Extraction Techniques and Analysis of Turbulence Quantities From In-Cylinder Velocity Data

1989 ◽  
Vol 111 (3) ◽  
pp. 466-478 ◽  
Author(s):  
A. E. Catania ◽  
A. Mittica
Keyword(s):  
Direct Injection ◽  
Detailed Comparison ◽  
Ensemble Average ◽  
Small Scale ◽  
Velocity Data ◽  
Mean Flow ◽  
Reciprocating Engine ◽  
Reduction Methods ◽  
The Mean ◽  
Correlation And Spectral Analysis

In addition to the frequently used statistical ensemble-average, non-Reynolds filtering operators have long been proposed for nonstationary turbulent quantities. Several techniques for the reduction of velocity data acquired in the cylinder of internal combustion reciprocating engines have been developed by various researchers in order to separate the “mean flow” from the “fluctuating motion,” cycle by cycle, and to analyze small-scale engine turbulence by statistical methods. Therefore a thorough examination of these techniques and a detailed comparison between them would seem to be a preliminary step in attempting a general study of unconventional averaging procedures for reciprocating engine flow application. To that end, in the present work, five different cycle-resolved data reduction methods and the conventional ensemble-average were applied to the same in-cylinder velocity data, so as to review and compare them. One of the methods was developed by the authors. The data were acquired in the cylinder of a direct-injection automotive diesel engine, during induction and compression strokes, using an advanced hot-wire anemometry technique. Correlation and spectral analysis of the engine turbulence, as determined from the data with the different procedures, were also performed.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

Numerical Modeling of Nonlinear Interactions of Spectral Components of Acoustic-Gravity Waves in the Middle and Upper Atmosphere

2020 ◽  
Author(s):  
Nikolai M. Gavrilov ◽  
Sergej P. Kshevetskii
Keyword(s):  
Gravity Waves ◽  
Upper Atmosphere ◽  
Jet Flows ◽  
Small Scale ◽  
Nonlinear Interactions ◽  
Mean Flow ◽  
Wave Source ◽  
Acoustic Gravity Waves ◽  
The Mean ◽  
Wave Modes

<p>Acoustic-gravity waves (AGWs) measuring at big heights may be generated in the troposphere and propagate upwards. A high-resolution three-dimensional numerical model was developed for simulating nonlinear AGWs propagating from the ground to the upper atmosphere. The model algorithms are based on the finite-difference analogues of the main conservation laws. This methodology let us obtaining the physically correct generalized wave solutions of the nonlinear equations. Horizontally moving sinusoidal structures of vertical velocity on the ground are used for the AGW excitation in the model. Numerical simulations were made in an atmospheric region having horizontal dimensions up to several thousand kilometers and the height extention up to 500 km. Vertical distributions of the mean temperature, density, molecular viscosity and thermal conductivity are specified using standard models of the atmosphere.</p><p>Simulations were made for different horizontal wavelengths, amplitudes and speeds of the wave sources at the ground. After “switch on” the tropospheric wave source, an initial AGW pulse very quickly (for several minutes) could propagate to heights up to 100 km and above. AGW amplitudes increase with height and waves may break down in the middle and upper atmosphere. Wave instability and dissipation may lead to formations of wave accelerations of the mean flow and to producing wave-induced jet flows in the middle and upper atmosphere. Nonlinear interactions may lead to instabilities of the initial wave and to the creation of smaller-scale perturbations. These perturbations may increase temperature and wind gradients and could enhance the wave energy dissipation.</p><p>In this study, the wave sources contain a superposition of two AGW modes with different periods, wavelengths and phase speeds. Longer-period AGW modes served as the background conditions for the shorter-period wave modes. Thus, the larger-scale AGWs can modulate amplitudes of small-scale waves. In particular, interactions of two wave modes could sharp vertical temperature gradients and make easier the wave breaking and generating  turbulence. On the other hand, small-wave wave modes might increase dissipation and modify the larger-scale modes.This study was partially supported by the Russian Basic Research Foundation (# 17-05-00458).</p>

Axisymmetric Flow in a Motored Reciprocating Engine

1978 ◽  
Vol 192 (1) ◽  
pp. 213-223 ◽  
Author(s):  
A. D. Gosman ◽  
A. Melling ◽  
J. H. Whitelaw ◽  
P. Watkins
Keyword(s):  
Laser Doppler Anemometry ◽  
Axisymmetric Flow ◽  
Flow Characteristics ◽  
Small Scale ◽  
Mean Velocity ◽  
Inlet Velocity ◽  
Reciprocating Engine ◽  
Laminar And Turbulent Flow ◽  
Flow Through ◽  
The Mean

A study was made of axisymmetric, laminar and turbulent flow in a motored reciprocating engine with flow through a cylinder head port. Measurements were obtained by laser-Doppler anemometry and predictions for the laminar case were generated by finite-difference means. Agreement between calculated and measured results is good for the main features of the flow field, but significant small scale differences exist, due partly to uncertainties in the inlet velocity distribution. The measurements show, for example, that the mean velocity field is influenced more strongly by the engine geometry than by the speed. In general, the results confirm that the calculation method can be used to represent the flow characteristics of motored reciprocating engines without compression and suggest that extensions to include compression and combustion are within reach.

scholarly journals Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170388 ◽  
Author(s):  
C. J. Cotter ◽  
G. A. Gottwald ◽  
D. D. Holm
Keyword(s):  
Large Scale ◽  
Particle Dynamics ◽  
Homogenization Theory ◽  
Small Scale ◽  
Mean Flow ◽  
Time Dynamics ◽  
Fluid Equations ◽  
Diffusive Limit ◽  
The Mean ◽  
Stochastic Fluid

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. ( doi:10.1098/rspa.2014.0963 )), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Parameterizing gravity waves in the DYNAMICO-Saturn Global Climate Model to understand Saturn's equatorial oscillation

2020 ◽  
Author(s):  
Deborah Bardet ◽  
Aymeric Spiga ◽  
Sandrine Guerlet ◽  
Ehouarn Millour ◽  
François Lott
Keyword(s):  
Gravity Waves ◽  
Climate Model ◽  
Global Climate ◽  
Global Climate Model ◽  
Life Cycles ◽  
Small Scale ◽  
Mean Flow ◽  
Time Step ◽  
Maximum Value ◽  
The Mean

<p>To address questions about the driving mechanisms of Saturn's equatorial oscillation, our team at the Laboratoire de Météorologie Dynamique built the DYNAMICO-Saturn Global Climate Model to study tropospheric dynamics, tropospheric waves activity (Spiga et al. 2020) and equatorial stratospheric dynamics (Bardet et al. 2020) of Saturn. Previous studies (Guerlet et al. 2014, Spiga et al. 2020, Cabanes et al. 2020) have shown that our model produces consistent thermal structure and seasonal variability compared to Cassini CIRS measurements, mid-latitude eddy-driven tropospheric eastward and westward jets commensurate to those observed and following the zonostrophic regime, and planetary-scale waves such as Rossby-gravity (Yanai), Rossby and Kelvin waves in the tropical channel. Extending the model top toward the upper stratosphere allowed our model to produce an almost semi-annual equatorial oscillation with opposite eastward and westward phases. Associated temperature anomalies have a similar behavior than the Cassini/CIRS observations, but the amplitude of the temperature oscillation is twice smaller than the observed one. The absence of sub-grid-scale waves in the model produces an imbalance in eastward- and westward-wave forcing on the mean flow and could be an explanation to the irregularity in both the oscillating period and the downward rate propagation of the resolved Saturn equatorial oscillation.</p> <p>To explore the impact of those small-scale waves on the spontaneous equatorial oscillation emerging in the DYNAMICO-Saturn GCM (Bardet et al. 2020), we add a sub-grid-scale non-orographic gravity waves drag parameterization in our model.<br />This parameterization is directly adapted from the stochastic terrestrial model of Lott et al. (2012). This formalism represents a broadband gravity wave spectrum, using the superposition of a large statistical set of monochromatic waves. As the time scale of the life cycles of gravity waves is much longer than the time step of our GCM, our parametrization can launch a few waves whose characteristics are randomly chosen at each time step. This stochastic gravity waves drag parameterization is applied in DYNAMICO-Saturn on all points of the horizontal grid.</p> <p>A key parameter used in the non-orographic gravity waves drag parameterization is the maximum value of the Eliassen-Palm flux. The Eliassen Palm flux represents the momentum carried by waves that could be transferred to the mean flow. This value has never been measured in Saturn's atmosphere and it represents an important degree of freedom in the parameterization of gravity waves.</p> <p>We performed several test simulations, lasting two Saturn years whose initial state is derived from Bardet et al (2020), with an horizontal resolution of 1/2° in longitude/latitude and a vertical resolution ranging between 3 bar to 1 μbar. For these test simulations, the maximum value of the Eliassen-Palm fulx is set to 10<sup>-6</sup>, 10<sup>-5</sup>, 10<sup>-4</sup> and 10<sup>-3</sup> kg m<sup>-1</sup> s<sup>-2</sup>. </p> <p>Preliminary results show that the appropriate value of our main parameter is between 10<sup>-5</sup> and 10<sup>-4</sup> kg m<sup>-1</sup> s<sup>-2</sup>. Eliassen-Palm flux value of 10<sup>-3</sup> kg m<sup>-1</sup> s<sup>-2</sup> demonstrates a too large impact: the equatorial oscillation is entirely vanished is this configuration. The simulation using the value of 10<sup>-6</sup> kg m<sup>-1</sup> s<sup>-2</sup> is equivalent to the control simulation without the gravity waves drag parameterization.  </p> <p>The next step is to test other parameters, as phase velocity of the gravity waves, horizontal wavenumber, to understand how gravity waves impact the equatorial oscillation.</p>

Three-dimensional structure and momentum transfer in a turbulent cylinder wake

1999 ◽  
Vol 394 ◽  
pp. 303-337 ◽  
Author(s):  
A. VERNET ◽  
G. A. KOPP ◽  
J. A. FERRÉ ◽  
FRANCESC GIRALT
Keyword(s):  
Velocity Field ◽  
Saddle Point ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Half Width ◽  
Small Scale ◽  
Spanwise Direction ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Simultaneous velocity and temperature measurements were made with rakes of sensors that sliced a slightly heated turbulent wake in the spanwise direction, at different lateral positions 150 diameters downstream of the cylinder. A pattern recognition analysis of hotter-to-colder transitions was performed on temperature data measured at the mean velocity half-width. The velocity data from the different ‘slices’ was then conditionally averaged based on the identified temperature events. This procedure yielded the topology of the average three-dimensional large-scale structure which was visualized with iso-surfaces of negative values of the second eigenvector of [S2+Ω2]. The results indicate that the average structure of the velocity fluctuations (using a triple decomposition of the velocity field) is found to be a shear-aligned ring-shaped vortex. This vortex ring has strong outward lateral velocities in its symmetry plane which are like Grant's mixing jets. The mixing jet region extends outside the ring-like vortex and is bounded by two foci separated in the spanwise direction and an upstream saddle point. The two foci correspond to what has been previously identified in the literature as the double rollers.The ring vortex extracts energy from the mean flow by stretching in the mixing jet region just upstream of the ring boundary. The production of the small-scale (incoherent) turbulence by the coherent field and one-component energy dissipation rate occur just downstream of the saddle point within the mixing jet region. Incoherent turbulence energy is extracted from the mean flow just outside the mixing jet region, but within the core of the structure. These processes are highly three-dimensional with a spanwise extent equal to the mean velocity half-width.When a double decomposition is used, the coherent structure is found to be a tube-shaped vortex with a spanwise extent of about 2.5l0. The double roller motions are integral to this vortex in spite of its shape. Spatial averages of the coherent velocity field indicate that the mixing jet region causes a deficit of mean streamwise momentum, while the region outside the foci of the double rollers has a relatively small excess of streamwise momentum.

scholarly journals Are cosmological N-body simulations reliable on scales below the mean separation length of particles?

2003 ◽  
Vol 208 ◽  
pp. 399-400
Author(s):  
Takashi Hamana ◽  
Naoki Yoshida ◽  
Yasushi Suto
Keyword(s):  
High Resolution ◽  
Particle Separation ◽  
Detailed Comparison ◽  
Mass Scale ◽  
Particle Mass ◽  
Dark Matter Halo ◽  
Small Scale ◽  
Fundamental Limitations ◽  
Point Correlation ◽  
The Mean

We critically examine the reliability of clustering below the mean separation length of particles in cosmological high-resolution N-body simulations. The particle discreteness effect imposes two fundamental limitations on those scales; the lack of the initial fluctuation power and the finite mass resolution. We address this problem applying the dark matter halo approach which makes us possible to examine separately how those two limitations affect the simulation results at later epochs. We find that the reliability of the simulations on scale below the mean particle separation is primarily determined by the mass of particles. Since the small scale matter clustering is dominated by the matter in a virialized halo, it is naturally expected that the small scale clustering becomes unreliable when the characteristic nonlinear mass for gravitationally collapsed objects at that time becomes smaller than the particle mass. This is confirmed by a detailed comparison with three major cosmological simulations. The characteristic mass, MNL(z), is approximately given by the condition σ(MNL, z) = 1. This mass scale should be much larger than the simulation particle mass mpart so as to reproduce the proper amplitude of the small scale clustering. This requirement can be translated to the criterion for the critical redshift zcrit when simulations reasonably resolve the clustering on scales below the mean separation: MNL(zcrit) = nhalompart, where we introduce a fudge factor, nhalo, of around ten. We conclude that at z > zcrit high-resolution N-body simulations are not reliable on scales below the mean particle separation. Although it is not obvious if the opposite is true at z < zcrit, our detailed comparison suggests that it is indeed the case at least as far as the two-point correlation functions of the matter are concerned. The detail discussions are presented in Hamana, Yoshida & Suto (2001).

scholarly journals Mixed layer sub-mesoscale parameterization – Part 1: Derivation and assessment

Ocean Science ◽  
2010 ◽  
Vol 6 (3) ◽  
pp. 679-693 ◽  
Author(s):  
V. M. Canuto ◽  
M. S. Dubovikov
Keyword(s):  
High Resolution ◽  
Mixed Layer ◽  
Wind Direction ◽  
Small Scale ◽  
Mean Flow ◽  
Mean Velocity ◽  
Geostrophic Velocity ◽  
Global Circulation Models ◽  
The Mean ◽  
Strong Winds

Abstract. Several studies have shown that sub-mesoscales (SM ~1 km horizontal scale) play an important role in mixed layer dynamics. In particular, high resolution simulations have shown that in the case of strong down-front wind, the re-stratification induced by the SM is of the same order of the de-stratification induced by small scale turbulence, as well as of that induced by the Ekman velocity. These studies have further concluded that it has become necessary to include SM in ocean global circulation models (OGCMs), especially those used in climate studies. The goal of our work is to derive and assess an analytic parameterization of the vertical tracer flux under baroclinic instabilities and wind of arbitrary directions and strength. To achieve this goal, we have divided the problem into two parts: first, in this work we derive and assess a parameterization of the SM vertical flux of an arbitrary tracer for ocean codes that resolve mesoscales, M, but not sub-mesoscales, SM. In Part 2, presented elsewhere, we have used the results of this work to derive a parameterization of SM fluxes for ocean codes that do not resolve either M or SM. To carry out the first part of our work, we solve the SM dynamic equations including the non-linear terms for which we employ a closure developed and assessed in previous work. We present a detailed analysis for down-front and up-front winds with the following results: (a) down-front wind (blowing in the direction of the surface geostrophic velocity) is the most favorable condition for generating vigorous SM eddies; the de-stratifying effect of the mean flow and re-stratifying effect of SM almost cancel each other out, (b) in the up-front wind case (blowing in the direction opposite to the surface geostrophic velocity), strong winds prevents the SM generation while weak winds hinder the process but the eddies amplify the re-stratifying effect of the mean velocity, (c) wind orthogonal to the geostrophic velocity. In this case, which was not considered in numerical simulations, we show that when the wind direction coincides with that of the horizontal buoyancy gradient, SM eddies are generated and their re-stratifying effect partly cancels the de-stratifying effect of the mean velocity. The case when wind direction is opposite to that of the horizontal buoyancy gradient, is analogous to the case of up-front winds. In conclusion, the new multifaceted implications on the mixed layer stratification caused by the interplay of both strength and directions of the wind in relation to the buoyancy gradient disclosed by high resolution simulations have been reproduced by the present model. The present results can be used in OGCMs that resolve M but not SM.

Dissipation in Small Scale Gaseous Flows

2003 ◽  
Vol 125 (5) ◽  
pp. 944-947 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Slip Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Slip Effects ◽  
Gaseous Flows ◽  
Constant Wall Heat Flux ◽  
Gravity Driven ◽  
The Mean ◽  
Slip Flow Regime ◽  
Mean Flow Velocity

We discuss the effect of shear work at solid boundaries in small scale gaseous flows where slip effects are present. The effect of shear work at the boundary on convective heat transfer is illustrated through solution of the constant-wall-heat-flux problem in the slip-flow regime. We also present predictions for the dissipation in terms of the mean flow velocity in pressure-driven and gravity-driven Poiseuille flows for arbitrary Knudsen numbers. All results are verified using direct Monte Carlo solutions of the Boltzmann equation.

Linear and nonlinear interactions between a columnar vortex and external turbulence

2000 ◽  
Vol 402 ◽  
pp. 349-378 ◽  
Author(s):  
TAKESHI MIYAZAKI ◽  
JULIAN C. R. HUNT
Keyword(s):  
Nonlinear Effects ◽  
Small Scale ◽  
Mean Flow ◽  
Mean Velocity ◽  
Azimuthal Component ◽  
Turbulent Eddies ◽  
Columnar Vortex ◽  
Axisymmetric Vortex ◽  
The Mean ◽  
External Turbulence

The structure of initially isotropic homogeneous turbulence interacting with a columnar vortex (with circulation Γ and radius σ), idealized both as a solid cylinder and a hollow core model is analysed using the inhomogeneous form of linear rapid distortion theory (RDT), for flows where the r.m.s. turbulence velocity u0 is small compared with Γ/σ. The turbulent eddies with scale Γ are distorted by the mean velocity gradient and also, over a distance Γ from the surface of the vortex, by their direct impingement onto it, whether it is solid or hollow. The distortion of the azimuthal component of turbulent vorticity by the differential rotation in the mean flow around the columnar vortex causes the mean-square radial velocity away from the cylinder to increase as (Γt/2πr2)2 (Γx/r)u20, when (r − σ) > Γx, but on the surface of the vortices ((r − σ) < Γx) where 〈u2r〉 is reduced, 〈u2z〉 increases to the same order, while the other components do not grow. Statistically, while the vorticity field remains asymmetric, the velocity field of small-scale eddies near the vortex core rapidly becomes axisymmetric, within a period of two or three revolutions of the columnar vortex. Calculation of the distortion of small-scale initially random velocity fields shows how the turbulent eddies, as they are wrapped around the columnar vortex, become like vortex rings, with similar properties to those computed by Melander & Hussain (1993) using a fully nonlinear direct numerical simulation. A mechanism is proposed for how interactions between the external turbulence and the columnar vortex can lead to non-axisymmetric vortex waves being excited on the vortex and damped fluctuations in its interior. If the columnar vortex is not significantly distorted by these linear effects, estimates are made of how nonlinear effects lead to the formation of axisymmetric turbulent vortices which move as result of their image vorticity (in addition to the self-induction velocity) at a velocity of order u0tΓ/σ2 parallel to the vortex. Even when the circulation (γ) of the turbulent vortices is a small fraction of Γ, they can excite self-destructive displacements through resonance on a time scale σ/u0.

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