A combined experimental and analytical modeling effort has been carried out to measure the skin friction response of the boundary layer in high Reynolds number adverse pressure gradient flow. The experiment was conducted in the United Technologies Research Center (UTRC) Acoustic Research Tunnel, an ultra-low freestream turbulence facility capable of laminar boundary layer research. Boundary layer computational fluid dynamics and stability modeling were used to provide pre-test predictions, as well as to aid in interpretation of measured results. Measurements were carried out at chord Reynolds numbers 2–3 × 10 6 , with the model set at multiple incidence angles to establish a range of relevant leading edge pressure gradients. The combination of pressure gradient and flight Reynolds number testing on a thin airfoil has produced a unique data set relevant to propulsion system turbomachinery.

The study of the boundary layer transition plays a fundamental role in the field of turbomachinery. The main reason is the strong influence of the transition on the flow field local parameters, such as skin friction and heat transfer, this variation is reflected on the global ones such as efficiency and heat load of the blade row. Turbulent transition models are nowadays commonly used tools in both CFD research and design practice. It is then of particular interest to understand if they are able to predict the effect of temperature on bypass transition and, in case of positive answer, the reasons of their behaviour. This becomes even more interesting as the effect of the flow aero-thermal coupling becomes prominent in the analysis of such phenomena and is typically not accounted for in the validation of turbulence models. In this work we focus our attention on two state of the art transition model that use two radically different approaches to describe transition. To isolate the effects of the temperature ratio on the transition the simulations have been performed keeping the same values of Reynolds and Mach numbers and changing the value of the wall to freestream Temperature Ratio (TR). The results of the two transition models have been compared between them as well as with experimental results. They show that both models are sensitive to TR, though a locally based (rather than correlation based) approach for transition modelling should be favoured.

Axial compressors may be operated under off-design incidences due to variable operating conditions. Therefore, a successful design requires accurate performance and stability limits predictions under a wide operating range. Designers generally rely both on correlations and on Reynolds-averaged Navier–Stokes (RANS), the accuracy of the latter often being questioned. The present study investigates profile losses in an axial compressor linear cascade using both RANS and wall-resolved large eddy simulation (LES), and compares with measurements. The analysis concentrates on “loss buckets,” local separation bubbles and boundary layer transition with high levels of free stream turbulence, as encountered in real compressor environment without and with periodic incoming wakes. The work extends the previous research with the intention of furthering our understanding of prediction tools and improving our quantification of the physical processes involved in loss generation. The results show that while RANS predicts overall profile losses with good accuracy, the relative importance of the different loss mechanisms does not match with LES, especially at off-design conditions. This implies that a RANS-based optimization of a compressor profile under a wide incidence range may require a thorough LES verification at off-design incidence.

A local, intermittency-function-based transition model was developed for the prediction of laminar-turbulent transitional flows with freestream turbulence intensity Tu at low (Tu < 1%), moderate (1% < Tu < 3%), and high Tu > 3% levels, and roughness effects in a broad range of industrial applications such as turbine and helicopter rotor blades, and in nature. There are many mechanisms (natural or bypass) that lead to transition. Surface roughness due to harsh working conditions could have great influence on transition. Accurately predicting both the onset location and length of transition has been persistently difficult. The current model is coupled with the k–ω Reynolds-averaged Navier–Stokes (RANS) model, that can be used for general computational fluid dynamics (CFD) purpose. It was validated on the ERCOFTAC experimental zero-pressure-gradient smooth flat plate boundary layer with both low and high leading-edge freestream turbulence intensities. Skin friction profiles agree well with the experimental data. The model was then tested on ERCOFTAC experimental flat plate boundary layer with favorable/adverse pressure gradients cases, periodic wakes, and flows over Stripf's turbine blades with roughness from hydraulically smooth to fully rough. The predicted skin friction and heat transfer properties by the current model agree well with the published experimental and numerical data.

A low-Reynolds number k-ε model for simulation of turbulent flow with high free stream turbulence is developed which can successfully predict turbulent kinetic energy profiles, skin friction coefficient, and Stanton number under high free stream turbulence. Modifications incorporating the effects of free stream velocity and length scale are applied. These include an additional term in turbulent kinetic energy transport equation, as well as reformulation of the coefficient in turbulent viscosity equation. The present model is implemented in OpenFOAM CFD code and applied together with other well-known versions of low-Reynolds number k-ε model in flow and heat transfer calculations in a flat plate turbulent boundary layer. Three different test cases based on the initial values of the free stream turbulence intensity (1%, 6.53%, and 25.7%) are considered and models predictions are compared with available experimental data. Results indicate that almost all low-Reynolds number k-ε models, including the present model, give reasonably good results for low free stream turbulence intensity case (1%). However, deviations between current k-ε models predictions and data become larger as turbulence intensity increases. Turbulent kinetic energy levels obtained from these models for very high turbulence intensity (25.7%) show as much as 100% underprediction while skin friction coefficient and Stanton number are overpredicted by more than 70%. Applying the present modifications, predictions of skin friction coefficient, and Stanton number improve considerably (only 15% and 8% deviations in average for very high free stream turbulence intensity). Turbulent kinetic energy levels are vastly improved within the boundary layer as well. It seems like the new developed model can capture the physics of the high free stream turbulence effects.

Based on detailed experimental work conducted at a low speed test facility, this paper describes the transition process in the presence of a separation bubble with low Reynolds number, low free-stream turbulence, and steady main flow conditions. A pressure distribution has been created on a long flat plate by means of a contoured wall opposite of the plate, matching the suction side of a modern low-pressure turbine aerofoil. The main flow conditions for four Reynolds numbers, based on suction surface length and nominal exit velocity, were varied from 80,000 to 300,000, which covers the typical range of flight conditions. Velocity profiles and the overall flow field were acquired in the boundary layer at several streamwise locations using hot-wire anemometry. The data given is in the form of contours for velocity, turbulence intensity, and turbulent intermittency. The results highlight the effects of Reynolds number, the mechanisms of separation, transition, and reattachment, which feature laminar separation-long bubble and laminar separation-short bubble modes. For each Reynolds number, the onset of transition, the transition length, and the general characteristics of separated flow are determined. These findings are compared to the measurement results found in the literature. Furthermore, the experimental data is compared with two categories of correlation functions also given in the literature: (1) correlations predicting the onset of transition and (2) correlations predicting the mode of separated flow transition. Moreover, it is shown that the type of instability involved corresponds to the inviscid Kelvin-Helmholtz instability mode at a dominant frequency that is in agreement with the typical ranges occurring in published studies of separated and free-shear layers.

To further the understanding of secondary flow loss, a set of surface measurements is presented for a planar turbine cascade tested at low Mach number (maximum of 0.23) and at an inlet axial chord Reynolds number of 5.9 × 10 5 . The endwall and airfoil surface measurements are of skin friction, limiting streamline direction, and static pressure. An oil film interferometry measurement technique applied to the endwall and airfoil surfaces (at some 2000 locations) provides an extensive passage surface map of skin friction values and limiting streamline topology. Measurements of pressures on the same passage surfaces are also presented, resulting in a complete picture of endwall and airfoil surface pressure and shear.

Skin friction coefficients and heat transfer coefficients are measured for a range of regular and random roughnesses on the suction side of a simulated gas turbine vane. The skin friction coefficients are calculated using boundary layer data and the momentum integral method. High resolution surface temperature data measured with an IR camera yield local heat transfer values. 80 grit, 50 grit, 36 grit, and 20 grit sandpapers along with a regular array of conical roughness elements are tested. Measured skin friction coefficient data show that the conical roughness array behaves very similar to the 50 grit, 36 grit, and 20 grit sandpapers in terms of the effect of the roughness on the hydrodynamic boundary layer. In terms of heat transfer, the conical roughness array is most similar to the 80 grit sandpaper, which are both lower than the roughest sandpapers tested. These data show that the particular regular array of roughness elements tested has fundamentally different behavior than randomly rough surfaces for this position on the simulated turbine vane. In addition, this difference is in the opposite direction as seen in previous experimental studies. In order to draw a more general conclusion about the nature of random and regular roughness, a parametric study of regular roughness arrays should be performed.

The flow near the leading edge stagnation line of a plane turbine cascade airfoil is analyzed using measurements, analytical modeling, and computational fluid dynamics modeling. New measurements of skin friction and pressure are used to show that the aerodynamics of the leading edge, within what we call the stagnation region, are well described by an exact analytical solution for laminar stagnation-point or Hiemenz flow. The skin friction measurements indicate the extent of the stagnation region. The same parameters that characterize Hiemenz flow also characterize stagnation-point potential flow. The thermal resistance of the laminar momentum boundary layer in Hiemenz flow is absent in the inviscid solution. Consequently, the heat transfer in stagnation-point potential flow is greater than the heat transfer in Hiemenz flow. Based on measurements from an earlier study, the highest heat transfer levels in the cascade occur along the leading edge stagnation line. Stagnation-point potential flow provides a close, upper bound for the measured heat transfer at this small but critical location within the stagnation region. This paper describes how to apply the analytical model for predicting cascade stagnation-line heat transfer using only surface pressure calculations.

The complex three-dimensional fluid flow on the endwall in an axial flow turbine blade or vane passage has been extensively investigated and reported on in turbomachinery literature. The aerodynamic loss producing mechanisms associated with the endwall flow are still not fully understood or quantitatively predictable. To better quantify wall friction contributions to endwall aerodynamic loss, low Mach number wind tunnel measurement of skin friction coefficients have been made on one endwall of a large scale cascade of high pressure turbine airfoils, at engine operating Reynolds numbers. Concurrently, predictive calculations of the endwall flow shear stress have been made using a computational fluid dynamics (CFD) code. Use of the oil film interferometry skin friction technique is described and applied to the endwall, to measure local skin friction coefficients and shear stress directions on the endwall. These are correlated with previously reported measured local endwall pressure gradients. The experimental results are discussed and compared to the CFD calculations, to answer questions concerning endwall aerodynamic loss predictive ability.

The discrete element method considers the total aerodynamic drag on a rough surface to be the sum of shear drag on the flat part of the surface and the form drag on the individual roughness elements. The total heat transfer from a rough surface is the sum of convection through the fluid on the flat part of the surface and the convection from each of the roughness elements. The discrete element method has been widely used and validated for predicting heat transfer and skin friction for rough surfaces composed of sparse, ordered, and deterministic elements. Real gas turbine surface roughness is different from surfaces with sparse, ordered, and deterministic roughness elements. Modifications made to the discrete element roughness method to extend the validation to real gas turbine surface roughness are detailed. Two rough surfaces found on high-hour gas turbine blades were characterized using a Taylor-Hobson Form Talysurf Series 2 profilometer. Two rough surfaces and two elliptical-analog surfaces were generated for wind tunnel testing using a three-dimensional printer. The printed surfaces were scaled to maintain similar boundary layer thickness to roughness height ratio in the wind tunnel as found in gas turbine operation. The results of the wind tunnel skin friction and Stanton number measurements and the discrete element method predictions for each of the four surfaces are presented and discussed. The discrete element predictions made considering the gas turbine roughness modifications are within 7% of the experimentally measured skin friction coefficients and are within 16% of the experimentally measured Stanton numbers.

A new correlation-based transition model has been developed, which is built strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) methods using unstructured grids and massive parallel execution. The model is based on two transport equations, one for the intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models), but form a framework for the implementation of correlation-based models into general-purpose CFD methods. Part I of this paper ( Menter, F. R., Langtry, R. B., Likki, S. R., Suzen, Y. B., Huang, P. G., and Völker, S., 2006, ASME J. Turbomach., 128(3), pp. 413–422 ) gives a detailed description of the mathematical formulation of the model and some of the basic test cases used for model validation. Part II (this part) details a significant number of test cases that have been used to validate the transition model for turbomachinery and aerodynamic applications, including the drag crisis of a cylinder, separation-induced transition on a circular leading edge, and natural transition on a wind turbine airfoil. Turbomachinery test cases include a highly loaded compressor cascade, a low-pressure turbine blade, a transonic turbine guide vane, a 3D annular compressor cascade, and unsteady transition due to wake impingement. In addition, predictions are shown for an actual industrial application, namely, a GE low-pressure turbine vane. In all cases, good agreement with the experiments could be achieved and the authors believe that the current model is a significant step forward in engineering transition modeling.

Boundary layer measurements have been made on the concave surfaces of two constant curvature blades using hot wire anemometry. All the current experiments were performed with negligible streamwise pressure gradient. Grids were used to produce a range of freestream turbulence levels between 1% and 4%. The freestream velocity increases with distance from a concave wall according to the free vortex condition making the determination of the boundary layer edge difficult. A flat plate equivalent boundary layer procedure was adopted, therefore, to overcome this problem. The Taylor–Goertler (TG) vortices resulting from the concave curvature were found to make the laminar and turbulent boundary layer profiles fuller and to increase the skin friction coeffiicent by up to 40% compared with flat plate values. This leads to a more rapid growth in boundary layer thickness. The evolution in the intermittency through transition is very similar to that for a flat plate, however, the shape factors are depressed slightly throughout the flow due to the fuller velocity profiles. For all the current experiments, curvature promoted transition. This was very marked at low freestream turbulence level but remained significant even at the highest levels. It appears that the velocity fluctuations associated with the TG vortices enhance the freestream turbulence resulting in a higher effective turbulence level. A new empirical correlation for start of transition based on this premise is presented. The ratio of end to start of transition momentum thickness Reynolds numbers was found to be approximately constant.

Oscillating vortex generator jets have been used to control boundary layer separation from the suction side of a low-pressure turbine airfoil. A low Reynolds number (Re=25,000) case with low free-stream turbulence has been investigated with detailed measurements including profiles of mean and fluctuating velocity and turbulent shear stress. Ensemble averaged profiles are computed for times within the jet pulsing cycle, and integral parameters and local skin friction coefficients are computed from these profiles. The jets are injected into the mainflow at a compound angle through a spanwise row of holes in the suction surface. Preliminary tests showed that the jets were effective over a wide range of frequencies and amplitudes. Detailed tests were conducted with a maximum blowing ratio of 4.7 and a dimensionless oscillation frequency of 0.65. The outward pulse from the jets in each oscillation cycle causes a disturbance to move down the airfoil surface. The leading and trailing edge celerities for the disturbance match those expected for a turbulent spot. The disturbance is followed by a calmed region. Following the calmed region, the boundary layer does separate, but the separation bubble remains very thin. Results are compared to an uncontrolled baseline case in which the boundary layer separated and did not reattach, and a case controlled passively with a rectangular bar on the suction surface. The comparison indicates that losses will be substantially lower with the jets than in the baseline or passively controlled cases.

Turbulent boundary layers were subjected to grid-generated free-stream turbulence to study the effects of length scale and intensity on heat transfer. Relative to conventional boundary layer thickness measures, test conditions included very small-scale free-stream turbulence. The boundary layers studied ranged from 400–2700 in momentum-thickness Reynolds number and from 450–1900 in enthalpy-thickness Reynolds number. Free-stream turbulence intensities varied from 0.1–8.0%. Ratios of free-stream length scale to boundary-layer momentum thickness ranged from 4.4–32.5. The turbulent-to-viscous length-scale ratios presented are the smallest found in the heat-transfer literature; the ratios spanned from 115–1020. The turbulent-to-thermal ratios (using enthalpy thickness as the thermal scale) are also the smallest reported; the ratios ranged from 3.2–12.3. Relative to clean-free-stream expectations based on the momentum- and enthalpy-thickness Reynolds numbers, the skin friction coefficient increased by up to 16%, and the Stanton number increased by up to 46%.

A conditional sampling technique was employed to separate the turbulent and nonturbulent parts of accelerated boundary layers undergoing laminar-turbulent transition on a uniformly heated flat plate. Tests were conducted with zero pressure gradient and two levels of streamwise acceleration parameter: K = 0.07 × 10 −6 and 0.16 × 10 −6 . The conditionally sampled distribution of the skin friction coefficients revealed that the values for C f in the nonturbulent and turbulent portions deviated significantly from the respective laminar and turbulent correlations. These deviations increased as acceleration increased. Reconstructing the local average C f values using the laminar and fully turbulent correlations consistently overestimated the unconditioned C f values. Using the conditionally sampled data for reconstructing C f values provided better results, but does not necessarily result in the same unconditioned C f values. The mean velocity profiles from the turbulent portions had the appearance of a low-Reynolds-number turbulent boundary layer with a large wake region. In the late transition region, as acceleration increased, the wake region in the turbulent portion was suppressed relative to the unconditioned result. The integral parameters, δ*, θ, and shape factor, H, were conditionally sampled and analyzed.

Turbulent wakes swept across a flat plate boundary layer simulate the phenomenon of wake-induced bypass transition. Benchmark data from a direct numerical simulation of this process are presented and compared to Reynolds-averaged predictions. The data are phase-averaged skin friction and mean velocities. The predictions and data are found to agree in many important respects. One discrepancy is a failure to reproduce the skin friction overshoot following transition. [S0889-504X(00)00503-1]

New techniques for the direct measurement of skin friction using nematic liquid crystal layers are demonstrated. Skin friction measurements can be made using a molecular rotation time technique or an equilibrium orientation technique. A mathematical model describing the molecular dynamics of the nematic liquid crystal layer has been introduced. Theoretical results from the proposed mathematical model are in excellent agreement with the current experimental measurements. It is thus demonstrated that the present model captures the essential physics of the nematic liquid crystal measurement techniques. Estimates based on the variance of the liquid crystal calibration data indicate that skin friction measurements to within ±4 percent should certainly be possible. The techniques offer the considerable advantage of simplicity, without any compromise on the accuracy, relative to other surface shear stress measurement techniques. The full surface measurement capacity of the equilibrium orientation technique is demonstrated by measuring the skin friction distribution around a cylindrical obstruction in a fully developed laminar flow.

Aerodynamic flow path losses and turbine airfoil gas side heat transfer are strongly affected by the gas side surface finish. For high aero efficiencies and reduced cooling requirements, airfoil designs dictate extensive surface finishing processes to produce smooth surfaces and enhance engine performance. The achievement of these requirements incurs additional manufacturing finishing costs over less strict requirements. The present work quantifies the heat transfer (and aero) performance differences of three cast airfoils with varying degrees of surface finish treatment. An airfoil, that was grit blast and Codep coated, produced an average roughness of 2.33 μm, one that was grit blast, tumbled, and aluminide coated produced 1.03 μm roughness, and another that received further postcoating polishing produced 0.81 μm roughness. Local heat transfer coefficients were experimentally measured with a transient technique in a linear cascade with a wide range of flow Reynolds numbers covering typical engine conditions. The measured heat transfer coefficients were used with a rough surface Reynolds analogy to determine the local skin friction coefficients, from which the drag forces and aero efficiencies were calculated. Results show that tumbling and polishing reduce the average roughness and improve performance. The largest differences are observed from the tumbling process, with smaller improvements realized from polishing.

Measurements of pressure distributions, profile losses, and flow deviation were carried out on a planar turbine cascade in incompressible flow to assess the effects of partial roughness coverage of the blade surfaces. Spanwise-oriented bands of roughness were placed at various locations on the suction and pressure surfaces of the blades. Roughness height, spacing between roughness elements, and band width were varied. A computational method based on the inviscid/viscous interaction approach was also developed; its predictions were in good agreement with the experimental results. This indicates that good predictions can be expected for a variety of cascade and roughness configurations from any two-dimensional analysis that couples an inviscid method with a suitable rough surface boundary-layer analysis. The work also suggests that incorporation of the rough wall skin-friction law into a three-dimensional Navier–Stokes code would enable good predictions of roughness effects in three-dimensional situations. Roughness was found to have little effect on static pressure distribution around the blades and on deviation angle, provided that it does not precipitate substantial flow separation. Roughness on the suction surface can cause large increases in profile losses; roughness height and location of the leading edge of the roughness band are particularly important. Loss increments due to pressure-surface roughness are much smaller than those due to similar roughness on the suction surface.