Research on data assimilation strategy of turbulent separated flow over airfoil

In order to increase the accuracy of turbulence field reconstruction, this paper combines experimental observation and numerical simulation to develop and establish a data assimilation framework, and apply it to the study of S809 low-speed and high-angle airfoil flow. The method is based on the ensemble transform Kalman filter(ETKF) algorithm, which improves the disturbance strategy of the ensemble members and enhances the richness of the initial members by screening high flow field sensitivity ...     

Open and closed-loop experiments to identify the separated flow dynamics of a thick turbulent boundary layer

Open and closed-loop flow control experiments were performed on the transient attachment and separation mechanisms of a thick turbulent boundary layer (TBL). Without actuation, the TBL is subjected to an adverse pressure gradient and separates downstream of a sharp variation in the wall geometry. Departing from a given geometry and steady operations of vortex generator actuators, the control objective was to attach the flow in the separated region with a minimum of injected fluid using adaptation of the closed-loop control. The large scale of the facility (i.e., δ = 20 cm upstream of separation) induces large time scales and large Reynolds numbers of the flow to be controlled. It is found to consequently induce large time scales of the separation/attachment mechanisms, making the dynamic closed-loop implementation easier. Open-loop tests were first performed to extract the adequate input/output variables for closed-loop implementations. The chosen input variable was the Duty Cycle, DC, which enables sending of a control action at least 10 times faster than the time scales of the attachment/separation process. The chosen output variable was the voltage signal from a hot-film probe located on the flap which characterizes the degree of separation. In open loop, both the large scale (i.e., large time scales) of the present facility (Carlier and Stanislas in J Fluid Mech 535(36):143–188, 2005) and the well-defined excitation (Braud and Dyment in Phys Fluids 24:047102, 2012) help to extract the different time scales involved and to identify the whole system (actuators, baseline flow and sensor). Three Reynolds numbers based on the momentum thickness of the boundary layer near the actuators and upstream of separation were investigated (Re _θ  = 7,500, 10,500 and 12,600) through variation of the free-stream velocity (U _∞ = 5, 8, 10 m/s). These three systems were found to behave like first-order linear systems, with coefficients that need to be adapted depending on the Reynolds number. From Re _θ  = 7,500 to Re _θ  = 12, 600, the time scale and static gain of the linear system needed to be almost doubled. A simple controller (Proportional-Integral) was implemented in closed-loop configuration, improving the reactivity of the system. Robustness was tested by varying the free-stream velocity. Closed-loop control based on a fixed reference was unsuccessful as it failed to account for the effect of the Reynolds number. This was successfully overcome by tracking a given state of the flow using a simple P controller to adapt the reference according to variations of Re. The P controller, acting on the DC variable, compensates the corresponding variations of VR (ratio between the free-stream and the jet exit velocity).     

Laminarization of boundary layer flow on a vibrating wing

A new type of Tollmien-Schlichting wave excitation, experimentally detected in [6] in investigating the unsteady perturbation field downstream from roughness on the surface of a vibrating wing, is studied. It is shown that the generation mechanism consists in the nonlinear interaction between the unsteady disturbance produced by the vibrations of the smooth wall and the steady nonuniformity of the boundary layer above the roughness.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 26–34, March–April, 1993.     

Scaling of the near-wall layer beneath turbulent separated flow

This paper is a continuation of an earlier paper [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438] in which it is proposed that each Reynolds stress has its own velocity scale. Two of these, $u_{\tau }^{\prime }$ and $w_{\tau }^{\prime }$, are directly related by definition to the r.m.s. of the wall-shear-stress fluctuations (${\tau }_x$ and ${\tau }_z$) in the streamwise and transverse directions. They are also velocity scales for the true dissipation of the turbulent kinetic energy and the Kolmogorov velocity and length scales at the surface. From asymptotic considerations it is shown that the other two scales are related to averages involving instantaneous gradients of wall-shear-stress fluctuations. The measurements, made using pulsed-wire anemometry into the viscous sublayer, show that $u_{\tau }^{\prime }$ and $w_{\tau }^{\prime }$ are also the velocity scales for the respective streamwise and transverse fourth-order velocity moments, together with the viscous velocity scale ($\nu /y$). Normalised, the fourth-order moments show an inner-layer-like behaviour independent of both position and direction, like that seen in the second-order moments [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438]. However, not surprisingly, the third order moments exhibit an effect of mean shear, seen in the skewing of the probability distributions. Though not measured directly, the measurements imply the behaviour of the averaged products of fluctuations in wall-shear-stress and wall-pressure-gradient ($\overline{{\tau }_x\partial p/\partial x}$ and $\overline{{\tau }_z\partial p/\partial z}$). Normalised, they also are independent of position and direction. Some of the results presented apply more generally to the near-wall region beneath turbulent flow.     

Cone in a supersonic flow near a surface with a turbulent boundary layer

The published information about the interaction of incident shocks and a turbulent boundary layer relate to cases of a thin boundary layer ( 1–3 mm) on a flat surface. The present study relates to supersonic flow with Mach number M = 3 and stagnation pressure p₀=1.2 MPa past cones near a surface with a thick boundary layer formed on a plate abutting the lower edge of a plane nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 177–180, July–August, 1991.     

Design and optimization of a two-element wing airfoil in a subsonic viscous flow

A numerical and analytical solution of the problem of designing a two-element wing airfoil providing maximum lift-drag ratio in a subsonic viscous flow is presented. In order to bring the theoretical results closer to the facts, viscosity and compressibility are taken into account within the framework of boundary layer theory and the Chaplygin gas model, respectively.     

A study of a turbulent boundary layer in stalled-airfoil-type flow conditions

The experimental study of the turbulent boundary layer under external flow conditions similar to those found on the suction side of airfoils in trailing-edge post-stall conditions has been performed. Detailed boundary layer measurements were carried out with a PIV system and a two-sensor wall probe. They cover the region downstream of the suction peak where the boundary layer is subjected to a very strong adverse pressure gradient and has suffered from an abrupt transition from strong favorable to strong adverse pressure gradients. The experiments show that in spite of these severe conditions, the boundary layer is surprisingly able to recover a state of near-equilibrium before separating. In this near-equilibrium zone, the mean velocity defect and all the measured Reynolds stresses are self-similar (in the outer region) with respect to the outer scales δ and U _e δ*/δ. The mean momentum balance indicates that for the upper half of the outer region, the advection terms dominate all the stress-gradient terms in the zone prior to separation. A large portion of the outer region has therefore become essentially an inertial flow zone where an approach toward equilibrium is expected.An erratum to this article can be found at     

Two-phase measurements of saltating turbulent boundary layer flow

Mean wind and particle speed measurements as functions of heigh were made for a saltating turbulent boundary layer flow. An exponential dependence of particle flux with height above the surface was found independent of windspeed and particle size. Particle-speed distributions as functions of height above the surface were measured for experiments conducted at two ambient pressures: atmospheric pressure and approximately 1% atmospheric pressure. The wind was shown to be a more efficient mover of particles at atmospheric pressure.High-speed motion pictures of saltating ground walnut shells (of diameter 500–1500 μm and density 1.1 g/cm³) were taken in an environmental wind tunnel to simulate the planetary boundary layer. These experiments verify the existence and magnitude of particle spin rates proposed by White & Schulz (1977). There was remarkable agreement between numerical trajectory solutions, including the spin effect, and the filmed trajectories. An observation was made that not all particles spin exclusively in the vertical longitudinal plane (in the direction of flow). At low pressures (0.6 kPa) the effect of spin forces on the particle's trajectory was shown to have little influence and was verified by a theoretical force ration balance of spin to drag force.     

The rapid expansion of a turbulent boundary layer in a supersonic flow

Rapid Distortion Approximations (RDA) may be used to simplify the Reynolds stress equations in rapidly distorted flows, as suggested by Dussauge and Gaviglio (1987). These approximations neglect diffusive and dissipative terms while retaining the production and pressure terms. The retained terms are then modeled as functions of the Reynolds stress tensor and gradients of the mean flow. The models for the pressure-strain term as developed by Lumley (1978) and Shih and Lumley (1985) are evaluated by comparing the calculated results with experimental data for the case of a Mach 2.84 turbulent boundary layer in a 20° centered expansion. The agreement between computed and experimentally obtained Reynolds stresses was found to be encouraging.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This work was supported by the U.S. Air Force under AFOSR Contract 89-0420. Monitored by Dr. James McMichael.     

Prediction of unsteady,separated boundary layer over a blunt body for laminar,turbulent, and transitional flow

The focus of this paper is to study the ability of unsteady RANS‐based CFD to predict separation over a blunt body for a wide range of Reynolds numbers particularly the ability to capture laminar‐to‐turbulent transition. A perfect test case to demonstrate this point is the cylinder‐in‐crossflow for which a comparison between experimental results from the open literature and a series of unsteady simulations is made. Reynolds number based on cylinder diameter is varied from 10⁴ to 10⁷ (subcritical through supercritical flow). Two methods are used to account for the turbulence in the simulations: currently available eddy–viscosity models, including standard and realizable forms of the k–ε model; and a newly developed eddy–viscosity model capable of resolving boundary layer transition, which is absolutely necessary for the type and range of flow under consideration. The new model does not require user input or ‘empirical’ fixes to force transition. For the first time in the open literature, three distinct flow regimes and the drag crisis due to the downstream shift of the separation point are predicted using an eddy–viscosity based model with transition effects. Discrepancies between experimental and computational results are discussed, and difficulties for CFD prediction are highlighted. Copyright © 2004 John Wiley & Sons, Ltd.     

Regularization modeling for LES of separated boundary layer flow

Regularization models for the turbulent stress tensor are applied to mixing and separated boundary layers. The Leray and the NS-α models in large-eddy simulation (LES) are compared to direct numerical simulation (DNS) and (dynamic) eddy-viscosity models. These regularization models are at least as accurate as the dynamic eddy-viscosity model, and can be derived from an underlying dynamic principle. This allows one to maintain central transport properties of the Navier-Stokes equations in the model and to extend systematically toward complex applications. The NS-α model accurately represents the small-scale variability, albeit at considerable resolution. The Leray model was found to be much more robust, allowing simulations at high Reynolds number. Leray simulations of a separated boundary layer are shown for the first time. The strongly localized transition to turbulence that arises under a blowing and suction region over a flat plate was captured accurately, quite comparable to the dynamic model. In contrast, results obtained with the Smagorinsky model, either with or without Van Driest damping, yield considerable errors, due to its excessive dissipation.     

Interaction of a turbulent boundary layer with a shock wave at transonic flow velocities

An asymptotic theory of the interaction of a turbulent boundary layer on a plate with a normal shock wave of low intensity has been constructed in various studies [1–4] under the assumption that the averaged velocity of the particles in the boundary layer in front of the interaction region satisfies a logarithmic law. In the present paper a different approach to this problem is proposed based on a power law of the velocity in the undisturbed boundary layer. The obtained results give different estimates for not only the sizes of the characteristic flow regions in the interaction region but also for the shock intensity leading to boundary layer separation.     

Influence of surface roughness on anisotropy in a turbulent boundary layer flow

The departure from isotropy of turbulent boundary layers over a smooth and a rough wall is presented. The experimental data are analyzed using an anisotropic invariant map. It is shown that the k-type roughness is characterized by a reduced anisotropy of the Reynolds stress tensor. Moreover, the approximation of the diffusive transport of u and v developed in the Hanjalic-Launder numerical model is compared with the experimental results over a smooth and a rough wall. Diffusive transport of u and v is modeled more accurately in the case of the rough surface than in the case of the smooth surface, which can be attributed to the more isotropic behavior of the Reynolds stress tensor for the structures in the rough-wall layer.     

Tomographic PIV investigation of coherent structures in a turbulent boundary layer flow

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in the logarithmic region of the turbulent boundary layer in a water tunnel.The Reynolds number based on momentum thickness is Reθ = 2 460.The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low speed fluid,which is flanked on either side by highspeed ones.Statistical support for the existence of hairpins is given by conditional averaged eddy within an increasing spanwise width as the distance from the wall increases,and the main vortex characteristic in different wall-normal regions can be reflected by comparing the proportion of ejection and its contribution to Reynolds stress with that of sweep event.The pre-multiplied power spectra and two-point correlations indicate the presence of large-scale motions in the boundary layer,which are consistent with what have been termed very large scale motions(VLSMs).The three dimen-sional spatial correlations of three components of velocity further indicate that the elongated low-speed and highspeed regions will be accompanied by a counter-rotating roll modes,as the statistical imprint of hairpin packet structures,all of which together make up the characteristic of coherent structures in the logarithmic region of the turbulent boundary layer(TBL).     

Effect of a local stationary flow disturbance on separated boundary layer stability

The separated flow past a transverse barrier on a plate surface is modeled in a wind tunnel. The linear stability of the two-dimensional laminar flow in the separation zone is investigated in the presence of a stationary disturbance imposed on the flow and concentrated in a narrow spanwise region. It is experimentally shown that the local flow nonuniformity leads to a change in the flow stability features, such as the frequencies of the growing oscillations, their growth rate, and the dispersion characteristics. As a result, the transverse velocity gradients induced in the separation zone exert a strong destabilizing influence on the flow. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 174–178, January–February, 2000. The study was carried out with the support of the INTAS Foundation under grant No, 96-2225.     

Visualization of flow structures in a turbulent boundary layer using a new technique

In this paper, an experimental investigation on the flow structures in a turbulent boundary layer employing a special laser light sheet-Hydrogen bubble flow visualization technique is described. It is observed that the high/low speed streaks are directly related to the hairpin or horseshoe-like vortices. This observation can give a better understanding of the physical mechanism in the turbulent boundary layer. Fluid Mechanic Institute, BUAA     

Computation of internal turbulent flow with a large separated flow region

An implicit two-equation turbulence solver, KEM. in generalized co-ordinates, is used in conjunction with the three-dimensional incompressible Navier–Stokes solver, INS3D, to calculate the internal flow in a channel and a channel with a sudden 2:3 expansion. A new and consistent boundary procedure for a low Reynolds number form of the κ-ε turbulence model is chosen to integrate the equations up to the wall. The high Reynolds number form of the equations is integrated using wall functions. The latter approach yields a faster convergence to the steady-state solution than the former. For the case of channel flow, both the wall-function and wall-boundary-condition approaches yield results in good agreement with the experimental data. The back-step (sudden expansion) flow is calculated using the wall-function approach. The predictions are in reasonable agreement with the experimental data.