Volume 25, Issue 11, November 2013

An integrated kineticsbased Large Eddy Simulation (LES) approach for soot evolution in turbulent reacting flows is applied to the simulation of a Pratt & Whitney aircraft gas turbine combustor, and the results are analyzed to provide insights into the complex interactions of the hydrodynamics, mixing, chemistry, and soot. The integrated approach includes detailed models for soot, combustion, and the unresolved interactions between soot, chemistry, and turbulence. The soot model is based on the Hybrid Method of Moments and detailed descriptions of soot aggregates and the various physical and chemical processes governing their evolution. The detailed kinetics of jet fuel oxidation and soot precursor formation is described with the Radiation Flamelet/Progress Variable model, which has been modified to account for the removal of soot precursors from the gasphase. The unclosed filtered quantities in the soot and combustion models, such as source terms, are closed with a novel presumed subfilter PDF approach that accounts for the high subfilter spatial intermittency of soot. For the combustor simulation, the integrated approach is combined with a Lagrangian parcel method for the liquid spray and stateoftheart unstructured LES technology for complex geometries. Two overall fueltoair ratios are simulated to evaluate the ability of the model to make not only absolute predictions but also quantitative predictions of trends. The Pratt & Whitney combustor is a RichQuenchLean combustor in which combustion first occurs in a fuelrich primary zone characterized by a large recirculation zone. Dilution air is then added downstream of the recirculation zone, and combustion continues in a fuellean secondary zone. The simulations show that large quantities of soot are formed in the fuelrich recirculation zone, and, furthermore, the overall fueltoair ratio dictates both the dominant soot growth process and the location of maximum soot volume fraction. At the higher fueltoair ratio, the maximum soot volume fraction is found inside the recirculation zone; at the lower fueltoair ratio, turbulent fluctuations in the mixture fraction promote the oxidation of soot inside the recirculation zone and suppress the accumulation of a large soot volume fraction. Downstream, soot exits the combustor in intermittent fuelrich pockets that are not mixed during the injection of dilution air and subsequent secondary fuellean combustion. At the higher fueltoair ratio, the frequency of these fuelrich pockets is increased, leading to higher soot emissions from the combustor. Quantitatively, the soot emissions from the combustor are overpredicted by about 50%, which is a substantial improvement over previous works utilizing RANS to predict such emissions. In addition, the ratio between the two fueltoair ratios predicted by LES compares very favorably with the experimental measurements. Furthermore, soot growth is dominated by an acetylenebased pathway rather than an aromaticbased pathway, which is usually the dominant mechanism in nonpremixed flames. This finding is the result of the interactions between the hydrodynamics, mixing, chemistry, and soot in the recirculation zone and the resulting residence times of soot at various mixture fractions (compositions), which are not the same in this complex recirculating flow as in nonpremixed jet flames.
 SPECIAL TOPIC: DIRECTIONS IN COMPUTATIONAL PHYSICS

 Foreword/Introduction/Preface
 Selected Papers from a Symposium Honoring Parviz Moin upon His 60th Birthday

Effect of diastolic flow patterns on the function of the left ventricle
View Description Hide DescriptionDirect numerical simulations are used to study the effect of intraventricular flow patterns on the pumping efficiency and the blood mixing and transport characteristics of the left ventricle. The simulations employ a geometric model of the left ventricle which is derived from contrast computed tomography. A variety of diastolic flow conditions are generated for a fixed ejection fraction in order to delineate the effect of flow patterns on ventricular performance. The simulations indicate that the effect of intraventricular blood flow pattern on the pumping power is physiologically insignificant. However, diastolic flow patterns have a noticeable effect on the blood mixing as well as the residence time of blood cells in the ventricle. The implications of these findings on ventricular function are discussed.

A nondiscrete method for computation of residence time in fluid mechanics simulations
View Description Hide DescriptionCardiovascular simulations provide a promising means to predict risk of thrombosis in grafts, devices, and surgical anatomies in adult and pediatric patients. Although the pathways for platelet activation and clot formation are not yet fully understood, recent findings suggest that thrombosis risk is increased in regions of flow recirculation and high residence time (RT). Current approaches for calculating RT are typically based on releasing a finite number of Lagrangian particles into the flow field and calculating RT by tracking their positions. However, special care must be taken to achieve temporal and spatial convergence, often requiring repeated simulations. In this work, we introduce a nondiscrete method in which RT is calculated in an Eulerian framework using the advectiondiffusion equation. We first present the formulation for calculating residence time in a given region of interest using two alternate definitions. The physical significance and sensitivity of the two measures of RT are discussed and their mathematical relation is established. An extension to a pointwise value is also presented. The methods presented here are then applied in a 2D cavity and two representative clinical scenarios, involving shunt placement for single ventricle heart defects and Kawasaki disease. In the second case study, we explored the relationship between RT and wall shear stress, a parameter of particular importance in cardiovascular disease.

A model for turbulent mixing based on shadowposition conditioning
View Description Hide DescriptionIn the modeling and simulation of mixing and reaction in turbulent flows using probability density function (PDF) methods, a key component is the mixing model , which represents the mixing effected by molecular diffusion. A new model, called the shadowposition mixing model (SPMM), is introduced and its performance is illustrated for two test cases. The model involves a new variable—the shadow position—and mixing is modeled as a relaxation of the composition to its mean conditional on the shadow position. The model is constructed to be consistent with turbulent dispersion theory, and to be local in the composition space, both to adequate approximations. The connections between the SPMM and previous mixing models are discussed. The first test case of a scalar mixing layer shows that the SPMM yields scalar statistics in broad agreement with experimental data. The second test case of a reactive scalar mixing layer with idealized nonpremixed combustion shows that the SPMM correctly yields stable combustion, whereas simpler models incorrectly lead to extinction. The model satisfies all required realizability and transformation properties and correctly yields Gaussian distributions in appropriate circumstances. The SPMM is generally applicable to turbulent reactive flows using different PDF approaches in the contexts of both Reynoldsaveraged NavierStokes modeling and largeeddy simulation.

Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ionselective surface
View Description Hide DescriptionWe present a comprehensive analysis of transport processes associated with electrohydrodynamic chaos in electrokinetic systems containing an ionselective surface. The system considered is an aqueous symmetric binary electrolyte between an ionselective surface and a stationary reservoir. Transport is driven by an external electric field. Using direct numerical simulations (DNS) of the coupled Poisson–Nernst–Planck and Navier–Stokes equations in 2D we show significant transitions in flow behavior from coherent vortex pairs to fully chaotic multilayer vortex structures with a broadband energy spectrum. Additionally, we demonstrate that these vortices can eject both positive and negative free charge density into the bulk of the domain and completely disrupt the structure of the traditionally described extended space charge region. The resulting dynamical behavior poses a challenge for traditional asymptotic modeling that relies on the quasielectroneutral bulk assumption. Furthermore, we quantify for the first time the relative importance of energy dissipation due to viscous effects in various transport regimes. Finally, we present a framework for the development of ensembleaveraged models (similar to Reynolds Averaged Navier–Stokes equations) and assess the importance of the unclosed terms based on our DNS data.

A hybrid subgridscale model constrained by Reynolds stress
View Description Hide DescriptionA novel constrained formulation for the dynamic subgridscale model for large eddy simulation (LES) is proposed. An externally prescribed Reynolds stress is used as the constraint and is imposed in the nearwall region of wallbounded flows. However, unlike conventional zonal approaches, Reynolds stress is not imposed as the solution, but used as a constraint on the subgridscale stress so that the computed Reynolds stress closely matches the prescribed one only in the mean sense. In the absence of an ideal wall model or adequate nearwall resolution, a LES solution at coarse resolution is expected to be erroneous very near the wall while giving reasonable predictions away from the wall. The Reynolds stress constraint is limited to the region where the LES solution is expected to be erroneous. The Germanoidentity error is used as an indicator of LES quality such that the Reynolds stress constraint is activated only where the Germanoidentity error exceeds a certain threshold. The proposed model is applied to LES of turbulent channel flow at various Reynolds numbers and grid resolutions to obtain significant improvement over the dynamic Smagorinsky model, especially at coarse resolutions. This constrained formulation can be extended to incorporate constraints on the mean of other flow quantities.

Interaction of a Mach 2.25 turbulent boundary layer with a fluttering panel using direct numerical simulation
View Description Hide DescriptionThe interaction between a thin metallic panel and a Mach 2.25 turbulent boundary layer is investigated using a direct numerical simulation approach for coupled fluidstructure problems. The solid solution is found by integrating the finitestrain, finitedeformation equations of elasticity using a nonlinear 3D finite element solver, while the direct numerical simulation of the boundary layer uses a finitedifference compressible NavierStokes solver. The initially laminar boundary layer contains low amplitude unstable eigenmodes that grow in time and excite traveling bending waves in the panel. As the boundary layer transitions to a fully turbulent state, with Reθ ≈ 1200, the panel's bending waves coalesce into a standing wave pattern exhibiting flutter with a final amplitude approximately 20 times the panel thickness. The corresponding panel deflection is roughly 25 wall units and reaches across the sonic line in the boundary layer profile. Once it reaches a limit cycle state, the panel/boundary layer system is examined in detail where it is found that turbulence statistics appear to be modified by the presence of the compliant panel, the effect of which is forgotten within one integral length downstream of the panel.

The flow of red blood cells through a narrow spleenlike slit
View Description Hide DescriptionSmall slits between endothelial cells in the spleen are perhaps the smallest blood passages in the body, and red blood cells must deform significantly to pass through them. These slits have been posited to participate in the removal of senescent blood cells from the circulation, a key function of the spleen. One of the effects of red blood cell aging is an increased cytosol viscosity; relaxation time measurements suggest their interior viscosity can increase by up to a factor of 10 toward the end of their normal 120 day circulating lifetime. We employ a boundary integral model to simulate red blood cells as they deform sufficiently to flow through such a small passage, whether in the spleen or in a microfluidic device. Different flow rates and cytosol viscosities show three distinct behaviors. (1) For sufficiently slow flow, the pressure gradient is insufficient to overcome elastic resistance and the cell becomes jammed. (2) For faster flow, the cell passes the slit, though more slowly for higher cytosol viscosity. This can be hypothesized to facilitate recognition of senescent cells. (3) A surprising behavior is observed for high elastic capillary numbers, due either to high velocity or high cytosol viscosity. In this case, the cells infold within the slit, with a finger of lowviscosity plasma pushing deeply into the cell from its upstream side. Such infolding might provide an additional mechanism for jamming, and the sharpness of the resulting features would be expected to promote cell degradation. Linear analysis of a model system shows a similar instability, which is analyzed in regard to the cell flow. This linear analysis also suggests a similar instability for unphysiologically low cytosol viscosity. Simulations confirm that a similar infolding also occurs in this case, which intriguingly suggests that normal cytosol viscosities are in a range that is protective against such deformations.

Large eddy simulations of turbulent channel and boundary layer flows at high Reynolds number with mean wall shear stress boundary condition
View Description Hide DescriptionIn this study, we investigate the applicability of the mean wall shear stress as a boundary condition for large eddy simulation of wallbounded turbulent flow with coarsegrid resolution near the wall. We consider turbulent channel flow up to Re τ = O(108) and turbulent boundary layer flow up to Re θ = O(107). The mean wall shear stress is determined based on the loglaw at every time step. It is shown that the mean wall shear stress boundary condition accurately predicts the logarithmic velocity profile and loworder turbulence statistics even with very coarsegrid spacing near the wall.

A mechanism for unsteady separation in overexpanded nozzle flow
View Description Hide DescriptionShock wave induced separation in an overexpanded planar nozzle is studied through numerical simulation. These LargeEddy Simulations (LES) model previous experiments which have shown unsteady motion of the shock wave in flows with similar geometries but offered little insight into the underlying mechanism. Unsteady separation in nozzle flow leads to “side loads” in the rocket engine which can adversely affect the stability of the rocket. A mechanism for the lowfrequency shock motion is identified and explained using the LES data. This mechanism is analyzed for a series of overexpanded planar nozzles of various area ratios and nozzle pressure ratios. The effect of grid resolution and Reynolds number on the instability is discussed. A simple reduced order model for the unsteady shock behavior is used to further validate the proposed mechanism. This model is derived from first principles and uses data from the LES calculations to capture the effects of the turbulent boundary layer and shear layer.

Experimental study of spectral energy fluxes in turbulence generated by a fractal, treelike object
View Description Hide DescriptionWe report on an experimental study of the kinetic energy fluxes between scales in the turbulent nearwake flow downstream of a fractal, treelike object. Experiments are performed in a liquid channel and data are acquired using planar Particle Image Velocimetry (PIV). The data are analyzed based on the filtering framework of relevance to Large Eddy Simulations. The flow and energy fluxes differ from the case of a canonical flow such as the cylinder wake, where typically kinetic energy is injected into turbulence by an object characterized by a single, welldefined, lengthscale. For a fractal treelike object, we find that the measured energy flux is strongly dependent on scale. In the present flow, scaledependent injection of kinetic energy into the cascade arises from production as well as spatial transport terms. The injection rate spectrum is evaluated directly from the data by quantifying the rate of change of spectral energy flux as a function of wavenumber. The net injection rate spectrum is observed to scale approximately as ∼k −7/3, in accordance with heuristic and dimensional arguments previously used for the kinetic energy production rate spectrum in shear flows. In order to scale the results, we consider an equivalent mixing lengthscale that can be obtained from the tree geometry by adding over the relevant scales of successive branch clusters. In prior work, this equivalent length scale has been found to collapse the eddyviscosity well. Here we find that this scale also collapses the energy flux and the net injection rate spectrum successfully.

Study of vortexsheddinginduced vibration of a flexible splitter plate behind a cylinder
View Description Hide DescriptionA computational analysis of vortexsheddinginduced vibration of a flexible splitter plate behind a cylinder at a low Reynolds number is conducted to understand effects of the length and flexibility of a splitter plate on the drag and lift of a cylinder and vibration of the attached plate. The drag and lift coefficients, the Strouhal number of vortex shedding, and the magnitude of tip displacements of a flexible splitter plate are found to be intricate functions of the plate flexibility. The deflection shape of a flexible splitter plate is dependent on the length of the plate, while the deflection magnitude is a function of the bending stiffness and natural frequencies of the corresponding plate. It is concluded in the present work that the Strouhal number of vortex shedding or the frequency of plate deflection is difficult to estimate using natural frequencies of the plate, which are calculated by inducing free vibration, since the fluid loading is distributed nonuniformly over the plate rather than concentrated at the tip of the plate. The present study suggests that the flexibility of a splitter plate, in general, adversely modulates the drag and lift forces acting on the cylinder surface while it promotes the oscillation of the plate.

Large eddy simulation of soot evolution in an aircraft combustor
View Description Hide DescriptionAn integrated kineticsbased Large Eddy Simulation (LES) approach for soot evolution in turbulent reacting flows is applied to the simulation of a Pratt & Whitney aircraft gas turbine combustor, and the results are analyzed to provide insights into the complex interactions of the hydrodynamics, mixing, chemistry, and soot. The integrated approach includes detailed models for soot, combustion, and the unresolved interactions between soot, chemistry, and turbulence. The soot model is based on the Hybrid Method of Moments and detailed descriptions of soot aggregates and the various physical and chemical processes governing their evolution. The detailed kinetics of jet fuel oxidation and soot precursor formation is described with the Radiation Flamelet/Progress Variable model, which has been modified to account for the removal of soot precursors from the gasphase. The unclosed filtered quantities in the soot and combustion models, such as source terms, are closed with a novel presumed subfilter PDF approach that accounts for the high subfilter spatial intermittency of soot. For the combustor simulation, the integrated approach is combined with a Lagrangian parcel method for the liquid spray and stateoftheart unstructured LES technology for complex geometries. Two overall fueltoair ratios are simulated to evaluate the ability of the model to make not only absolute predictions but also quantitative predictions of trends. The Pratt & Whitney combustor is a RichQuenchLean combustor in which combustion first occurs in a fuelrich primary zone characterized by a large recirculation zone. Dilution air is then added downstream of the recirculation zone, and combustion continues in a fuellean secondary zone. The simulations show that large quantities of soot are formed in the fuelrich recirculation zone, and, furthermore, the overall fueltoair ratio dictates both the dominant soot growth process and the location of maximum soot volume fraction. At the higher fueltoair ratio, the maximum soot volume fraction is found inside the recirculation zone; at the lower fueltoair ratio, turbulent fluctuations in the mixture fraction promote the oxidation of soot inside the recirculation zone and suppress the accumulation of a large soot volume fraction. Downstream, soot exits the combustor in intermittent fuelrich pockets that are not mixed during the injection of dilution air and subsequent secondary fuellean combustion. At the higher fueltoair ratio, the frequency of these fuelrich pockets is increased, leading to higher soot emissions from the combustor. Quantitatively, the soot emissions from the combustor are overpredicted by about 50%, which is a substantial improvement over previous works utilizing RANS to predict such emissions. In addition, the ratio between the two fueltoair ratios predicted by LES compares very favorably with the experimental measurements. Furthermore, soot growth is dominated by an acetylenebased pathway rather than an aromaticbased pathway, which is usually the dominant mechanism in nonpremixed flames. This finding is the result of the interactions between the hydrodynamics, mixing, chemistry, and soot in the recirculation zone and the resulting residence times of soot at various mixture fractions (compositions), which are not the same in this complex recirculating flow as in nonpremixed jet flames.

The importance of wallnormal Reynolds stress in turbulent rough channel flows
View Description Hide DescriptionIn this paper, it is demonstrated by DNS of turbulent rough channels that a proportionality between (the wallnormal Reynolds stress at the top of the roughness elements) and the roughness function does exist. This observation confirmed by experiments allows the derivation of a simple expression for the velocity profile in the logregion. This parameterization of rough walls through is suggested by the direct link between wall structures and . Identification of the wall structures, near smooth and different kinds of rough surfaces, demonstrates flow isotropization near rough walls, corroborated by profiles of , is depicted by visualizations of ∇2 p. The relationship between the roughness function and allows the derivation of a new kind of Moody diagram, useful in the prediction of friction factors of rough flows at high Reynolds numbers.

How linear is wallbounded turbulence?
View Description Hide DescriptionThe relevance of Orr's inviscid mechanism to the transient amplification of disturbances in shear flows is explored in the context of bursting in the logarithmic layer of wallbounded turbulence. The linearized problem for the wall normal velocity is first solved in the limit of small viscosity for a uniform shear and for a channel with turbulentlike profile, and compared with the quasiperiodic bursting of fully turbulent simulations in boxes designed to be minimal for the logarithmic layer. Many properties, such as time and length scales, energy fluxes between components, and inclination angles, agree well between the two systems. However, once advection by the mean flow is subtracted, the directly computed linear component of the turbulent acceleration is found to be a small part of the total. The temporal correlations of the different quantities in turbulent bursts imply that the classical model, in which the wallnormal velocities are generated by the breakdown of the streamwisevelocity streaks, is a better explanation than the purely autonomous growth of linearized bursts. It is argued that the best way to reconcile both lines of evidence is that the disturbances produced by the streak breakdown are amplified by an Orrlike transient process drawing energy directly from the mean shear, rather than from the velocity gradients of the nonlinear streak. This, for example, obviates the problem of why the crossstream velocities do not decay once the streak has broken down.

A numerical study of the effects of superhydrophobic surface on skinfriction drag in turbulent channel flow
View Description Hide DescriptionSuperhydrophobic surfaces have attracted much attention lately as they present the possibility of achieving a substantial skinfriction drag reduction in turbulent flows. In this paper, the effects of a superhydrophobic surface, consisting of microgrates aligned in the flow direction, on skinfriction drag in turbulent flows were investigated through direct numerical simulation of turbulent channel flows. The superhydrophobic surface was modeled through a shearfree boundary condition on the airwater interface. Dependence of the effective slip length and resulting skinfriction drag on Reynolds number and surface geometry was examined. In laminar flows, the effective slip length depended on surface geometry only, independent of Reynolds number, consistent with an existing analysis. In turbulent flows, the effective slip length was a function of Reynolds number, indicating its dependence on flow conditions near the surface. The resulting drag reduction was much larger in turbulent flows than in laminar flows, and nearwall turbulence structures were significantly modified, suggesting that indirect effects resulting from modified turbulence structures played a more significant role in reducing drag in turbulent flows than the direct effect of the slip, which led to a modest drag reduction in laminar flows. It was found that the drag reduction in turbulent flows was well correlated with the effective slip length normalized by viscous wall units.

Vortex dynamics in 3D shockbubble interaction
View Description Hide DescriptionThe dynamics of shockbubble interaction involve an interplay of vortex stretching, dilation, and baroclinic vorticity generation. Here, we quantify the interplay of these contributions through high resolution 3D simulations for several Mach and Atwood numbers. We present a volume rendering of density and vorticity magnitude fields of shockbubble interaction at M = 3 and air/helium density ratio η = 7.25 to elucidate the evolution of the flow structures. We distinguish the vorticity growth rates due to baroclinicity, stretching, and dilatation at low and high Mach numbers as well as the late time evolution of the circulation. The results demonstrate that a number of analytical models need to be revised in order to predict the late time circulation of shockbubble interactions at high Mach numbers. To this effect, we propose a simple model for the dependence of the circulation to Mach number and ambient to bubble density ratio for air/helium shockbubble interactions.

On the mechanism of elastoinertial turbulence
View Description Hide DescriptionElastoinertial turbulence (EIT) is a new state of turbulence found in inertial flows with polymer additives. The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 (based on the bulk and the channel height) are used to study the formation and dynamics of elastic instabilities and their effects on the flow. The flow topology of EIT is found to differ significantly from Newtonian wallturbulence. Structures identified by positive (rotational flow topology) and negative (extensional/compressional flow topology) second invariant Q a isosurfaces of the velocity gradient are cylindrical and aligned in the spanwise direction. Polymers are significantly stretched in sheetlike regions that extend in the streamwise direction with a small upward tilt. The Q a cylindrical structures emerge from the sheets of high polymer extension, in a mechanism of energy transfer from the fluctuations of the polymer stress work to the turbulent kinetic energy. At subcritical Reynolds numbers, EIT is observed at modest Weissenberg number (Wi, ratio polymer relaxation time to viscous time scale). For supercritical Reynolds numbers, flows approach EIT at large Wi. EIT provides new insights on the nature of the asymptotic state of polymer drag reduction (maximum drag reduction), and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian flows observed in some polymeric flows.

Towards scalable parallelintime turbulent flow simulations
View Description Hide DescriptionWe present a reformulation of unsteady turbulent flow simulations. The initial condition is relaxed and information is allowed to propagate both forward and backward in time. Simulations of chaotic dynamical systems with this reformulation can be proven to be wellconditioned time domain boundary value problems. The reformulation can enable scalable parallelintime simulation of turbulent flows.

Simulation and modeling of turbulence subjected to a period of uniform plane strain
View Description Hide DescriptionDirect numerical simulation is used to evaluate the effect of plane strain on isotropic homogeneous turbulence. The subsequent return to isotropy after the removal of the strain is also investigated. Large, moderate, and small strain rates are computed at moderate turbulence Reynolds numbers. The initial turbulence is generated via mechanical mixing so that the large scale turbulence develops relatively naturally. Turbulence length scales, Reynolds numbers, decay rates, and anisotropy are computed over the range of the simulations, with the goal of quantifying how anisotropic decay behaves. The simulations indicate that large scale anisotropy may not decay to zero at very large times. In agreement with experimental data, the presence of a recovery region is discerned before the return process is observed. Trajectory crossing is observed on the anisotropy invariant map indicating that anisotropy itself is not sufficient to determine its time evolution. Model constants for classic returntoisotropy models are determined from the data and shown to vary with time. The orientededdy collision model [M. B. Martell and J. B. Perot, “The orientededdy collision turbulence model,” Flow, Turbul. Combust. 89(3), 335 (2012)], which includes turbulent structure information, is shown to predict the salient structure of the straining and return process.