Measured Transition Locations Research Articles

Influence of deep gaps on laminar–turbulent transition in two-dimensional boundary layers at subsonic Mach numbers

Systematic experimental investigations on the influence of deep gaps on the location of laminar–turbulent transition are reported. The tests were conducted in the Cryogenic Ludwieg–Tube Göttingen, a blow-down wind tunnel with good flow quality, at eight different unit Reynolds numbers ranging from Re_1 = {17.5,,times 10^{6},mathrm{{m}^{-1}}} to 80,times,10^{6},mathrm{m}^{-1}, three Mach numbers, M= 0.35, 0.50 and 0.65, and various pressure gradients. A flat-plate configuration, the extended two-dimensional wind tunnel model PaLASTra was modified in order to allow the installation of gaps with nominal widths of 30 upmu m, 100 upmu m and 200 upmu m and a depth of d = {9,mathrm{mm}}. A maximum Reynolds number based on the gap width Re_{w} = Re_1 cdot w approx {16{,}000} was reached. Transition Reynolds numbers ranging from Re_{tr}approx 1 × 106 to 11 × 106 were measured, as a function of gap width, pressure gradient and Mach and Reynolds number. This systematic investigation facilitates a linear approximation of Re_{tr} dependent on the boundary layer shape factor H_{12} for various flow conditions and gap widths. It was therefore possible to conduct an investigation of Re_{tr} depending on Re_{1} and the relative change of the transition location depending on the gap width w. Incompressible linear stability analysis was used to calculate amplification rates of Tollmien–Schlichting waves and determine critical N-factors by correlation with measured transition locations. The change in the critical N-factor varDelta N by installation of the gap is investigated as a function of w and Re_w. It was found that a gap width of 30 upmu m reduces the critical N-factors in the range of varDelta N approx 0.5 pm 0.25, while gap widths of 100 upmu m and 200 upmu m reduce the critical N-factor in the range of varDelta N approx 1.5 pm 1. Interestingly, an increase in gap width from 100 to 200 upmu m was not found to induce smaller transition Reynolds numbers or reduced N-factors, which might be due to resonance effects.

Step-induced transition in compressible high Reynolds number flow

The effect of sharp forward-facing steps on boundary-layer transition is systematically investigated in this work in combination with the influence of variations in Mach number, Reynolds number and streamwise pressure gradient. Experiments have been conducted in a quasi-two-dimensional flow at Mach numbers up to 0.77 and chord Reynolds numbers up to 13 million in the Cryogenic Ludwieg-Tube Göttingen. The adopted experimental set-up allows an independent variation of the aforementioned parameters and enables a decoupling of their respective effects on the boundary-layer transition, which has been measured accurately and non-intrusively by means of a temperature-sensitive paint. The functional relations determined between a non-dimensional transition parameter and the non-dimensional step parameters allow the step effect on transition to be isolated from the influence of variations in Mach number, Reynolds number and pressure gradient. Criteria for acceptable heights of forward-facing steps on natural laminar flow surfaces for the examined test conditions are derived from the present functional relations. The measured transition locations are also correlated with the results of linear, local stability analysis for the smooth configuration, enabling the estimation of the step-induced increment of the amplification factor ΔN of Tollmien–Schlichting waves, which can be incorporated in the eN transition prediction method.

Computational Fluid Dynamics Transition Models Validation for Rotors in Unsteady Flow Conditions

Computational fluid dynamics transition models are evaluated for rotors in unsteady axial and in forward flight conditions. The study is carried out using CREATETM-AV Helios. Three transition models are considered: amplification factor transport (AFT), Langtry–Menter (LM), and the LM with a crossflow transition model. The LM model is modified to allow for Galilean invariance. The first rotor configuration is the German Aerospace Center (DLR) rotor tested in the Rotor Test Facility in Göttingen (RTG). It is a four-blade, 2.13-foot-radius rotor in axial flow with pitching blades, operating at Reynolds numbers of and at three quarter radius, for the two test cases studied. The second configuration is the pressure-sensitive-paint rotor. It is a model-scale, 5.58-foot-radius, three-blade rotor operating at a high-advance-ratio, high-thrust forward flight condition and a hover Reynolds number of at three quarter radius. For both rotors, good agreement is found between the computed and the measured transition locations, obtained using the differential infrared thermography technique. The AFT and LM models produced remarkably consistent predictions. The crossflow model predicted an early transition onset compared with the test data.

Unit Reynolds number, Mach number and pressure gradient effects on laminar\u2013turbulent transition in two-dimensional boundary layers

The influence of unit Reynolds number (Re_1=17.5times 10^{6}–80times 10^{6},text {m}^{-1}), Mach number (M= 0.35–0.77) and incompressible shape factor (H_{12} = 2.50–2.66) on laminar–turbulent boundary layer transition was systematically investigated in the Cryogenic Ludwieg-Tube Göttingen (DNW-KRG). For this investigation the existing two-dimensional wind tunnel model, PaLASTra, which offers a quasi-uniform streamwise pressure gradient, was modified to reduce the size of the flow separation region at its trailing edge. The streamwise temperature distribution and the location of laminar–turbulent transition were measured by means of temperature-sensitive paint (TSP) with a higher accuracy than attained in earlier measurements. It was found that for the modified PaLASTra model the transition Reynolds number (Re_{text {tr}}) exhibits a linear dependence on the pressure gradient, characterized by H_{12}. Due to this linear relation it was possible to quantify the so-called ‘unit Reynolds number effect’, which is an increase of Re_{text {tr}} with Re_1. By a systematic variation of M, Re_1 and H_{12} in combination with a spectral analysis of freestream disturbances, a stabilizing effect of compressibility on boundary layer transition, as predicted by linear stability theory, was detected (‘Mach number effect’). Furthermore, two expressions were derived which can be used to calculate the transition Reynolds number as a function of the amplitude of total pressure fluctuations, Re_1 and H_{12}. To determine critical N-factors, the measured transition locations were correlated with amplification rates, calculated by incompressible and compressible linear stability theory. By taking into account the spectral level of total pressure fluctuations at the frequency of the most amplified Tollmien–Schlichting wave at transition location, the scatter in the determined critical N-factors was reduced. Furthermore, the receptivity coefficients dependence on incidence angle of acoustic waves was used to correct the determined critical N-factors. Thereby, a found dependency of the determined critical N-factors on H_{12} decreased, leading to an average critical N-factor of about 9.5 with a standard deviation of sigma approx 0.8.

Buoyant jets with three-dimensional trajectories

Details of an experimental investigation into the behaviour of discharges with three-dimensional (3D) trajectories are presented. A light attenuation technique is employed to track the position of peak concentrations in the flow and the transition from weakly to strongly advected behaviour can be clearly observed: two peaks are evident at a given cross-section in the strongly advected region, whereas only a single peak occurs at cross-sections in the weakly advected region. Length scales, based on dominant momentum fluxes in the weakly and strongly advected regions, can be employed to locate the transitions between these distinctly different flow forms. Coefficients for these length scales have been determined based on numerous studies of discharges following an essentially 2D path. Length scale estimates, based on the 2D path coefficients, and the measured transition locations from the present study indicate that the transition to strongly advected behaviour can be delayed significantly, if the discharged fluid follows a 3D path. This delay has significant implications for the dilution rates of the effluent.

Boundary-Layer Stability Analysis of the Hypersonic International Flight Research Transition Experiments

Boundary-layer stability analysis is performed by computational fluid dynamics simulation of experiments conducted in theCalspan–University at BuffaloResearchCenter Large EnergyNational ShockTunnel in support of the first flight of the Hypersonic International Flight Research Experimentation program. From the laminar flow solutions, disturbances are calculated using the linear parabolized stability equations method and instability is quantified by integrating the resulting disturbance growth rates. Comparisons aremade between the experimentally measured transition locations and the results of the parabolized stability equations analysis. The results show that for the cases tested, the e transition correlation works better than the commonly usedRe =Me engineering criterion for predicting the onset of boundary-layer transition from laminar to turbulent flow.

EN Transition Prediction in Three-Dimensional Boundary Layers on Inclined Prolate Spheroids

The capability of the e n method to predict transition in complex three-dimensional, laminar boundary layers is demonstrated. Flows around inclined prolate spheroids are ideally suited for investigation because they exhibit highly divergent and convergent three-dimensional viscous flows on curved surfaces. The invicid flowfield is described by the theory and the viscous layer by a three-dimensional laminar boundary-layer method. This approach is applied in weak viscous/inviscid interaction regions only, that is, in attached laminar flow regions, and validated by comparison with measured wall pressure and skin friction in magnitude and direction. For the determination of the transition location, the laminar boundary layer is analyzed by the two N factor e n method. Excited Tollmien-Schlichting waves of constant frequencies and stationary crossflow waves of constant wavelength are computed by the local, linear stability theory. Both N factor integrations are executed along 21 streamlines, which regularly cover the surface of the prolate spheroid. First, the values of both N factors at the measured transition locations are calculated, which deliver the stability limit of the prolate spheroid in the considered wind tunnel. Second, based on the knowledge of the stability limit, the transition locations are evaluated. The prolate spheroid with an aspect ratio of 6:1 was tested in two wind tunnels at angles of attack from 0 to 30 deg and Reynolds numbers from 1.5 x 10 6 to 43 x 10 6 . The measured transition locations compare remarkably well with computations for all investigated flow cases.

Infinite Swept-Wing Navier-Stokes Computations with eN Transition Prediction.

The flow around infinite swept wings is computed using a Reynolds-averaged Navier-Stokes method coupled to a boundary layer and a transition prediction method based on the e N approach. This approach applies the two N factor e N strategy, which allows the differentiation between excited Tollmien-Schlichting waves of constant frequency and stationary crossflow waves of constant spanwise wave number. The applicability is documented by comparing computations with infinite swept-wing experiments on four configurations, where one configuration was tested in two different wind tunnels. The limiting N factors for both types of waves are a priori unknown. Hence, firstly the limiting N factors, which represent the stability limit, are deduced from the measured transition locations. Subsequently, iterative computations are executed to determine the transition location using the coupled system, Navier-Stokes, boundary-layer, and two N factor e N method in combination with the stability limit

Two-phase flow patterns and transition characteristics for in-tube condensation with different surface inclinations

In-tube condensation of R-11 was experimentally investigated with various surface inclination angle between the direction of the vapor flow and the gravitational force, φ. The two-phase flow patterns were observed visually and the transition locations between different flow patterns were measured in a transparent test section. The vapor quality distribution along the test tube and the measured transition locations were used to prepare a flow pattern map. The experimental results indicated that the surface inclination, φ, strongly influenced the vapor and condensate distribution. Annular flow spanned the whole tube for φ = 0° at various vapor flow rates. Annular flow and stratified flow patterns were observed for φ = 45° and 60°. Annular flow, stratified flow, half-slug flow, and slug flow exist in sequence for φ = 90–120°. Annular flow, churn flow and slug flow occurred for φ = 180°. The possible prediction of flow patterns for in-tube condensation in a microgravity environment was discussed briefly.

Prediction of High-Lift Flows Using Turbulent Closure Models

The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.

Transition correlations in three-dimensional boundary layers

The stability and transition characteristics of three-dimensional boundary-layer flows are examined. First, the flow over a rotating cone is considered computationally. An increase of stagnation temperature is found to be only slightly stabilizing. Parameter studies on the simple rotating-cone geometry provide a large database of three-dimensional boundary-layer profiles and associated stability characteristics. To determine the possibility of correlating transition location with parameters based purely on basic-state three-dimensional boundary-layer profile characteristics, an empirical transition location of N = 9 is assumed. Transition location does not correlate with the traditional crossflow Reynolds number. A more appropriate definition for crossflow Reynolds number is found and termed R(sub cf(new)). This new parameter appears to correlate for transition location when plotted against maximum crossflow velocity. Then, the flow over a yawed cone is considered experimentally. The correlation results obtained from the rotating-cone work are applied to the actual measured transition locations on two different yawed-cone models under various angle-of-attack conditions in two different experimental facilities and are verified. This correlation is only suggested as a tool for preliminary transition prediction and design in three-dimensional boundary layers; once a preliminary shape is selected, further linear stability theory or parabolized stability equation calculations are strongly urged.

Simplified linear stability transition prediction method for separated boundary layers

An existing transition prediction method for attached, two-dimensional, incompressible boundary layers based on linear stability analysis is extended to separated, two-dimensional, incompressible boundary layers such as those found in laminar (transitional) separation bubbles. It is shown why the present method, which tracks the growth of disturbances at many different frequencies, is more accurate than the so-called envelope methods for nonsimilar boundary-layer developments. Reliance on a database of precalculated stability characteristics of known velocity profiles makes this method much faster than traditional stability calculations of similar accuracy. The Falkner-Skan self-similar profiles are used for attached flow, and a new, very general family of profiles is used for separated flow. Comparisons with measured transition locations inside the bubble show good agreement over the range of chord Reynolds numbers and airfoil angles of attack of interest.