on the suction side of low-pressure turbine (LPT) blades. Under steady inflow conditions, the separated-flow laminar-to-turbulent transition is initiated by self-sustained vortex shedding due to Kelvin-Helmholtz (KH) instability. In LPTs the dynamics are further complicated by the passage of the wakes shed by the previous stage of blades. The wake-passing effect is modeled here by introducing a harmonic variation of the inflow conditions. Three inflow oscillation frequencies and three amplitudes are considered. The frequencies are comparable to the wake-passing frequencies in practical LPTs. The amplitudes range from 1% to 10% of the inflow total pressure. The dynamics of the separated flow are studied by isolating the flow components that are respectively coherent with and uncorrelated to the inflow oscillation. Three scenarios are identified. The first one is analogous to the steady inflow case. In the second one, the KH vortex shedding is replaced during a part of the inflow period by the formation and release of a large vortex cluster. The third scenario consists solely of the periodic formation and release of the vortex cluster; it leads to a consistent reduction of the separated flow length over the entire period compared to the steady inflow case and would be the most desirable flow condition in a practical application.
Published by the American Physical Society 2024
... The contour of the upper inviscid wall is generated following Suzen et al. (2003). The spanwise extent is defined by 50 % of the computed separation bubble size with RANS-γ. ...
... This parameter was introduced by Spalart [53] as a pressure gradient parameter in studies of flow relaminarization under favorable pressure gradients (K > 0) but it is also used to quantify the flow deceleration associated with an adverse pressure gradient (K < 0) [36,48,54,55] in boundary layer flows. In the ideal scenario of a boundary layer that is unbounded on the wall-normal direction, the free-stream value of the streamwise velocity would be used and Bernoulli's equation would relate it directly to the streamwise pressure gradient. ...
The separated flow over a wall-mounted bump geometry under harmonic oscillations of the inflow stream is investigated by direct numerical simulations. The bump geometry gives rise to streamwise pressure gradients similar to those encountered on the suction side of low-pressure turbine (LPT) blades. Under steady inflow conditions, the separated-flow laminar-to-turbulent transition is initiated by self-sustained vortex shedding due to Kelvin-Helmholtz (KH) instability. In LPTs, the dynamics are further complicated by the passage of the wakes shed by the previous stage of blades. The wake-passing effect is modeled here by introducing a harmonic variation of the inflow conditions. Three inflow oscillation frequencies and three amplitudes are considered. The frequencies are comparable to the wake-passing frequencies in practical LPTs. The amplitudes range from 1% to 10% of the inflow total pressure. The dynamics of the separated flow are studied by isolating the flow components that are respectively coherent with and uncorrelated to the inflow oscillation. Three scenarios are identified. The first one is analogous to the steady inflow case. In the second one, the KH vortex shedding is replaced during a part of the inflow period by the formation and release of a large vortex cluster. The third scenario consists solely of the periodic formation and release of the vortex cluster; it leads to a consistent reduction of the separated flow length over all the period compared to the steady inflow case and would be the most desirable flow condition in a practical application.
... Value γ determines intensity of turbulent kinetic energy production and dissipation in RANS models of k-ω class as follows (γ-sst model) [40][41][42]: ...
... The current review will focus on the first and the last of these three approaches. Although there has been considerable work applied to the development of empirical transition onset criteria [61,1,113,183,9,10,137], the focus of recent work in the literature has been on the integration of these criteria in transport-equation-based transition models to simplify their implementation in modern CFD codes [92,29,133,180]. ...
Aircraft configurations that exploit significant regions of natural laminar flow could play a key role in reducing the environmental impact of aviation. The design of natural-laminar-flow configurations can be accelerated using computational tools capable of accurately and efficiently predicting boundary-layer transition. Toward the development of a suitable computational design tool, methods for the efficient prediction of boundary-layer transition in a Reynolds-averaged Navier-Stokes-based flow solver and integration in a discrete-adjoint gradient-based optimization algorithm are presented. A local correlation-based transition model is modified and coupled to the Spalart-Allmaras turbulence model and integrated in a Newton-Krylov-Schur flow solver. Modifications to the solution strategy are introduced, including a source-term time step restriction, in order to prevent unstable solution updates for the fully coupled, fully implicit solver. A smooth-variant of the transition model is developed with approximations to discontinuous and stiff source-term functions. Both transition models are validated using two- and three-dimensional subsonic transition test cases, with the new, smooth model producing significantly improved iterative convergence. Compressibility corrections are developed and applied to extend the transition model empirical correlations to transonic flow regimes typical of commercial transport aircraft, with the resulting model investigated using two- and three-dimensional transonic transition test cases. The results demonstrate that the compressibility corrections produce substantially improved agreement with the experimental transition locations, particularly for higher Reynolds number applications. Finally, the smooth transition model is integrated in a discrete-adjoint gradient-based optimization algorithm and applied to two- and three-dimensional drag-minimization studies across a range of design conditions. The results demonstrate that the capability of the current framework to explore the natural-laminar-flow configuration design space is sensitive to the streamwise grid resolution in the transition regions, with grid requirements increasing as the transition length decreases with increasing Reynolds number. The light aircraft design space is found to be multi-modal, with the optimization framework producing two distinct local minima. Transonic drag minimizations demonstrate that the optimization framework can successfully trade a decrease in viscous drag with an increase in wave drag, and an infinite swept wing optimization demonstrates that the framework can delay both Tollmien-Schlichting and stationary crossflow instabilities.
In this paper, we present an overview of numerical simulation methods for the flow around typical underwater vehicles at high Reynolds numbers, which highlights the dominant flow structures in different regions of interest. This overview covers the forebody, midbody, stern, wake region, and appendages and summarizes flow phenomena, including laminar-to-turbulent transition, turbulent boundary layers, flow under the influence of curvatures, wake interactions, and all associated complex vortex structures. Furthermore, the current issues and challenges of capturing these flow structures are addressed. This overview provides a deep insight into the use of numerical simulation methods, including the Reynolds-averaged Navier–Stokes (RANS) method, large eddy simulation (LES) method, and the hybrid RANS/LES method, and evaluates their applicability in capturing detailed flow features.
This article describes the spatial development of a laminar separation bubble (LSB), its transition, and eventual breakdown under the influence of adverse pressure gradients (APGs) similar to those experienced by low-pressure turbine blades. The investigation combines a comprehensive experimental approach with a well-resolved large eddy simulation (LES). The streamwise pressure gradients were varied by manipulating the upper wall within the test section. The Reynolds number (Re), based on the plate length and inlet velocity, was 0.2 × 106 with a freestream turbulence intensity of 1.02%. The particle image velocimetry (PIV) and hotwire data were used to illustrate the vortex dynamics, growth of perturbations, and intermittency. The onset and end of transition progressively shift upstream, resulting in a reduction of the laminar shear layer length and bubble length with increasing APG. Interestingly, the flow features exhibit self-similarity in velocity profiles and the growth rate of velocity fluctuations when normalized against the bubble length. The formation of two-dimensional Kelvin–Helmholtz (K–H) rolls is apparent in the beginning, resulting in the selective amplification of frequency and exponential growth of fluctuations. Linear stability theory explains the most amplified frequency and phase speed of convective vortices, apart from the growth of disturbances. Analysis of LES data reveals intricate inviscid–viscous interactions that trigger shear layer breakdown. In brief, evolving perturbations within the braid region of vortices in the latter half interact with the advecting K–H rolls, culminating in the breakdown and the onset of turbulent flow downstream.
Detailed velocity measurements were made along a flat plate subject to the same dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil. Reynolds numbers based on wetted plate length and nominal exit velocity were varied from 50,000 to 300,000, covering cruise to takeoff conditions. Low and high inlet free-stream turbulence intensities (0.2 and 7 percent) were set using passive grids. The location of boundary-layer separation does not depend strongly on the free-stream turbulence level or Reynolds number, as long as the boundary layer remains non turbulent prior to separation. Strong acceleration prevents transition on the upstream part of the plate in all cases. Both free-stream turbulence and Reynolds number have strong effects on transition in the adverse pressure gradient region. Under low free-stream turbulence conditions, transition is induced by instability waves in the shear layer of the separation bubble. Reattachment generally occurs at the transition start. At Re = 50,000 the separation bubble does not close before the trailing edge of the modeled airfoil. At higher Re, transition moves upstream, and the boundary layer reattaches. With high free-stream turbulence levels, transition appears to occur in a by pass mode, similar to that in attached boundary layers. Transition moves upstream, resulting in shorter separation regions. At Re above 200,000, transition begins before separation. Mean velocity, turbulence, and intermittency profiles are presented.
This paper summarises recent progress which has been made in evaluating by-pass transition models as part of a European Research Community On Flow Turbulence And Combustion (ERCOFTAC) Special Interest Group Project. In particular new results, from a variety of closure models, are presented for a wider range of Test Cases based on both experimental studies and Direct Numerical Simulations. It would appear that a Reynolds stress scheme offers the best predictive capability for 2D by-pass transition under high free-stream turbulence intensities and variable pressure gradient or Reynolds number conditions. Such a scheme also has the potential to handle both anisotropic and lower intensity free-stream turbulence effects. However present low-Re treatments need to be refined against DNS for transitional flow (so that a clearer distinction can be made between low-Re near-wall and low-Re transition region modelling) before additional curvature, heat transfer and leading edge separation effects can be considered.
Low pressure turbine blades suffer from separation losses while operating at low Reynolds numbers typical of loiter missions for UAVs. Experiments with a set of seven times scale engine blades have been performed in a modified Aerolab windtunnel at Wright-Patterson Air Force Base. The baseline suction surface of the blades were modified and retested for a range of Reynolds numbers and two turbulence intensities. The three modifications included recessed dimples, recessed V-grooves, and a trip wire. Each modification was tested for reductions of the separation losses and improvements in the region of attached flow over the blade.
Detailed velocity measurements were made along a flat plate subject to the same dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil. Reynolds numbers based on wetted plate length and nominal exit velocity were varied from 50, 000 to 300, 000, covering cruise to takeoff conditions. Low and high inlet free-stream turbulence intensities (0.2% and 7%) were set using passive grids. The location of boundary-layer separation does not depend strongly on the free-stream turbulence level or Reynolds number, as long as the boundary layer remains non-turbulent prior to separation. Strong acceleration prevents transition on the upstream part of the plate in all cases. Both free-stream turbulence and Reynolds number have strong effects on transition in the adverse pressure gradient region. Under low free-stream turbulence conditions transition is induced by instability waves in the shear layer of the separation bubble. Reattachment generally occurs at the transition start. At Re = 50, 000 the separation bubble does not close before the trailing edge of the modeled airfoil. At higher Re, transition moves upstream, and the boundary layer reattaches. With high free-stream turbulence levels, transition appears to occur in a bypass mode, similar to that in attached boundary layers. Transition moves upstream, resulting in shorter separation regions. At Re above 200,000, transition begins before separation. Mean velocity, turbulence and intermittency profiles are presented.
Boundary layer measurements are presented through transition for six different free-stream turbulence levels and a complete range of adverse pressure gradients for attached laminar flow.
Measured intermittency distributions provide an excellent similarity basis for characterizing the transition process under all conditions tested when the Narasimha procedure for determining transition inception is used. This inception location procedure brings consistency to the data.
Velocity profiles and integral parameters are influenced by turbulence level and pressure gradient and do not provide a consistent basis. Under strong adverse pressure gradients transition occurs rapidly and the velocity profile has not fully responded before the completion of transition. The starting turbulent layer does not attain an equilibrium velocity profile.
A change in pressure gradient from zero to even a modest adverse level is accompanied by a severe reduction in transition length. Under diffusing conditions the physics of the transition process changes and the spot formation rate increases rapidly; instead of the “breakdown in sets” regime experienced in the absence of a pressure gradient, transition under strong adverse pressure gradients is more related to the amplification and subsequent instability of the Tollmien-Schlichting waves. Measurements reveal an exponential decrease in transition length with increasing adverse pressure gradient; a less severe exponential decrease is experienced with increasing turbulence level. Correlations of transition length are provided which facilitate its prediction in the form of suitable length parameters including spot formation rate.
Natural transition of boundary layers is investigated for a flat plate in a low-speed wind tunnel with free-stream turbulence intensities ranging from 0.3 to 5 per cent, and with pressure-gradient histories typical of turbomachinery blades without separation.
Empirical relationships are proposed for the prediction of the start and end of transition, as well as the development of the boundary layer during transition. These relations are based on the recent measurements made with a hot-wire anemometer, and augmented, mainly for the start of transition, by results of previously reported research.
Finally, these experimental relationships are used in conjunction with well established methods to predict the entire unseparated boundary layer. To utilize the prediction, all that is required is a knowledge of the free-stream turbulence level and the free-stream velocity distribution, which itself can be derived from potential flow theory.
A transport equation for the intermittency factor is employed to predict the transitional flows in low-pressure turbine applications. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity μt with the intermittency factor γ. Turbulence quantities are predicted by using Menter's shear stress transport two-equation turbulence model, and the intermittency factor is obtained from the solution of a recently developed transport equation model. The transport equation model not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but it also provides a realistic cross-stream variation of the intermittency profile. The current model is applied to predictions of a modern low-pressure turbine experiment, and detailed comparisons of the computational results with the experimental data are presented. The model has been shown to be capable of predicting the low-pressure turbine flow transition under a variety of Reynolds number and freestream turbulence conditions.
The transition region is considered to be characterized by the intermittent appearance of turbulent spots, which grow as they move downstream until they finally merge into one another to form the turbulent boundary layer. The intermittency factor for arbitrary axisymmetric body with zero angle of attack has been derived in an expression which can be reduced to the form of universal intermittency distribution of Dhawan and Narasimha in the case of straight tube or flat plate. A key factor to control flow conditions in the transition zone appears to be the spot formation rate, which has been deduced from the available data of the extent of transition zone. It was found that the spot formation rate depends not only on the transition Reynolds number but also on the Mach number. A comparison of the deduced spot formation rate with the neutral stability curves indicated that the neutral stability curves can be used as a guide to relate the spot formation rate to the transitional Reynolds number. Calculations of the transitional heat-transfer rate on a sphere in supersonic flow agree well with the experimental results.
The present study considers the use of low-Reynolds number, single-point closures for transition prediction at high levels of free-stream turbulence. The work is focused on two differential Reynolds Stress Transport models, which are compared with the k - epsilon model of Launder and Sharma. Calculations are carried our for attached boundary layer flow on a flat plate equipped with a sharp lending edge at zero-pressure gradient and for various free-stream turbulence levels. Comparisons with results from a large eddy simulation reveal significant shortcomings in the modeling of the dissipation, with a large overprediction in the pretransitional boundary layer. The present results are in some cases in conflict with other results reported in the literature, and it is shown that the discrepancies can be ascribed to the implementation of the free-stream boundary conditions.