Transition of boundary layer flows in the presence of Goertler vortices

Transition of boundary layer flows in the presence of longitudinal counter-rotating Goertler vortices was experimentally investigated on a concave surface of 1.0 m radius of curvature in a perspex (plexiglass) curved rectangular duct connected to a low speed wind tunnel for a free-stream velocity range of 5.7–11.8 m/s. Quantitative measurements were carried out using a single sensor hot-wire anemometer, while the boundary layer transitions were detected using frequency spectrum method. The results confirm that in the presence of Goertler vortices, transition is initiated at the boundary layer upwash regions, and also agree well with the predicted values obtained using the two existing empirical transition criteria for concave surface boundary layer flows.     

Investigation of boundary layer stability in a gradient flow with a high degree of free-stream turbulence

The results of an experimental investigation of boundary layer stability in a gradient flow with a high degree of free-stream turbulence are presented. The question of the possible artificial generation, the further development and the effect on laminar-turbulent transition of instability waves (Tollmien-Schlichting waves) in the boundary layer on a wing profile is considered for a level of free-stream turbulence =1.75% of the free-stream velocity; the sensitivity of the flow to the disturbances and their control by means of boundary layer suction are investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 52–58, March–April, 1990.     

Numerical prediction of the formation of Goertler vortices on a concave surface with suction and blowing

This paper presents a numerical prediction of the formation of Goertler vortices on a concave surface with suction and blowing. Suction stabilizes the boundary layer flow on the surface, whereas blowing destabilizes the flow. The criterion on the position marking the onset of Goertler vortices is defined in the present paper. For facilitating the numerical study, the computation is carried out in the transformed x–η plane. The results show that the onset position characterized by the Goertler number depends on the local suction/blowing parameter, the Prandtl number and the wavenumber. The value of the critical Goertler number increases with the increase in suction, while the value of the Goertler number decreases with the increase in blowing. Both the experimental and the numerical data can be correlated by G_θ*=10.2(a′θ)*^3/2 without suction and blowing and by a simple relation G*_x=(G*_x)_γ=0 e^−γ with suction and blowing. The obtained critical Goertler number and wavenumber are in good agreement with the previous experimental data. Copyright © 1999 John Wiley & Sons, Ltd.     

Detection of flow separation and reattachment using shear-sensitive liquid crystals

Coatings of pure chiral nematic liquid crystals are known to change colour under different levels of surface shear stress. In this study, the liquid crystal was used to provide information about flow separation and reattachment on both a two-dimensional aerofoil and a delta wing. The tests were carried out at a free-stream velocity of 28 m/s and a number of incidence angles. The Reynolds numbers based on the central chord length of the models were 200,000 and 270,000 for the aerofoil and delta wing models, respectively. The study showed that locations of boundary layer separation and reattachment can be identified from spatial variations in the surface colour; the agreement between the results and those obtained using surface oil flow was good. Issues relating to interpretation of the crystal colour pattern and the limitation of this technique in detection of flow separation were also discussed.     

Effect of rotation on the formation of longitudinal vortices in mixed convection flow over a flat plate

This paper presents a numerical study of the effect of rotation on the formation of longitudinal vortices in mixed convection flow over a flat plate. The criterion on the position of marking the onset of longitudinal vortices is defined in this paper. The onset position characterized by the Goertler number G _δ depends on the Grashof number, the rotation number Ro, the Prandtl number Pr and the wave number. The results show that negative rotation stabilizes the boundary layer flow on the surface. On the contrary, positive rotation destabilizes the flow. The numerical data are compared with the experimental results.     

Effects of free-stream turbulence on a transitional separated–reattached flow over a flat plate with a sharp leading edge

The transitional separated–reattached flow on a flat plate with a blunt leading edge under 2% free-stream turbulence (FST) is numerically simulated using the Large-eddy simulation (LES) approach. The Reynolds number based on the free-stream velocity and the plate thickness is 6500. A dynamic subgrid-scale model is employed and the LES results compare well with the available experimental data.It is well known that FST enhances shear-layer entrainment rates, reduces the mean reattachment distance, and causes early transition to turbulence leading to an early breakdown of the separated boundary layer. Many experimental studies have shown that different vortex shedding frequencies exist, specially the so called low-frequency flapping when there is a separation bubble but its mechanism is still not completely understood. The previous study by us without free-stream turbulence (NFST) did not show the existence of such a low-frequency flapping of the shear layer and it is not clear what the effects of FST will have on these shedding modes. Detailed analysis of the LES data has been presented in the present paper and the low-frequency flapping has not been detected in the current study.     

Effects of free stream turbulence on the distribution of heat transfer around turbine blade sections

Local convective heat transfer coefficients to a number of modern gas turbine blade sections have been measured under a wide range of mainstream conditions, from notionally steady flows to highly perturbed turbulent flows. The paper discusses the results and, through a detailed analysis of the pertinent boundary layer flow parameters and their relation to the observed experimental results, tests criteria for the occurrence of transition from laminar to turbulent boundary layers, a factor which all the data from this work confirm as critical in predicting the quantitative effects of mainstream turbulence on heat transfer rates. Artificially induced mainstream turbulence, which is endemic in the flows in a real turbine, enhances significantly the heat transfer rates, especially to the leading edge regions and on the pressure surface, particularly when the acceleration is tending to suppress transition. The results presented here confirm existing criteria for laminarisation and the applicability of some of those available for predicting laminar-turbulent transition. The observations also demonstrate how surface geometry can influence the stability of the flows, and the uncertainties which remain in assessing the effect of Goertler vortices and their role in the convective heat transfer process.     

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

Direct numerical simulation of the transition to turbulence in a supersonic boundary layer on smooth and rough surfaces

Direct numerical simulations of instability development and transition to turbulence in a supersonic boundary layer on a flat plate are performed. The computations are carried out for moderate supersonic (free-stream Mach number M = 2) and hypersonic (M = 6) velocities. The boundary layer development is simulated, which includes the stages of linear growth of disturbances, their nonlinear interaction, stochastization, and turbulent flow formation. A laminar–turbulent transition initiated by distributed roughness of the plate surface at the Mach number M = 2 is also considered.     

Momentum and heat transfer in the magnetohydrodynamic stagnation-point flow of a viscoelastic fluid toward a stretching surface

An analysis is made of the steady two-dimensional stagnation-point flow of an incompressible viscoelastic fluid over a flat deformable surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that for a viscoelastic conducting fluid of short memory (obeying Walters’ Bʹ model), a boundary layer is formed when the stretching velocity of the surface is less than the inviscid free-stream velocity and velocity at a point increases with increase in the Hartmann number. On the other hand an inverted boundary layer is formed when the surface stretching velocity exceeds the velocity of the free stream and the velocity decreases with increase in the Hartmann number. A novel result of the analysis is that the flow near the stretching surface is that corresponding to an inviscid stagnation-point flow when the surface stretching velocity is equal to the velocity of the free stream. Temperature distribution in the boundary layer is found when the surface is held at constant temperature and surface heat flux is determined. It is found that in the absence of viscous and Ohmic dissipation and strain energy in the flow, temperature at a point decreases with increase in the Hartmann number.     

Extension of an algebraic intermittency model for better prediction of transition in separated layers under strong free-stream turbulence

A constitutive law describing the Reynolds stresses in boundary layers undergoing laminar-to-turbulent transition, constructed in previous work by elastic-net regression on an experimental data base, is used to improve an algebraic intermittency model for cases with transition in a separated layer influenced by a high level of free-stream turbulence. The intermittency model is combined with a k-ω turbulence model and the basic version, developed in previous work, functions well for bypass transition in attached boundary layers and for transition in separated boundary layers under a low free-stream turbulence level. The basic model version is extended by an additional production term in the transport equation for turbulent kinetic energy. A sensor detects the front part of a separated layer and activates the production term. The term expresses the effect of Klebanoff streaks generated upstream of separation on the Kelvin-Helmholtz instability rolls in the separated part of the layer. The Klebanoff streaks cause faster breakdown by the combined effects of a large adverse pressure gradient and an elevated free-stream turbulence level. The extended model does not alter the results of the basic model version for bypass transition in an attached boundary layer and for transition in a separated boundary layer under a low free-stream turbulence level. The extended model significantly improves the predictions of the previous model version for transition in a separated boundary layer under a high free-stream turbulence level.     

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a ‘high-lift’ and an ‘ultra high-lift’ turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in ‘ultra high-lift’ design when compared to the ‘high-lift’ design. Stronger ‘Klebanoff streaks’ are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The ‘part-span’ Kelvin–Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging.     

Effect of rotation on Goertler vortices in the boundary layer flow on a curved surface

This paper presents a numerical prediction of the formation of Goertler vortices on a curved surface with effect of rotation. The criterion of flow visualization marking the onset position of Goertler vortices is employed in the present paper. For facilitating the numerical study, the computation is carried out in the transformed x and ηplane. The results show that the onset position characterized by the Goertler number, depends on the rotation number Ro, the Prandtl number and the wave number. The value of critical Goertler number increases with the increase in negative rotation, while the value of Goertler number decreases with the increase in positive rotation on a concave surface. On the contrary, the value of critical Goertler number decreases with the increase in negative rotation on a convex surface. The obtained critical Goertler number and wave number are compared with the previous theoretical and experimental data. Copyright © 2002 John Wiley & Sons, Ltd.     

Effect of surface steps on boundary layer transition

An experimental study has been carried out to examine the effect of a sharp-edged step on boundary layer transition. The transition position and disturbance spectra in the boundary layer for different step heights and free-stream velocities were measured by hot-wire anemometry. A correlation between the transition Reynolds number and the relative step height has been established for both backward-facing and forward-facing steps. The transition position is associated with the “N-factor” that defines the integrated growth of instability waves at transition. The boundary layer over a step has an earlier transition position than that on a smooth plate, since the instability waves amplify more rapidly than those on a smooth surface. The transition N-factor for the flow containing a step, calculated using the amplification rates on a smooth plate, will, therefore, be smaller than that on surfaces without a step. The observed reduction of the N-factor occurring with a step has been shown to correlate with the height of the step, thus, providing an empirical tool that can be used to estimate the transition position when steps occur. An appropriate value of N can be determined from knowledge of the step height.     

Modeling of convective structures in a thin layer of silicone oil in air flow under heating

Numerical simulation was performed to study convective structures in a thin silicone oil layer heated from below, whose free surface is exposed to air flow generating drift flow. The basic equations are transformation to a form suitable for spectral methods. The steady flow velocity profile obtained in a laboratory experiment is calculated. It is shown that increasing the Reynolds number leads to the transition from polygonal convective cells to longitudinal rolls (elongated along the flow). The dependence of the transition Reynolds number on the temperature on the lower boundary of the layer is obtained. The calculation results are compared with experimental data.     

Some features of a turbulent wing–body junction vortical flow

Laser-Doppler velocimeter measurements of a wing/body junction flow field made within a plane to the side of the wing/wall junction and perpendicular both to a 3:2 elliptical nose—NACA 0020 tail wing, and a flat wall are presented. Reynolds number of the approach boundary layer was, Re_θ = 5940, and free-stream air velocity was, U_ref = 27.5 m/s. A large vortical structure residing in the outer region redirects the low-turbulence free-stream flow to the vicinity of the wing/wall junction, resulting in thin boundary layers with velocity magnitudes higher than free-stream flow. Lateral pressure gradients result in a three-dimensional separation on the uplifting side of the vortex. Additionally, a high vorticity vortical structure with opposite sense to the outer-layer vortex forms beneath the outer-layer vortex. Normal and shear stresses increase to attain values an order of magnitude larger compared to values measured in a three-dimensional boundary layer just outside the junction vortex. Bimodal histograms of the w fluctuating velocity occur under the outer-layer vortex near the wall due to the time-dependent nature of the horseshoe vortex. In such a flow the shear-stress angle (SSA) highly lags the flow-gradient angle (FGA), and the turbulence diffusion is highly altered due to presence of vortical structures.     

Simulation of the Effect of the Freestream Turbulence Parameters on the Boundary Layer of a Curvilinear Airfoil

Modified variants of differential turbulence models which make it possible continuously to calculate both the entire flow region with laminar, transition and turbulent regimes and local low Reynolds number zones are proposed for investigating the flow and heat transfer in the boundary layers developing in compressible gas flow past curvilinear airfoils. The effect of the intensity and scale of free-stream turbulence and their variability along the outer boundary layer edge, as well as the combined action of the turbulence intensity and the streamwise pressure gradient in flow past blade profiles, on the heat transfer and near-wall turbulence characteristics is analyzed. The numerical results are compared with experimental and theoretical data.     

Transition to Turbulence in the Boundary Layer on a Plate in the Presence of a Negative Free-Stream Pressure Gradient

Transition to turbulence in the boundary layer on a flat plate is investigated numerically for an incompressible fluid flow with a given negative free-stream pressure gradient. The transition is investigated using the three-parameter turbulence model developed by the authors. The calculation results are compared with the available experimental data.     

Application of a Virtual-Boundary Method for the Numerical Study of Oscillations Developing Behind a Cylinder Near A Plane Wall

The conditions of onset and the character of the oscillations developing behind a circular cylinder located above a plane wall (screen) in a flow with a velocity profile of the boundary layer type are studied numerically. The dependence of the critical Reynolds number (at which a steady flow regime in the wake behind the cylinder is replaced by an oscillatory regime) on the cylinder-wall gap and the free-stream boundary layer thickness is found.     

The capability of large eddy simulation to predict relaminarization

The boundary layer which represents the narrow zone between a solid body and the free stream can have a laminar or a turbulent state. This state influences on the one hand the properties of the near-wall flow like skin friction or heat transfer and on the other hand also the free-stream flow itself, e.g. the downstream flow angle of a turbomachinery blade. Thus it is important for designers of fluid machinery to understand and predict the state of the boundary layer as well as the transition processes between the two states.In this work the so-called relaminarization is investigated which represents a reverse transition from a turbulent to a laminar boundary layer. At the Institute for Thermal Turbomachinery and Machine Dynamics at Graz University of Technology a test bench has been designed in order to produce a highly accelerated flow, thus triggering relaminarization. In the present work, the flow in this test bench is numerically investigated with Reynolds-averaged Navier-Stokes (RANS) flow simulation as well as with a large eddy simulation (LES).An outcome of this paper is, that the LES shows a very good agreement to the measurement results and is capable of predicting relaminarization.