Trailing Edge Flow Research Articles

Structure and energetics of a turbulent trailing edge flow

Results from a direct numerical simulation (DNS) of turbulent flow over a rectangular trailing edge geometry are used to study energy transfers in detail. The numerical procedure employs a separate boundary layer simulation which is used to generate inflow turbulence and provide the inflow boundary condition data for the trailing edge flow simulation. The calculations are performed at a Reynolds number of 1000 based on the trailing edge thickness and free stream velocity. Characteristics of the vortex shedding are identified from instantaneous flow visualizations, two-point time correlations, and spectra. Turbulence kinetic energy production is found to be negative in the region behind the trailing edge, in agreement with simple analysis. The topology of the turbulence kinetic energy flux field is studied in conjunction with the production and dissipation, revealing pathways by which turbulence energy is transported from zones of creation to zones of destruction.

Embedded micromachined fiber-optic fabry-perot pressure sensors in aerodynamics applications

Small size, high bandwidth pressure sensors are required for instrumentation of probes and test models in aerodynamic studies of complex unsteady flows. Optical-fiber pressure sensors promise potential advantages of small size and low cost in comparison with their electrical counterparts. We describe miniature Fabry-Perot cavity pressure sensors constructed by micromachining techniques in a turbine test application. The sensor bodies are 500 /spl mu/m squared, 300 /spl mu/m deep with a /spl sim/2 /spl mu/m-thick copper diaphragm electroplated on one face. The sensor cavity is formed between the diaphragm and the cleaved end of a single mode fiber sealed to the sensor by epoxy. Each sensor is addressed interferometrically in reflection by three wavelengths simultaneously, giving an unambiguous phase determination; a pressure sensitivity of 1.6 radbar/sup -1/ was measured, with a typical range of vacuum to 600 kPa. Five sensors were embedded in the trailing edge of a nozzle guide vane installed upstream of a rotor in a full-scale turbine stage transient test facility. Pressure signals in the trailing edge flow show marked structure at the 8 kHz blade passing frequency. To our knowledge, this is the first report of sensors located at the trailing edge of a normal-sized turbine blade.

Direct Numerical Simulation of Turbulent Trailing-Edge Flow with Base Flow Control

Direct numericalsimulationhas been carried out for turbulent flow over a rectangular trailing edge at a Reynolds number of 1x10(3) (based on the freestream quantities and the trailing-edge thickness) and ratio of boundarylayerdisplacement thickness to trailing-edge thickness close to unity. Two types of flow control were studied: base transpiration and secondary splitter plate. Simulation of base transpiration was performed using different slit heights and volume flow rates. It was found that even small flow rates could produce significant changes in overallaerodynamic performance, measured, for example, by the base pressure coefficient. It was also found that for the same volume flow rate, a greater increase in base pressure (drag reduction) was obtained by blowing slowly through a wide slit rather than quickly through a narrowslit. The effectiveness of a secondary splitter plate located on the trailing-edge centerline was investigated by varying the plate length from one to five times the trailing-edge thickness. A significant increase in the base pressure coefficient (about 25%) was achieved, even with the shortest splitter plate equal to the trailing-edge thickness. The base pressure coeffi cient increased monotonically with the splitter plate length, and no intermediate maximum value was found.

Experimental investigation of trailing-edge devices at transonic speeds

AbstractThe influence of trailing-edge devices such as Gurney flaps and divergent trailing edges of different height on the aerodynamic performance of an aerofoil at transonic speeds has been investigated experimentally. The investigation has been carried out in the Transonic Wind Tunnel Göttingen (TWG) using the two-dimensional aerofoil model VC-Opt at freestream Mach numbers of M ε [0.755, 0.775, 0.790] and a Reynolds number of Re = 5.0 x 106.The results have shown that the trailing-edge devices increase the circulation of the aerofoil leading to a lift enhancement and pitching-moment decrease as well as an increase in minimum drag compared to the baseline configuration. The maximum lift-to-drag ratio is considerably improved and the onset of trailing-edge flow separation is shifted to higher lift. Besides the increased rear-loading, a downstream displacement of the shock provides the main lift enhancement in transonic flow.The simple Gurney flap provides the largest additional circulation of all geometries tested. The smoother turning of the flow due to the additional ramp of the divergent trailing edge leads to a smaller increase of circulation. Slightly less lift but considerably less viscous (pressure) drag is generated enhancing the maximum lift-to-drag ratio compared to the Gurney flap. The negative affect of the Gurney flap on the pitching moment is also reduced.For the high divergent trailing edges, different ramp slopes have a significant influence on the aerodynamic performance whereas at low device heights the influence is considerably diminished.The results show that the divergent trailing edge proves to be the better trailing-edge device at transonic speeds. The application as an element for an adaptive wing is generally possible.

Direct numerical simulation of turbulent trailing-edge flow with base flow control

Direct numerical simulation of turbulent trailing-edge flow with base flow control

Simulation and modelling of turbulent trailing-edge flow

Computations of turbulent trailing-edge flow have been carried out at a Reynolds number of 1000 (based on the free-stream quantities and the trailing-edge thickness) using an unsteady 3D Reynolds-Averaged Navier–Stokes (URANS) code, in which two-equation (k–e) turbulence models with various low-Re near wall treatments were implemented. Results from a direct numerical simulation (DNS) of the same flow are available for comparison and assessment of the turbulence models used in the URANS code. Two-dimensional URANS calculations are carried out with turbulence mean properties from the DNS used at the inlet; the inflow boundary-layer thickness is 6.42 times the trailing-edge thickness, close to typical turbine blade flow applications. Many of the key flow features observed in DNS are also predicted by the modelling; the flow oscillates in a similar way to that found in bluff-body flow with a von Karman vortex street produced downstream. The recirculation bubble predicted by unsteady RANS has a similar shape to DNS, but with a length only half that of the DNS. It is found that the unsteadiness plays an important role in the near wake, comparable to the modelled turbulence, but that far downstream the modelled turbulence dominates. A spectral analysis applied to the force coefficient in the wall normal direction shows that a Strouhal number based on the trailing-edge thickness is 0.23, approximately twice that observed in DNS. To assess the modelling approximations, an a priori analysis has been applied using DNS data for the key individual terms in the turbulence model equations. A possible refinement to account for pressure transport is discussed.

Instability of the flow in the vicinity of trailing edge of a class of thin aerofoils

A numerical study has been undertaken to investigate the notion of absolute/convective instability in laminar incompressible trailing edge flows past wedge-like shapes with curved boundaries of the form y= α(− x) m . The effects of various trailing edge shapes m and relative thickness α on the flow separation and the development of instabilities in the vicinity of trailing edge are investigated. The nonlinear viscous–inviscid interaction equations, which have been derived by means of the asymptotic theory of flow separation, are solved first numerically to construct genuine mean velocity profiles representing the correct flow in the vicinity of the trailing edge. The absolute/convective nature of the asymptotically formed velocity profiles via a composite expansion is then ascertained by using a spatio-temporal analysis based on the Briggs–Bers pinching criterion. Although no absolute growth is encountered upstream of the trailing edge of the airfoil shapes considered, in particular the wake region behind the trailing edge of Joukowski type profiles is found to be persistently susceptible to absolute instability. It is found that separation is enhanced as the relative thickness of the airfoil gets bigger. This, in turn, is shown to lead to an additional enhancement of the absolute instability character by both increasing the absolute growth rate as well as the extent of the unstable region. Shedding frequency of the Karman vortex street is also determined behind the trailing edge shapes considered.

Direct Numerical Simulation of Turbulent Flow over a Rectangular Trailing Edge

This paper describes a direct numerical simulation (DNS) study of turbulent flow over a rectangular trailing edge at a Reynolds number of 1000, based on the freestream quantities and the trailing edge thickness h; the incoming boundary layer displacement thickness '* is approximately equal to h. The time-dependent inflow boundary condition is provided by a separate turbulent boundary layer simulation which is in good agreement with existing computational and experimental data. The turbulent trailing edge flow simulation is carried out using a parallel multi-block code based on finite difference methods and using a multi-grid Poisson solver. The turbulent flow in the near-wake region of the trailing edge has been studied first for the effects of domain size and grid resolution. Then two simulations with a total of 256 2 512 2 64 (~ 8.42106) and 512 2 1024 2 128 (~ 6.72107) grid points in the computational domain are carried out to investigate the key flow features. Visualization of the instantaneous flow field is used to investigate the complex fluid dynamics taking place in the near-wake region; of particular importance is the interaction between the large-scale spanwise, or Karman, vortices and the small-scale quasi-streamwise vortices contained within the inflow boundary layer. Comparisons of turbulence statistics including the mean flow quantities are presented, as well as the pressure distributions over the trailing edge. A spectral analysis applied to the force coefficient in the wall normal direction shows that the main shedding frequency is characterized by a Strouhal number based on h of approximately 0.118. Finally, the turbulence kinetic energy budget is analysed.

Computation of trailing-edge flow and noise using large-eddy simulation

Computation of trailing-edge flow and noise using large-eddy simulation

Experimental investigation of the unsteady rotor aerodynamics of a transonic turbine stage

This paper describes some results of a large experimental programme on unsteady flow through the rotor of a transonic turbine stage in the large Compression Tube Turbine Facility at the von Karman Institute for Fluid Dynamics. The tests were carried out as part of a Brite EURAM project. The test programme covered the investigation of the effects of a variation in the rotational speed of the rotor, the axial stator-rotor distance and the stator trailing-edge coolant flow ejection. The paper aims at presenting the measurements of the relative inlet total pressure and the rotor blade surface pressure at rotor mid-span.

The effect of smooth deceleration of the external stream on an aligned flat-plate boundary layer

A numerical and analytical investigation of the non-interactive unsteady (Prandtl) boundary layer is undertaken for an unsteady external mainstream flow past an aligned finite flat plate, where initially the mainstream flow is steady and uniform. In contrast to previous investigations for flow past smooth bodies, the importance of the trailing edge is clearly identified, in particular with regard to the appearance of reversed flow, both on the plate and in the wake. A small-time analytical solution is presented first to consider the effect of the plate smoothly decelerating. This is then combined with a numerical solution for a parametric family of mainstreams which vary sinusoidally with time and hence subject the flow to varying degrees of deceleration and acceleration. Above a critical parametric value, and at a finite time, reversed flow appears near the trailing edge, before moving upstream along the plate. Various numerical solutions are presented, under increasing grid resolution, together with an analysis of the trailing-edge flow near the critical time when reversed flow first enters. The study here tends to highlight the appearance of strong short-wave instabilities.

Transonic trailing-edge flow

The structure of the flowfield in the vicinity of the trailing edge of a flat plate at zero incidence in mixed transonic flow has been studied using viscous-inviscid interaction methods. The resulting nonlinear partial differential equations governing the flow were solved numerically using finite-difference methods for a range of values of a transonic similarity parameter which occurs in the mathematical formulation of the problem. Of special interest is the formula for the total drag coefficient of the plate as a function of the similarity parameter. Values of the similarity parameter have been chosen to ensure that subcritical, supercritical and mixed flow regimes are all considered.

Effect of riblets on the drag of a body of revolution with trailing-edge flow separation

The results of measurements of the drag of axisymmetric bodies with smooth and ribbed central cylindrical sections and affinely similar trailing edges of various lengths are given. The experimental data were obtained for zero angle of attack and the numbers M=0.25–0.85 and Re=107–2.4·107 (calculated on the basis of the length of the body without the trailing section). The trailing-edge flow separation was visualized by the oil film method. It is shown that ribbing can lead to a decrease in drag due not only to a reduction in turbulent friction but also to reduction of the separation zone on the smooth trailing section of the body.

In-Flight pressure measurements on a subsonic transport high-lift wing section

The NASA Langley Transport Systems Research Vehicle (B737-100 aircraft) was used to obtain in-flight flow characteristics including surface pressures and surface shear stresses for a full-chord wing section, including the slat, main-wing, and triple-slotted, Fowler-flap elements. Chordwise pressure distributions were obtained at the 58% semispan station using thin pressure belts. Flow characteristics observed in the chordwise pressure distributions included leading-edge regions of high-subsonic flows, leading-edge attachment-line locations, slat and main-wing cove-flow separation and reattachment, and trailing-edge flow separation. In addition, surface shear-stress measurements were made using Preston-tube probes on each element. Computational analysis of the in-flight pressure measurements using two-dimensional, viscous-flow, multielement methods and simplesweep theory showed reasonable agreement. However, overprediction of the suction pressures on the flap elements indicates a need for more detailed (off-surface) measurements of the flow and the in-flight flap geometry to aid modeling of the complex three-dimensional flowfield.

An experimental study of the trailing edge flow of an NLR 7702 airfoil, using laser-Doppler anemometry

Detailed measurements of mean flow and turbulence quantities have been performed in the vicinity of the trailing edge of a supercritical NLR 7702 airfoil using laser-Doppler anemometry (LDA). The two-dimensional (2-D) model, put at an angle of attack of 4°, was tested at a Reynolds number of 1.47 × 10 6. Under these conditions the upper surface boundary layer is close to separation at the trailing edge. Downstream of the trailing edge, both shear layers merge into a strongly curved, highly asymmetric near wake. Our main objective is to provide reliable experimental data for the development of turbulence closure models for trailing edge flows and to offer validation of computational methods. Besides the presentation of measured flow quantities, special attention is given to evaluate the accuracy and self-consistency of the data set obtained.

Preconditioned Conjugate Gradient Methods for the Navier-Stokes Equations

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several pre-conditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Numerical investigation of laminar separated trailing-edge flows

An efficient time-marching numerical method has been developed for solving problems involving supersonic laminar separated trailing-edge flows using a triple-deck formulation. The accuracy of the numerical method was tested for the case of a flat plate embedded in a supersonic flow at angles of incidence below stall. A range of numerical solutions is presented for angles of incidence beyond stall in the form of streamline and shear contour plots. The trailing-edge shear on the side of the plate where separation occurs reaches an asymptotic value as the angle of incidence is increased; beyond this point numerical instability was encountered.

Experimental investigation of loading effects on compressor trailing-edge flowfields

This article describes an experimental investigation of the flowfield development in the trailing-edge region of a simulated compressor airfoil having pressure-to-suction surface loading. The study represents a continuation of an effort to study turbulent, separated airfoil trailing-edge flows. Previous experimentation had addressed airfoil trailing-edge separation phenomena in the absence of pressure loading. The objective of the current study was to explore the effects of loading and thereby to provide a more realistic simulation of the compressor airfoil flow environment. The present approach was to conduct a large-scale cascade simulation of the airfoil trailingedge flowfield for both a nominal design condition and a higher loading off-design condition. For the design condition, the airfoil boundary layers separated on the blunt trailing edge. For the off-design condition, separation occurred on the suction surface upstream of the trailing edge. A principal result of the study was that pressure loading was found to alter the trailing-edge time mean velocity field from that observed in the previous unloaded airfoil experiment. The relative base pressure for the nominal design condition was unaltered from the unloaded experiment but significantly lower for the off-design condition. Increased loading was found to induce greater cascade exit flow deviation from the exit metal angle, thus, reducing the relative cascade flow turning.

Boundary layer flow noise—The direct radiation

The farfield sound radiation due to the transitional and turbulent boundary layer flow over a rigid, finite body of revolution is addressed quantitatively. Three statistically independent sources of flow noise are analyzed; namely, the intermittent laminar-to-turbulent transition zone that occurs near the nose, the fully developed turbulent boundary layer that covers nearly all of the body surface, and the unsteady trailing edge flow that occurs on the body stabilizer fins. The modeling is used to predict the radiated noise spectra measured in a deep lake along the trajectory of a test body that was released from the bottom and propelled by buoyancy. These experimental data are from the Huddle and Skudrzyk [J. Acoust. Soc. Am. 46, 130–157 (1969)] flow noise experiments. In these experiments the radiated noise was found to be independent of the body composition (both metal and wooden units were used) and the authors concluded that flow unsteadyness was the primary source of farfield radiation. The predictions presented here support that conclusion in that the transition zone and trailing edge flows are very unsteady and their acoustic emissions are significantly more intense than those from the relatively stable turbulent boundary layer flow. [ Work supported by Applied Research Laboratory under contract with U. S. Navy.]

The Trailing Edge Loss of Transonic Turbine Blades

Trailing edge loss is one of the main sources of loss for transonic turbine blades, contributing typically 1/3 of their total loss. Transonic trailing edge flow is extremely complex, the basic flow pattern is understood but methods of predicting the loss are currently based on empirical correlations for the base pressure. These correlations are of limited accuracy. Recent findings that the base pressure and loss can be reasonably well predicted by inviscid Euler calculations are justified and explained in this paper. For unstaggered choked blading, it is shown that there is a unique relationship between the back pressure and the base pressure and any calculation that conserves mass, energy and momentum should predict this relationship and the associated loss exactly. For realistic staggered blading, which operates choked but with subsonic axial velocity, there is also a unique relationship between the back pressure and the base pressure (and hence loss) but the relationship cannot be quantified without knowing a further relationship between the base pressure and the average suction surface pressure downstream of the throat. Any calculation that conserves mass, energy and momentum and also predicts this average suction surface pressure correctly will again predict the base pressure and loss. Two-dimensional Euler solutions do not predict the suction surface pressure exactly because of shock smearing but nevertheless seem to give reasonably accurate results. The effects of boundary layer thickness and trailing edge coolant ejection are considered briefly. Coolant ejection acts to reduce the mainstream loss. It is shown that suction surface curvature downstream of the throat may be highly beneficial in reducing the loss of blades with thick trailing edges operating at high subsonic or low supersonic outlet Mach numbers.