Freestream Pressure Gradient Research Articles

A data-driven analysis of short and long laminar separation bubbles

This work investigates the statistical response of short and long laminar separation bubbles to external flow parameters, such as Reynolds number, free-stream turbulence intensity and streamwise pressure gradient, known to govern bubble formation and characteristics. A parametric experimental campaign has been performed using particle image velocimetry on a flat plate to provide a comprehensive database for the characterization of separation-induced transition in both short and long separation bubbles. The proper orthogonal decomposition (POD) was applied to the data set of all dividing streamlines commonly used to identify a laminar separation bubble. This provides an optimal state-space basis for the data-driven classification of the state of a laminar separation bubble, with the leading modes capturing the change in length and height of the laminar separation bubble in response to changes in the flow parameters. When projected onto the POD subspace constituted by the first three leading modes, the normalized data from the present study and the results from prior investigations not used in the modal analysis collapse on the same trajectory in the low-dimensional space. The present POD basis can be therefore adopted for the description of the general response of the time-mean shape of a laminar separation bubble to changes in the main influencing parameters. A well-defined pattern was observed in the case of short laminar separation bubbles in the reduced-order space defined by the first three POD coefficients, whereas a higher dispersion in the long-bubble regime indicates an increased sensitivity of long bubbles to the external flow characteristics.

Evaluation of Turbulence Models in Unsteady Separation

Unsteady separation is a phenomenon that occurs in many flows and results in increased drag, decreased lift, noise emission, and loss of efficiency or failure in flow devices. Turbulence models for the steady or unsteady Reynolds-averaged Navier–Stokes equations (RANS and URANS, respectively) are commonly used in industry; however, their performance is often unsatisfactory. The comparison of RANS results with experimental data does not clearly isolate the modeling errors, since differences with the data may be due to a combination of modeling and numerical errors, and also to possible differences in the boundary conditions. In the present study, we use high-fidelity large-eddy simulation (LES) results to carry out a consistent evaluation of the turbulence models. By using the same numerical scheme and boundary conditions as the LES, and a grid on which grid convergence was achieved, we can isolate modeling errors. The calculations (both LES and RANS) are carried out using a well-validated, second-order-accurate code. Separation is generated by imposing a freestream velocity distribution, that is modulated in time. We examined three frequencies (a rapid, flutter-like oscillation, an intermediate one in which the forcing and the flow have the same timescales, and a quasi-steady one). We also considered three different pressure distributions, one with alternating favorable and adverse pressure gradients (FPGs and APGs, respectively), one oscillating between an APG and a zero-pressure gradient (ZPG), and one with an oscillating APG. All turbulence models capture the general features of this complex unsteady flow as well or better than in similar steady cases. The presence, during the cycle, of times in which the freestream pressure-gradient is close to zero affects significantly the model performance. Comparing our results with those in the literature indicates that numerical errors due to the type of discretization and the grid resolution are as significant as those due to the turbulence model.

Quantifying How Turbulence Enhances Boundary Layer Skin Friction and Surface Heat Transfer

Transitional and turbulent boundary layer (BL) flows possess dramatically larger wall-shear stresses and surface heat fluxes than their laminar counterparts. Locally, this can be explained by appealing to the presence of spatiotemporally coherent velocity and temperature regions that enhance the momentum and thermal transport across the BL. However, these coherent structures are seldom present alone, but usually influenced by other physical phenomena, such as the streamwise growth of BLs or freestream pressure gradients. A moment of enthalpy integral equation is introduced to quantify how turbulence and other flow phenomena enhance surface heat flux. Results from a direct numerical simulation of a transitional and turbulent BL are used to demonstrate the proposed analysis method and to form a quantitative assessment of the BL physics. The integral analysis demonstrated in this paper for canonical turbulent flows provides an interpretable analysis tool for unlocking key BL physics, including future extensions to compressible BLs, freestream pressure gradients, and the evaluation of flow control schemes.

On the enhancement of boundary layer skin friction by turbulence: an angular momentum approach

Turbulence enhances the wall shear stress in boundary layers, significantly increasing the drag on streamlined bodies. Other flow features such as free stream pressure gradients and streamwise boundary layer growth also strongly influence the local skin friction. In this paper, an angular momentum integral (AMI) equation is introduced to quantify these effects by representing them as torques that alter the shape of the mean velocity profile. This approach uniquely isolates the skin friction of a Blasius boundary layer in a single term that depends only on the Reynolds number most relevant to the flow's engineering context, so that other torques are interpreted as augmentations relative to the laminar case having the same Reynolds number. The AMI equation for external flows shares this key property with the so-called FIK relation for internal flows (Fukagata et al., Phys. Fluids, vol. 14, 2002, pp. L73–L76). Without a geometrically imposed boundary layer thickness, the length scale in the Reynolds number for the AMI equation may be chosen freely. After a brief demonstration using Falkner–Skan boundary layers, the AMI equation is applied as a diagnostic tool on four transitional and turbulent boundary layer direct numerical simulation datasets. Regions of negative wall-normal velocity are shown to play a key role in limiting the peak skin friction during the late stages of transition, and the relative strengths of terms in the AMI equation become independent of the transition mechanism a very short distance into the fully turbulent regime. The AMI equation establishes an intuitive, extensible framework for interpreting the impact of turbulence and flow control strategies on boundary layer skin friction.

Development of an intermittency transport equation for modeling bypass, natural and separation-induced transition

The objective of this paper is to propose a new intermittency transport equation that is naturally capable of capturing the effects of free-stream turbulence and pressure gradient on bypass and natural transition without need for any extra parameters/terms to take into account the free-stream turbulence and the pressure gradient. This new intermittency transport equation is obtained by derivation and, in it, only its production term is modeled via two empirical functions in order to detect the onset location of transition and to control the growth rate of transition process. Only one sensing parameter is used to detect the transition onset for both natural and bypass transition. For the purpose of not altering the original form of the base turbulence model, the effective intermittency factor is used to describe the separation-induced transition. The base turbulence model remains unmodified in conjunction with the effective intermittency factor as a regulator to control the net turbulent generation rate. For the evaluation of model performance, the modeled intermittency equation is tested against (1) the transitional boundary layer on a flat plate with zero and non-zero pressure gradients, (2) the transitional flow over a compressor blade with a laminar separation bubble, and (3) the transitional flow over a wind turbine airfoil at various angles of attack. The present results are also compared to those of the transition model of Menter et al. [1] and those of the transition model of Langtry and Menter [2]. The evaluation results reveal that the new intermittency transport equation is capable of predicting the bypass, natural and separation-induced transition.

Adaptive detached eddy simulation of transition under the influence of free-stream turbulence and pressure gradient

Abstract

An accurate data base on laminar-to-turbulent transition in variable pressure gradient flows

An experimental data base on attached and separated-flow transitional boundary layers, under various levels of free-stream turbulence, Reynolds number and pressure gradient has been composed, with the aim of providing high-accuracy data and boundary conditions for development and testing of laminar-to-turbulent transition models. Experiments were carried out on the boundary layer developing on a flat plate installed within a channel with a variable opening angle. The test section imposes acceleration to the boundary layer followed by deceleration, which can be varied. Time Resolved Particle Image Velocimetry (TR-PIV) and Laser Doppler Velocimetry (LDV) data have been acquired on the boundary layer evolution, as well as the free-stream properties in terms of mean velocity and fluctuating velocity components. The overall test matrix spans 3 Reynolds numbers (70,000;150,000;220,000), 4 free-stream turbulence intensity levels (Tu=1.5;2.5;3.5;5%) and 4 pressure gradients (opening angle α=0;5;9;12deg). This large variation of flow parameters allows a gradual shift of the mode of transition from a bypass process in attached flow, occurring with zero (Blasius like) and mild adverse pressure gradients at high free-stream turbulence, to separated-flow transition, occurring with low Reynolds number, low free-stream turbulence intensity and elevated adverse pressure gradient.

By-pass transition control with a DBD plasma actuator model coupled with a laminar kinetic energy turbulence model

The effect of a DBD plasma actuator on the by-pass boundary layer transition control is numerically investigated. A two-equation DBD plasma actuator model is coupled with a three-equation eddy-viscosity turbulence model, which adopts the laminar kinetic energy concept. The investigated test-cases concern zero and variable freestream pressure gradient transitional flows on a flat plate with a sharp leading edge, which belong to the ERCOFTAC experimental database. The experimental data describe the transition characteristics with no plasma actuation and hence, they are used to assess the turbulence model behaviour and as a reference point in order to quantify the coupling effect of the plasma actuator model with the laminar kinetic energy concept. The investigation is focused on the effect of the varying plasma actuator voltage on transitional and turbulent boundary layer characteristics, such as the Reynolds-stresses, the turbulent dissipation and the laminar kinetic energy distributions. The results show that with the DBD actuator activated, the turbulent quantities are suppressed, the transition onset location moves downstream and a boundary layer transition delay is observed.

By-pass transition control with a DBD plasma actuator model coupled with a laminar kinetic energy turbulence model

The effect of a DBD plasma actuator on the by-pass boundary layer transition control is numerically investigated. A two-equation DBD plasma actuator model is coupled with a three-equation eddy-viscosity turbulence model, which adopts the laminar kinetic energy concept. The investigated test-cases concern zero and variable freestream pressure gradient transitional flows on a flat plate with a sharp leading edge, which belong to the ERCOFTAC experimental database. The experimental data describe the transition characteristics with no plasma actuation and hence, they are used to assess the turbulence model behaviour and as a reference point in order to quantify the coupling effect of the plasma actuator model with the laminar kinetic energy concept. The investigation is focused on the effect of the varying plasma actuator voltage on transitional and turbulent boundary layer characteristics, such as the Reynolds-stresses, the turbulent dissipation and the laminar kinetic energy distributions. The results show that with the DBD actuator activated, the turbulent quantities are suppressed, the transition onset location moves downstream and a boundary layer transition delay is observed.

Influence of pressure gradients on wall pressure beneath a turbulent boundary layer

This study investigates the effects of a pressure gradient on the wall pressure beneath equilibrium turbulent boundary layers. Excitation of the walls of a vehicle by turbulent boundary layers indeed constitutes a major source of interior noise and it is necessary to take into account the presence of a pressure gradient to represent the effect of the curvature of the walls. With this aim, large-eddy simulations of turbulent boundary layers in the presence of both mild adverse and mild favourable pressure gradients are carried out by solving the compressible Navier–Stokes equations. This method provides both the aeroacoustic contribution and the hydrodynamic wall-pressure fluctuations. A critical comparison with existing databases, including recent measurements, is conducted to assess the influence of a free stream pressure gradient. The analyses of wall-pressure spectral densities show an increase in the low-frequency content from adverse to favourable conditions, yielding higher integrated levels of pressure fluctuations scaled by the wall shear stress. This is accompanied by a steeper decay rate in the medium-frequency portion for adverse pressure gradients. No significant difference is found for the mean convection velocity. Frequency–wavenumber spectra including the subconvective region are presented for the first time in the presence of a pressure gradient. A scaling law for the convective ridge is proposed, and the acoustic domain is captured by the simulations. Direct acoustic emissions have similar features in all gradient cases, even if slightly higher levels are noted for boundary layers subjected to an adverse gradient.

Micro-slot injection into a boundary layer driven by a favourable pressure gradient

We investigate the effects of injection through a streamwise-aligned ‘micro-slot’ into a laminar boundary layer driven by a favourable pressure gradient of power-law type. The injection slot exists at all downstream locations, and is ‘micro’ in the sense that it has a finite spanwise width that is a fixed ratio of the local boundary-layer thickness. This approach is motivated by recent studies of micro-jets (of small spanwise and streamwise extents), which have indicated that for short spanwise scales, injection does not necessarily lead directly to separation. Injection in the absence of a free-stream pressure gradient has recently been analysed by Hewitt et al. (J Fluid Mech 822:617–639, 2017), and here we show that boundary layers in a favourable pressure gradient behave qualitatively differently. We present three-dimensional boundary-layer solutions affected by slot injection and contrast these with the corresponding zero pressure-gradient states. In the absence of a pressure gradient, injection results in low-speed streamwise-aligned streaks, where the amplitude and spanwise width of the injection determine the geometry of the streaks as one of the three possible types. The introduction of a favourable pressure gradient greatly reduces the spanwise extent of injection-driven streaks and removes the delineation between the three distinct flow regimes found in the zero pressure-gradient case. We present an asymptotic description in the limit of a large injection-slot width, thereby approaching the macro-slot limit from the micro-slot formulation. This description shows that not all injection rates and pressure gradients recover the expected Falkner–Skan solution at the centreline of the injection slot in the macro-slot limit. We explain this disagreement in terms of local spatial (cross flow) eigenmodes that are associated with a cross-flow collisional process at the centre of the injection slot.

Combined Effects of Freestream Pressure Gradient and Density Ratio on the Film Cooling Effectiveness of Round and Shaped Holes on a Flat Plate

The combined effects of a favorable, mainstream pressure gradient and coolant-to-mainstream density ratio have been investigated. Detailed film cooling effectiveness distributions have been obtained on a flat plate with either cylindrical (θ = 30 deg) or laidback, fan-shaped holes (θ = 30 deg and β = γ = 10 deg) using the pressure-sensitive paint (PSP) technique. In a low-speed wind tunnel, both nonaccelerating and accelerating flows were considered, while the density ratio varied from 1 to 4. In addition, the effect of blowing ratio was considered, with this ratio varying from 0.5 to 1.5. The film produced by the shaped hole outperformed the round hole under the presence of a favorable pressure gradient for all the blowing and density ratios. At the lowest blowing ratio, in the absence of freestream acceleration, the round holes outperformed the shaped holes. However, as the blowing ratio increases, the shaped holes prevent lift-off of the coolant and offer enhanced protection. The effectiveness afforded by both the cylindrical and shaped holes, with and without freestream acceleration, increased with density ratio.

Aerodynamic Characteristics of Steam Turbine Prismatic Blade Section

For the needs of high-performance steam turbines producer the data of a blade section measurement have been analyzed in detail using an experimental and numerical approach. The blade section is used on prismatic blades in high and medium pressure steam turbine parts. The linear blade cascade was tested at four pitch/chord ratios at two different stagger angles. The blade cascade was tested under two levels of Reynolds number in the range of output izentropic Mach numbers from 0.4 to 0.9.The inlet of the test section was measured pitch-wise by five-hole probe to determine the inlet flow angle. The free stream turbulence of inlet flow was determined at 2.5% what is very close to the operating conditions on first high pressure stages. Two-dimensional flow field at the center of the blades was traversed pitch-wise downstream the cascade by means of a five-hole needle pressure probe to find out the overall integral characteristics. The blade loading was measured throughout surface pressure taps at the blade center. An in-house code based on a system of Favre-averaged Navier-Stokes equation closed by non-linear two-equation EARSM k-ω turbulence model was adopted for the predictions. The code utilizes an algebraic model of bypass transition valid for both attached and separated flows taking into account the effect of free-stream turbulence and pressure gradient. Results are presented by integral characteristic in means of kinetic energy loss coefficient and velocity or pressure distribution in the blade wakes or on the blade surface. In this article, the effect of investigated criteria and comparison of experimental and numerical approach are presented and discussed.

A comparison of experimental and numerical studies performed on a low-pressure turbine blade cascade at high-speed conditions, low reynolds numbers and various turbulence intensities

This paper focuses on a comparison of experimental and numerical investigations performed on a low-pressure mid-loaded turbine blade at operating conditions comprised of a wide range of Mach numbers (from 0.5–1.1), Reynolds numbers (from 0.4e+5–3.0e+5), flow incidence (−15–15 degrees) and three levels of free-stream turbulence intensities (2, 5 and 10%). The experimental part of the work was performed in a high-speed linear cascade wind tunnel. The increased levels of turbulence were achieved by a passive grid placed at the cascade inlet. A two-dimensional flow field at the center of the blade was traversed pitch-wise upstream and downstream the cascade by means of a five-hole probe and a needle pressure probe, respectively. The blade loading was measured using the surface pressure taps evenly deployed at the blade mid-span along the suction and the pressure side. The inlet turbulence was investigated using the constant temperature anemometer technique with a dual sensor probe. Experimentally evaluated values of turbulent kinetic energy and its dissipation rate were then used as inputs for the numerical simulations. An in-house code based on a system of the Favre-averaged Navier-Stokes equation closed by a two-equation k-ω turbulence model was adopted for the predictions. The code utilizes an algebraic model of bypass transition valid both for attached as for separated flows taking in account the effect of free-stream turbulence and pressure gradient. The resulting comparison was carried out in terms of the kinetic energy loss coefficient, distributions of downstream wakes and blade velocity. Additionally a flow visualization was performed by means of the Schlieren technique in order to provide a further understanding of the studied phenomena. A few selected cases with a particular interest in the attached and separated flow transition are compared and discussed.

Nonlinear MHD Flow and Heat Transfer over a Power-Law Stretching Plate with Free Stream Pressure Gradient and Viscous Dissipation in Presence of Variable Thermal Diffusivity

The numerical analysis is carried out on steady nonlinear magnetohydrodynamic flow and heat transfer over a power-law stretching plate with free stream pressure gradient and viscous dissipation in the presence of variable thermal diffusivity and variable transverse magnetic field. The thermal diffusivity is assumed to vary as linear functions of temperature. Using similarity transformation, the nonlinear partial differential equations are converted into nonlinear ordinary differential equations. Numerical solutions of these equations are obtained with the help of Runge-Kutta shooting method. The effects of magnetic field, stretching parameter, Prandtl number, free stream velocity ratio, Eckert number and thermal diffusivity parameter on skin friction, velocity, rate of heat transfer and temperature are thoroughly discussed. It is found that the effect of magnetic field is to decrease the velocity and enhance the temperature.

Experimental evaluation and set-up of a new apparatus designed for transitional flow experiments

Experimental exercise has been conducted to validate the capability of a new test apparatus. The test stand has been designed and constructed at the laboratory of aerodynamics, University of Defence to carry out the experimental investigation of transitional flow prediction and development over flat plate. The test facility consists of a rectangular duct set on the suction side of air source apparatus. The working section is 2 m long with a cross section of 0.44 m in width and 0.25 m in height. The exercise is performed into two stages. In the first stage, the basic parameters such as freestream velocity, turbulence intensity and pressure gradient in streamwise direction were measured and manipulated to set- up acceptable values. Second stage of the exercise, the bottom wall of the test section was used as a flat plate model to conduct turbulent boundary-layer experiment. The characteristics of the boundary layer obtained by using the apparatus are represented by a qualitative and quantitative agreement with those predicted by boundary-layer theory for turbulent boundary layer while more improvements seems to be required to satisfy the rules of boundary layer stability experiments. The results are show a fair agreement for mean velocity profile, U� , boundary layer thickness, � , momentum thickness, , and skin friction coefficient, Cf

Heat transfer on a power law stretching sheet subjected to free stream pressure gradient

The present work deals with the numerical study of temperature distribution in the laminar boundary layer driven by the stretching boundary surface subjected to pressure gradient. The similarity transformation obeying the same power law based on composite reference velocity (union of velocities of the stretching boundary and free stream) has been employed that leads to a single set of equations, irrespective of the condition whether U w > U ∞ or U w < U ∞, containing three parameters: β measuring the stretch rate of the moving boundary, ε is the ratio of free stream velocity to composite reference velocity and Pr is the Prandtl number of the ambient fluid. The numerical solutions of the thermal boundary layer equations are obtained for three Prandtl numbers 0.7, 1.0 and 10 for 0 ⩽ ε ⩽ 1 and for 0 ⩽ β ⩽ 2. The heat transfer coefficient show appreciable dependence on the ratio of free stream velocity to union of velocities of the stretching surface boundary and free stream.

On the downstream development and breakup of systems of trailing-line vortices

The downstream evolution of two configurations of trailing-line vortex systems is considered and analysed from the point of view of bi-global instability. The results lead to predictions for the breakup of the systems considered, based primarily on stability analysis. Throughout, the analysis is entirely rational from the theoretical (asymptotic, large Reynolds number) point of view, with a relatively long developmental lengthscale in the streamwise direction for the base flow, and a relatively short streamwise wavelength for the bi-global stability analysis. As such, the stability modes are inviscid in nature, and therefore likely to be one of the dominant instability mechanisms. The issue of adverse streamwise freestream pressure gradients is also addressed, and it is suggested that these can lead to a rapid breakdown/up of a vortex system, analogous to the axisymmetric case discussed by Hall (Ann Rev Fluid Mech 4:195–218, 1972).

Correlations for modeling transitional boundary layers under influences of freestream turbulence and pressure gradient

This paper presents mathematical expressions for two significant parameters which control the onset location and length of transition in the γ– Re θ transition model of Menter et al. [Menter, F.R., Langtry, R.B., Volker, S., Huang, P.G., 2005. Transition modelling for general purpose CFD codes. In: ERCOFTAC International Symposium on Engineering Turbulence Modelling and Measurements]. The expressions are formulated and calibrated by means of numerical experiments for predicting transitional boundary layers under the influences of freestream turbulence and pressure gradient. It was also found that the correlation for transition momentum thickness Reynolds number needs only to be expressed in terms of local turbulence intensity, so that the more complex form that includes pressure gradient effects is unnecessary. Transitional boundary layers on a flat plate both with and without pressure gradients are employed to assess the performance of these two expressions for predicting the transition. The results show that the proposed expressions can work well with the model of Menter et al. (2005).

A Critical Assessment of Reynolds Analogy for Turbine Flows

The application of Reynolds analogy 2St/cf≅1 for turbine flows is critically evaluated using experimental data collected in a low-speed wind tunnel. Independent measurements of St and cf over a wide variety of test conditions permit assessments of the variation of the Reynolds analogy factor (i.e., 2St/cf) with Reynolds number, freestream pressure gradient, surface roughness, and freestream turbulence. While the factor is fairly independent of Reynolds number, it increases with positive (adverse) pressure gradient and decreases with negative (favorable) pressure gradient. This variation can be traced directly to the governing equations for momentum and energy which dictate a more direct influence of pressure gradient on wall shear than on energy (heat) transfer. Surface roughness introduces a large pressure drag component to the net skin friction measurement without a corresponding mechanism for a comparable increase in heat transfer. Accordingly, the Reynolds analogy factor decreases dramatically with surface roughness (by as much as 50% as roughness elements become more prominent). Freestream turbulence has the opposite effect of increasing heat transfer more than skin friction, thus the Reynolds analogy factor increases with turbulence level (by up to 35% at a level of 11% freestream turbulence). Physical mechanisms responsible for the observed variations are offered in each case. Finally, synergies resulting from the combinations of pressure gradient and freestream turbulence with surface roughness are evaluated. With this added insight, the Reynolds analogy remains a useful tool for qualitative assessments of complex turbine flows where both heat load management and aerodynamic efficiency are critical design parameters.