Direct Numerical Simulation of Turbulent Flow over a Rectangular Trailing Edge

Liquid film atomization from trailing edges is found in numerous applications. These include air blast atomization in pre-filming type fuel injectors and shedding from airfoils. This study investigates the effect of trailing edge thickness on liquid sheet breakup and droplet formation using NACA0012 airfoils with rounded trailing edges of 0.5 mm, 1.0 mm, and 2.0 mm, in high-speed airflow of up to 175 m/s. Water was introduced on the airfoil surface through 26 holes, each 0.5 mm in diameter and spaced 1 mm apart. These holes were located at 65 mm upstream of the trailing edge along the approximately 100 mm chord length. Three liquid flow rates, i.e., 1.4 cm3/(s·cm), 2.0 cm3/(s·cm), and 2.6 cm3/(s·cm) were tested. A variety of experimental techniques were implemented to analyze liquid film breakup and droplet behavior. High-speed video imaging captured film flow on the surface, the accumulation of liquid, ligament formation, and breakup at the trailing edge. Microscopic high-speed imaging was used to observe droplet behavior as a function of distance downstream of the trailing edge. This imaging reveals the transition from ligament formation to secondary atomization to the final droplet size distribution with downstream distance. At 70 mm downstream, atomization is essentially complete, and Laser Diffraction is also used to measure droplet Sauter mean diameters (SMD). The results show that thicker trailing edges and higher liquid mass flow rates promote liquid accumulation at the trailing edge. This, in turn, leads to increased ligament length and sheet breakup time. In the region just downstream of the ligament breakup, droplet sizes increase with increasing trailing edge thickness and liquid volume flow rate. Once the secondary atomization is complete (∼70 mm from the trailing edge), the drop sizes were found to be less affected by the trailing edge thickness and liquid flow and mainly determined by the air velocity. An analysis of variance was performed and a model to predict SMD as a function of weber number, air to liquid mass flow rate, downstream distance and trailing edge thickness was developed. Liquid film thickness as a characteristics length scale was selected as it directly influences the liquid accumulation and maximum ligament breakup length.

Combustion in a CI engine is initiated by self-ignition of fuel–air mixture caused by high pressure and high temperature; a process known as autoignition. Autoignition is a challenging problem to simulate as the temperature increases from initial temperature to the adiabatic flame temperature in a very short duration. Numerical study of a turbulent flow using RANS/LES encounters a closure problem. Accuracy of closure models can be improved through experimental results, theoretical reasoning and direct numerical simulation (DNS) data. A review of DNS of autoignition in a turbulent non-premixed medium is presented in this chapter. As observed from DNS study, autoignition sites in a turbulent non-premixed medium are not randomly distributed but follow a pattern in the mixture fraction-scalar dissipation rate space. Turbulent flow is always three-dimensional in nature. 2D DNS of autoignition shows that ignition delay time increases with increase in initial turbulence intensity, which contradicts with the experimental observation. 3D DNS of autoignition resolves this conflict. The conflict is mainly due to the absence of vortex-stretching phenomenon in 2D DNS. Homogeneous charge compression ignition (HCCI) is being considered as one of the strategies toward improving performance of conventional CI engines. However, HCCI engines suffer from drawbacks like lack of control over combustion and limited operating regime. One of the modifications suggested in the HCCI technology to overcome these drawbacks is the use of stratification in the fuel–air mixture. Therefore, a few DNS studies on autoignition in the stratified medium have been discussed here. Further, discussion on the conditional moment closure (CMC) model and its validation using DNS data has been presented. Ignition delay time predicted by CMC was found to be in good agreement with DNS predictions.

The effect of nozzle trailing edge thickness on broadband acoustic radiation and the production of tones is investigated for coannular nozzles. Experiments were performed for a core nozzle trailing edge thickness between 0.38 mm and 3.17 mm. The on-set of discrete tones was found to be predominantly affected by the velocity ratio, the ratio of the fan velocity to the core velocity, although some dependency on trailing edge thickness was also noted. For a core nozzle trailing edge thickness greater than or equal to 0.89 mm, tones were produced for velocity ratios between 0.91 and 1.61. For a constant nozzle trailing edge thickness, the frequency varied almost linearly with the core velocity. The Strouhal number based on the core velocity changed with nozzle trailing edge thickness and varied between 0.16 and 0.2 for the core nozzles used in the experiments. Increases in broadband noise with increasing trailing edge thickness were observed for tone producing and non-tone producing conditions. A variable thickness trailing edge (crenellated) nozzle resulted in no tonal production and a reduction of the broadband trailing edge noise relative to that of the corresponding constant thickness trailing edge.

An experimental study of a high-Reynolds-number turbulent wake in supersonic flow is performed using space and space–time correlation measurements by means of hot-wire anemometry. The correlations for the streamwise component of the mass-flux fluctuations are given for six stations starting from the trailing edge down to the asymptotic part. The validity of the Taylor's hypothesis is tested, the convection velocities are determined and the downstream evolution of the optimum space–time correlation is given; the frequency spectra are discussed and the integral lengths are analysed. Finally, the three-dimensional isocorrelation surfaces are given at the six test stations and discussed in relation to classical incompressible-flow results. The downstream evolution of the correlations shows that the two sides of the wake are statistically independent near the trailing edge, and a statistical link is gradually established during the wake development. A three-zonal description of wakes generated by fully developed turbulent boundary layers applies as well for mean quantities (velocity, width) as for turbulence correlations. In the near-wake region the overall structure of the isocorrelation curves is close to that observed in turbulent boundary layers in incompressible flows; some low-frequency phenomena are observed in this region. In the latest part of the wake, an asymptotic state is reached for all the correlation characteristics; the final state reached is not explained by the double-roller-eddy model established for lower-Reynolds-number wakes; it appears that wakes generated by fully turbulent boundary layers behave quite differently from initially laminar wakes, and new turbulent structure models for high-Reynolds-number wakes are to be devised.

Impact of unresolved smaller scales on the scalar dissipation rate in direct numerical simulations of wall bounded flows

Our main objective of this study is to clarify the energy transfer near the isothermal and adiabatic walls in the compressible turbulent flows. To this end we investigate the turbulent kinetic, mean kinetic and internal energy budgets using two cases of direct numerical simulation (DNS), Case 1 and Case 2. Case 1 is the compressible turbulent flow between isothermal walls and Case 2 is one between adiabatic and isothermal walls. In Case 1 and Case 2, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5 and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3 000. Moreover, two cases of DNS of the incompressible turbulent channel flow with the passive scalar transport, Case A and Case B, are carried out for comparing with the compressible one. The wall boundary conditions of Case A and Case B correspond to those of Case 1 and Case 2, respectively. In Case A and Case B, the Reynolds number based on the friction velocity, the channel half-width, and the kinematic viscosity is 150. The main results are as follows: (1) The turbulent and mean kinetic energy budgets of compressible turbulent channel flow agree well with the data of the incompressible one, when these profiles are scaled by the local mean variables. (2) The compressibility term of turbulent energy equation is very small and that of mean kinetic energy equation is small near the wall. The direction of energy transfer of these terms near the isothermal wall is opposite to that near the adiabatic wall. (3) The compressible part of the turbulent energy dissipation is not negligible near the isothermal wall, while it is negligible near the adiabatic wall. (4) The compressible part of the mean kinetic energy dissipation is negligible near the isothermal and adiabatic walls.

Conventional airliners use two to four engines in a Cayley-type arrangement to provide thrust, and the thrust is concentrated right behind the engine. Distributed propulsion is the idea of redistributing the thrust across most, or all, of the wingspan of an aircraft. This can be accomplished by using several large engines and using a duct to spread out the exhaust flow to form a jet-wing or by using many small engines spaced along the span of the wing. Jet-wing distributed propulsion was originally suggested as a way to improve propulsive efficiency. A previous study at Virginia Tech assessed the potential gains in propulsive efficiency. The purpose of this study was to assess the performance benefits of jet-wing distributed propulsion. The Reynolds-averaged, finitevolume, Navier-Stokes code GASP was used to perform parametric computational fluid dynamics (CFD) analyses on two-dimensional jet-wing models. The jet-wing was modeled by applying jet boundary conditions on the trailing edges of blunt trailing edge airfoils such that the vehicle was self-propelled. As this work was part of a BlendedWing-Body (BWB) distributed propulsion multidisciplinary optimization (MDO) study, two airfoils of different thickness were modeled at BWB cruise conditions as examples. One airfoil, representative of an outboard BWB wing section, was 11% thick. The other airfoil, representative of an inboard BWB wing section, was 18% thick. Furthermore, in an attempt to increase the propulsive efficiency, the trailing edge thickness of the 11% thick airfoil was doubled in size. The studies show that jet-wing distributed propulsion can be used to obtain propulsive efficiencies on the order of turbofan engine aircraft. If the trailing edge thickness is expanded, then jet-wing distributed propulsion can give improved propulsive efficiency. However, expanding the trailing edge must be done with care, as there is a drag penalty.

Modern gas turbines operate at high temperatures, which exceed the endurance limit of material, and therefore the turbines components are cooled by the air taken from the compressor. The cooling provides positive impact on lifetime of GT has negative impact on its performance. In convection-cooled turbine blade the coolant is usually discharged through the trailing edge and it leads to limitation on the minimal size of trailing edge and thereby negatively affects the losses. Moreover, the injection of cooling air in the turbine disturbs the main flow, and may lead to additional increase of losses, and the trailing edge loss is a significant part of the overall loss in modern gas turbines. This study comprises investigations of losses in cooled blades. Four cascades with different unguided part of aerofoil with and without coolant injection were studied both experimentally and numerically. This analysis provides split of losses caused by different factors, and offers the opportunities for efficiency and lifetime improvements of real engine designs/upgrades. In particular it is shown that an increase in the unguided turning angle results in a reduction of loss in case of relatively thick trailing edge. It is also shown that injection through the trailing edge slot parallel to the main flow leads to neutral loss impact and even loss reduction in subsonic range and loss increase in the supersonic range of exit Mach numbers.

In this paper, the effects of adiabatic and isothermal conditions on the statistics in compressible turbulent channel flow are investigated using direct numerical simulation (DNS). DNS of two compressible turbulent channel flows (Cases 1 and 2) are performed using a mixed Fourier Galerkin and B-spline collocation method. Case 1 is compressible turbulent channel flow between isothermal walls, which corresponds to DNS performed by Coleman et al. (1995). Case 2 is the flow between adiabatic and isothermal walls. The flow of Case 2 can be a very useful framework for the present objective, since it is the simplest turbulent channel flow with an adiabatic wall and provides ideal information for modelling the compressible turbulent flow near the adiabatic wall. Note that compressible turbulent channel flow between adiabatic walls is not stationary if there is no sink of heat. In Cases 1 and 2, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5, and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3000. To compare compressible and incompressible turbulent flows, DNS of two incompressible turbulent channel flows with passive scalar transport (Cases A and B) are performed using a mixed Fourier Galerkin and Chebyshev tau method. The wall boundary conditions of Cases A and B correspond to those of Cases 1 and 2, respectively. Case A corresponds to the DNS of Kim & Moin (1989). In Cases A and B, the Reynolds number based on the friction velocity, the channel half-width, and the kinematic viscosity is 150. The mean velocity and temperature near adiabatic and isothermal walls for compressible turbulent channel flow can be explained using the non-dimensional heat flux and the friction Mach number. It is found that Morkovin's hypothesis is not applicable to the near-wall asymptotic behaviour of the wall-normal turbulence intensity even if the variable property effect is taken into account. The mechanism of the energy transfers among the internal energy, mean and turbulent kinetic energiesis investigated, and the difference between the energy transfers near isothermal and adiabatic walls is revealed. Morkovin's hypothesis is not applicable to the correlation coeffcient between velocity and temperature fluctuations near the adiabatic wall.

The drive for ever higher aircraft efficiency inevitably leads to a reduction in core compressor size; over the past 30 years the height of the rear stages of a typical aeroengine has reduced by 40%. This trend will continue; a further reduction of almost 50% is expected by 2050. It is shown in this paper that the two greatest sources of increased profile loss as core size is reduced comes from the mechanical and manufacturing constraints placed on the maximum and trailing edge thickness. Furthermore, mitigation strategies are presented which successfully minimized or eliminated these loss sources. An experimental study showed that local modification to the trailing edge shape from a semi-circle to a more elliptical shape almost entirely eliminated the increase in trailing edge loss associated with a reduction in compressor size. Elliptical trailing edges improved loss by both narrowing the wake and increasing the base pressure. Despite the local nature of the modification, the elliptical trailing edges had a powerful effect on flow turning. This was accounted for by redesigning each design to achieve the specified exit flow angle. A set of “as manufactured” small core blades was created by combining measured data from existing manufacture methods with airfoils scaled to ensure minimum thicknesses necessary for mechanical integrity along the blade were not breached. Core sizes down to 40% of current designs were run in CFD. It is often assumed that the loss in efficiency as core size is reduced is unavoidable. However, it was shown that approximately half of this is directly due to the increase in thickness to satisfy tolerancing. Part to part deviation has negligible effect at all but the smallest compressor size tested (at 40% of current values).

The aim of this experimental study is to scrutinize the flow in the vicinity of a non zero thickness trailing edge, i.e. just upstream and downstream of the base, using Laser Doppler Anemometry. Indeed, boundary layer surveys as well as wake surveys have been performed for different thicknesses and shapes of trailing edges. Experiments have been conducted with two-dimensional trailing edges in both two- and threedimensional flows. Much of the discussion presented in this paper is relevant to flow field modification induced by thick cambered trailing edges.

Flow in the wake of a blunt trailing edge profiled body, comprised of an elliptical leading edge and a rectangular trailing edge, has been investigated experimentally, to identify and characterize the secondary instabilities accompanying the von Karman vortices. The experiments, which involve laser-induced fluorescence for visualization and particle image velocimetry for quantitative measurement of the wake instabilities, cover Reynolds numbers ranging from 250 to 2,150 based on thickness of the body, to include the wake transition regime. The dominant secondary instability appears as spanwise undulations in von Karman vortices, which evolve into pairs of counter-rotating vortices, with features resembling the instability mechanism predicted by Ryan et al. (J Fluid Mech 538:1–29, 2005). Feasibility of a flow control approach based on interaction with the secondary instability using a series of discrete trailing edge injectors has also been investigated. The control approach mitigates the adverse effects of vortex shedding in certain conditions, where it is able to amplify the secondary instability effectively.

The turbulence in plane Couette flow subjected to system rotation is investigated.The anti-cyclonic rotation rate is well above the range in which roll-cells occur and close to the upper bound, beyond which no stationary turbulent states of motion exist.The mean velocity profile exhibits a linear region over 80% of the cross-section, in which the mean absolute vorticity is driven to zero.Viscous effects still prevail in narrow regions next to the walls, whereas the quasi-homogeneous central core exhibits abnormal anisotropies of the Reynolds stress tensor, the vorticity tensor and the energy dissipation rate tensor.In spite of the distinctly higher turbulence level observed, a 13% drag reduction is found.This paradoxical finding is ascribed to configurational changes in the turbulence field brought about by the system rotation.

Geometrical effects on the airfoil flow separation and transition

Although turbulent flows are common in the world around us, a solution to the fundamental equations that govern turbulence still eludes the scientific community. Turbulence has often been called one of the last unsolved problem in classical physics, yet it is clear that the need to accurately predict the effect of turbulent flows impacts virtually every field of science and engineering. As an example, a critical step in making modern computational tools useful in designing aircraft is to be able to accurately predict the lift, drag, and other aerodynamic characteristics in numerical simulations in a reasonable amount of time. Simulations that take months to years to complete are much less useful to the design cycle. Much work has been done toward this goal (Lee-Rausch et al. 2003, Jameson 2003) and as cost effective accurate tools for simulating turbulent flows evolve, we will all benefit from new scientific and engineering breakthroughs. The problem of simulating high Reynolds number (Re) turbulent flows of engineering and scientific interest would have been solved with the advent of Direct Numerical Simulation (DNS) techniques if unlimited computing power, memory, and time could be applied to each particular problem. Yet, given the current and near future computational resources that exist and a reasonable limit on the amount of time an engineer or scientist can wait for a result, the DNS technique will not be useful for more than 'unit' problems for the foreseeable future (Moin & Kim 1997, Jimenez & Moin 1991). The high computational cost for the DNS of three dimensional turbulent flows results from the fact that they have eddies of significant energy in a range of scales from the characteristic length scale of the flow all the way down to the Kolmogorov length scale. The actual cost of doing a three dimensional DNS scales as Re{sup 9/4} due to the large disparity in scales that need to be fully resolved. State-of-the-art DNS calculations of isotropic turbulence have recently been completed at the Japanese Earth Simulator (Yokokawa et al. 2002, Kaneda et al. 2003) using a resolution of 40963 (approximately 10{sup 11}) grid points with a Taylor-scale Reynolds number of 1217 (Re {approx} 10{sup 6}). Impressive as these calculations are, performed on one of the world's fastest super computers, more brute computational power would be needed to simulate the flow over the fuselage of a commercial aircraft at cruising speed. Such a calculation would require on the order of 10{sup 16} grid points and would have a Reynolds number in the range of 108. Such a calculation would take several thousand years to simulate one minute of flight time on today's fastest super computers (Moin & Kim 1997). Even using state-of-the-art zonal approaches, which allow DNS calculations that resolve the necessary range of scales within predefined 'zones' in the flow domain, this calculation would take far too long for the result to be of engineering interest when it is finally obtained. Since computing power, memory, and time are all scarce resources, the problem of simulating turbulent flows has become one of how to abstract or simplify the complexity of the physics represented in the full Navier-Stokes (NS) equations in such a way that the 'important' physics of the problem is captured at a lower cost. To do this, a portion of the modes of the turbulent flow field needs to be approximated by a low order model that is cheaper than the full NS calculation. This model can then be used along with a numerical simulation of the 'important' modes of the problem that cannot be well represented by the model. The decision of what part of the physics to model and what kind of model to use has to be based on what physical properties are considered 'important' for the problem. It should be noted that 'nothing is free', so any use of a low order model will by definition lose some information about the original flow.