Design and Validation of a Probe for Spatially and Temporally Resolved Measurements of Vorticity and Strain Rates in Compressible Turbulence Interactions

A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed computation of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of the kinetic energy term and full rate-of-strain tensor. The probe has been validated experimentally in low-speed boundary layers and used in the CCNY Shock Tube Research Facility, where interactions of planar expansion waves or shock waves with homogeneous and isotropic turbulence have been investigated at several Reynolds numbers.

Download Full-text

Velocity and vorticity in weakly compressible isotropic turbulence under longitudinal expansive straining

Journal of Fluid Mechanics ◽

10.1017/s002211200700674x ◽

2007 ◽

Vol 584 ◽

pp. 301-335 ◽

Cited By ~ 5

Author(s):

SAVVAS XANTHOS ◽

MINWEI GONG ◽

YIANNIS ANDREOPOULOS

Keyword(s):

Shock Wave ◽

Mach Number ◽

Pressure Gradient ◽

Shock Tube ◽

Isotropic Turbulence ◽

Strain Tensor ◽

Velocity Fluctuations ◽

Total Enthalpy ◽

Expansion Waves ◽

Custom Made

The response of homogeneous and isotropic turbulence to streamwise straining action provided by planar expansion waves has been studied experimentally in the CCNY shock tube research facility at several Reynolds numbers. The reflection of a propagating shock wave at the open endwall of the shock tube generated an expansion fan travelling upstream and interacting with the induced flow behind the incident shock wave which has gone through a turbulence generating grid.A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three-dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed the computations of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of kinetic energy term and full rate-of-strain tensor. The longitudinal size of the straining zone was substantial so that measurements within it were possible. The flow accelerated from a Mach number of 0.23 to about 0.56, a value which is more than twice the initial one.Although the average value of the applied straining was only betweenS11= 130 s−1andS11= 240 s−1and the gradient Mach number was no more than 0.226, the amplitude of fluctuations of the strain rateS11were of the order of 4000 s−1before the application of straining and were reduced by about 2.5 times downstream of the interaction. This characteristic of high-amplitude bursts and the intermittent behaviour of the flow play a significant role in the dynamics of turbulence.One of the most remarkable features of the suppression of turbulence is that this process peaks shortly after the application of the straining where the pressure gradient is substantial. It was also found that the total enthalpy variation follows very closely the temporal gradient of pressure within the straining region and peaks at the same location as the pressure gradient.Attenuation of longitudinal velocity fluctuations has been observed in all experiments. It appears that this attenuation depends strongly on the characteristics of the incoming turbulence for a given straining strength and flow Mach number. The present results clearly show that in most of the cases, attenuation occurs at large times or distances from the turbulence generating grids where length scales of the incoming flow are high and turbulence intensities are low. Thus, large eddies with low-velocity fluctuations are affected the most by the interaction with the expansion waves. Spectral analysis has indicated that attenuation of fluctuations is not the same across all wavenumbers of the spectrum. The magnitude of attenuation appears to be higher in cases of finer mesh grids.

Download Full-text

Experiments of Compressible Homogeneous and Isotropic Turbulence Interacting With Expansion Waves

Volume 2: Symposia, Parts A, B, and C ◽

10.1115/fedsm2003-45075 ◽

2003 ◽

Author(s):

Savvas S. Xanthos ◽

Yiannis Andreopoulos

Keyword(s):

Mach Number ◽

Shock Tube ◽

Total Pressure ◽

Large Scale ◽

Isotropic Turbulence ◽

Pressure Fluctuations ◽

Incident Shock ◽

Expansion Waves ◽

Curvature Effects ◽

Homogeneous And Isotropic Turbulence

The interaction of traveling expansion waves with grid-generated turbulence was investigated in a large-scale shock tube research facility. The incident shock and the induced flow behind it passed through a rectangular grid, which generated a nearly homogeneous and nearly isotropic turbulent flow. As the shock wave exited the open end of the shock tube, a system of expansion waves was generated which traveled upstream and interacted with the grid-generated turbulence; a type of interaction free from streamline curvature effects, which cause additional effects on turbulence. In this experiment, wall pressure, total pressure and velocity were measured indicating a clear reduction in fluctuations. The incoming flow at Mach number 0.46 was expanded to a flow with Mach number 0.77 by an applied mean shear of 100 s−1. Although the strength of the generated expansion waves was mild, the effect on damping fluctuations on turbulence was clear. A reduction of in the level of total pressure fluctuations by 20 per cent was detected in the present experiments.

Download Full-text

Nonlinear amplification in hydrodynamic turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.914 ◽

2021 ◽

Vol 930 ◽

Author(s):

Kartik P. Iyer ◽

Katepalli R. Sreenivasan ◽

P.K. Yeung

Keyword(s):

Reynolds Number ◽

Isotropic Turbulence ◽

Stokes Equations ◽

Three Dimensional ◽

Reynolds Numbers ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Developed Turbulence ◽

Advection Term ◽

Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Download Full-text

Vortex rings impinging on walls: axisymmetric and three-dimensional simulations

Journal of Fluid Mechanics ◽

10.1017/s0022112093002903 ◽

1993 ◽

Vol 256 ◽

pp. 615-646 ◽

Cited By ~ 116

Author(s):

Paolo Orlandi ◽

Roberto Verzicco

Keyword(s):

Numerical Simulations ◽

Strain Tensor ◽

Three Dimensional ◽

Reynolds Numbers ◽

Vortex Rings ◽

Compression Phase ◽

Vortex Pairing ◽

The Impact ◽

Good Agreement ◽

Three Dimensional Simulations

Accurate numerical simulations of vortex rings impinging on flat boundaries revealed the same features observed in experiments. The results for the impact with a free-slip wall compared very well with previous numerical simulations that used spectral methods, and were also in qualitative agreement with experiments. The present simulation is mainly devoted to studying the more realistic case of rings interacting with a no-slip wall, experimentally studied by Walker et al. (1987). All the Reynolds numbers studied showed a very good agreement between experiments and simulations, and, at Rev > 1000 the ejection of a new ring from the wall was seen. Axisymmetric simulations demonstrated that vortex pairing is the physical mechanism producing the ejection of the new ring. Three-dimensional simulations were also performed to investigate the effects of azimuthal instabilities. These simulations have confirmed that high-wavenumber instabilities originate in the compression phase of the secondary ring within the primary one. The large instability of the secondary ring has been explained by analysis of the rate-of-strain tensor and vorticity alignment. The differences between passive scalars and the vorticity field have been also investigated.

Download Full-text

Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.510 ◽

2012 ◽

Vol 693 ◽

pp. 201-215 ◽

Cited By ~ 57

Author(s):

Yoshiyuki Tagawa ◽

Julián Martínez Mercado ◽

Vivek N. Prakash ◽

Enrico Calzavarini ◽

Chao Sun ◽

...

Keyword(s):

Experimental Data ◽

Isotropic Turbulence ◽

Response Times ◽

Three Dimensional ◽

Voronoi Cell ◽

Reynolds Numbers ◽

Point Particle ◽

Heavy Particles ◽

Data Set ◽

Light Particles

AbstractThree-dimensional Voronoï analysis is used to quantify the clustering of inertial particles in homogeneous isotropic turbulence using data sets from numerics in the point particle limit and one experimental data set. We study the clustering behaviour at different density ratios, particle response times (i.e. Stokes numbers $\mathit{St}$) and two Taylor–Reynolds numbers (${\mathit{Re}}_{\lambda } = 75$ and 180). The probability density functions (p.d.f.s) of the Voronoï cell volumes of light and heavy particles show different behaviour from that of randomly distributed particles, i.e. fluid tracers, implying that clustering is present. The standard deviation of the p.d.f. normalized by that of randomly distributed particles is used to quantify the clustering. The clustering for both light and heavy particles is stronger for higher ${\mathit{Re}}_{\lambda } $. Light particles show maximum clustering for $\mathit{St}$ around 1–2 for both Taylor–Reynolds numbers. The experimental data set shows reasonable agreement with the numerical results. The results are consistent with previous investigations employing other approaches to quantify the clustering. We also present the joint p.d.f.s of enstrophy and Voronoï volumes and their Lagrangian autocorrelations. The small Voronoï volumes of light particles correspond to regions of higher enstrophy than those of heavy particles, indicating that light particles cluster in higher vorticity regions. The Lagrangian temporal autocorrelation function of Voronoï volumes shows that the clustering of light particles lasts much longer than that of heavy or neutrally buoyant particles. Due to inertial effects arising from the density contrast with the surrounding liquid, light and heavy particles remain clustered for much longer times than the flow structures which cause the clustering.

Download Full-text

The modified cuinulant expansion for two-dimensional isotropic turbulence

Journal of Fluid Mechanics ◽

10.1017/s0022112081000840 ◽

1981 ◽

Vol 110 ◽

pp. 475-496 ◽

Cited By ~ 21

Author(s):

Tomomasa Tatsumi ◽

Shinichiro Yanase

Keyword(s):

Numerical Solutions ◽

Isotropic Turbulence ◽

Initial Period ◽

Three Dimensional ◽

Critical Time ◽

Reynolds Numbers ◽

Inviscid Limit ◽

Inertial Subrange ◽

Quasi Equilibrium ◽

Two Dimensional

The two-dimensional isotropic turbulence in an incompressible fluid is investigated using the modified zero fourth-order cumulant approximation. The dynamical equation for the energy spectrum obtained under this approximation is solved numerically and the similarity laws governing the solution in the energy-containing and enstrophy-dissipation ranges are derived analytically. At large Reynolds numbers the numerical solutions yield the k−3 inertial subrange spectrum which was predicted by Kraichnan (1967), Leith (1968) and Batchelor (1969) assuming a finite enstrophy dissipation in the inviscid limit. The energy-containing range is found to satisfy an inviscid similarity while the enstrophy-dissipation range is governed by the quasi-equilibrium similarity with respect to the enstrophy dissipation as proposed by Batchelor (1969). There exists a critical time tc which separates the initial period (t < tc) and the similarity period (t > tc) in which the enstrophy dissipation vanishes and remains non-zero respectively in the inviscid limit. Unlike the case of three-dimensional turbulence, tc is not fixed but increases indefinitely as the viscosity tends to zero.

Download Full-text

A similarity theory of locally homogeneous and isotropic turbulence generated by a Smagorinsky-type LES

Journal of Fluid Mechanics ◽

10.1017/s0022112096008105 ◽

1996 ◽

Vol 325 ◽

pp. 239-260 ◽

Cited By ~ 53

Author(s):

Andreas Muschinski

Keyword(s):

Newtonian Fluid ◽

Material Parameter ◽

Isotropic Turbulence ◽

Similarity Theory ◽

Reynolds Numbers ◽

Finite Difference Approximation ◽

Difference Approximation ◽

Spectral Models ◽

Homogeneous And Isotropic Turbulence ◽

Locally Homogeneous

A Kolmogorov-type similarity theory of locally homogeneous and isotropic turbulence generated by a Smagorinsky-type large-eddy simulation (LES) at very large LES Reynolds numbers is developed and discussed. The underlying concept is that the LES equations may be considered equations of motion of specific hypothetical fully turbulent non-Newtonian fluids, called ‘LES fluids’. It is shown that the length scale ls = csδ, which scales the magnitude of the variable viscosity in a Smagorinsky-type LES, is the ‘Smagorinsky-fluid’ counterpart of Kolmogorov's dissipation length $\eta = v^{3/4}\epsilon^{-1/4}$ for a Newtonian fluid where ν is the kinematic viscosity and ε is the energy dissipation rate. While in a Newtonian fluid the viscosity is a material parameter and the length ν depends on ε, in a Smagorinsky fluid the length ls is a material parameter and the viscosity depends on ε. The Smagorinsky coefficient cs may be considered the reciprocal of a ‘microstructure Knudsen number’ of a Smagorinsky fluid. A combination of Lilly's (1967) cut-off model with two well-known spectral models for dissipation-range turbulence (Heisenberg 1948; Pao 1965) leads to models for the LES-generated Kolmogorov coefficient αLES as a function of cs. Both models predict an intrinsic overestimation of αLES for finite values of cs. For cs = 0.2 Heisenberg's and Pao's models provide αLES = 1.74 (16% overestimation) and αLES = 2.14 (43% overestimation), respectively, if limcs → (αLES) = 1.5 is ad hoc assumed. The predicted overestimation becomes negligible beyond about cs = 0.5. The requirement cs > 0.5 is equivalent to Δ < 2ls. A similar requirement, L < 2η where L is the wire length of hot-wire anemometers, has been recommended by experimentalists. The value of limcs → (αLES) for a Smagorinsky-type LES at very large LES Reynolds numbers is not predicted by the models and remains unknown. Two critical values of cs are identified. The first critical cs is Lilly's (1967) value, which indicates the cs below which finite-difference-approximation errors become important; the second critical cs is the value beyond which the Reynolds number similarity is violated.

Download Full-text

Lagrangian cascade in three-dimensional homogeneous and isotropic turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.1 ◽

2014 ◽

Vol 741 ◽

Cited By ~ 7

Author(s):

Yongxiang Huang ◽

François G. Schmitt

Keyword(s):

Dissipation Rate ◽

Isotropic Turbulence ◽

Three Dimensional ◽

Energy Dissipation Rate ◽

Inertial Range ◽

Order Moment ◽

Scaling Exponent ◽

Tracer Particles ◽

Homogeneous And Isotropic Turbulence ◽

Multiplicative Cascade

AbstractIn this work, the scaling statistics of the dissipation along Lagrangian trajectories are investigated by using fluid tracer particles obtained from a high-resolution direct numerical simulation with $\mathit{Re}_{\lambda }=400$. Both the energy dissipation rate $\epsilon $ and the local time-averaged $\epsilon _{\tau }$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $\rho (\tau )$ of $\ln (\epsilon (t))$ and variance $\sigma ^2(\tau )$ of $\ln (\epsilon _{\tau }(t))$ obey a log-law with scaling exponent $\beta '=\beta =0.30$ compatible with the intermittency parameter $\mu =0.30$. The $q{\rm th}$-order moment of $\epsilon _{\tau }$ has a clear power law on the inertial range $10<\tau /\tau _{\eta }<100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-\zeta _L(2q)$ where $\zeta _L(2q)$ is the scaling exponent estimated using the Hilbert methodology. All of these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.

Download Full-text

Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.754 ◽

2016 ◽

Vol 789 ◽

pp. 669-707 ◽

Cited By ~ 49

Author(s):

Shriram Jagannathan ◽

Diego A. Donzis

Keyword(s):

Mach Number ◽

Scaling Laws ◽

Isotropic Turbulence ◽

Qualitative Change ◽

Reynolds Numbers ◽

Compressible Turbulence ◽

Stationary Flows ◽

Energy Exchanges ◽

Mach Numbers ◽

The Individual

We report results from direct numerical simulation (DNS) of stationary compressible isotropic turbulence at very-high resolutions and a range of parameters using a massively parallel code at Taylor Reynolds numbers ($R_{{\it\lambda}}$) ranging from $R_{{\it\lambda}}=38$ to $430$ and turbulent Mach numbers ($M_{t}$) ranging from 0.1 to 0.6 on up to $2048^{3}$ grid resolutions. A stationary state is maintained by a stochastic solenoidal forcing at the largest scales. The focus is on the mechanisms of energy exchanges, namely, dissipation, pressure-dilatation correlation and the individual contributing variables. Compressibility effects are studied by decomposing velocity and pressure fields into solenoidal and dilatational components. We suggest a critical turbulent Mach number at about 0.3 that separate two different flow regimes – only at Mach numbers above this critical value do we observe dilatational effects to affect the flow behaviour in a qualitative manner. The equipartition of energy between the dilatational components of kinetic and potential energy, originally proposed for decaying flows at low $M_{t}$, presents significant scatter at low $M_{t}$, but appears to be valid at high $M_{t}$ for stationary flows, which is explained by the different role of dilatational pressure in decaying and stationary flows, and at low and high $M_{t}$. While at low $M_{t}$ pressure possesses characteristics of solenoidal pressure, at high $M_{t}$ it behaves in similar ways to dilatational pressure, which results in significant changes in the dynamics of energy exchanges. This also helps explain the observed qualitative change in the skewness of pressure at high $M_{t}$ reported in the literature. Regions of high pressure are found to be correlated with regions of intense local expansions. In these regions, the density–temperature correlation is also seen to be relatively high. Classical scaling laws for low-order moments originally proposed for incompressible turbulence appear to be only weakly affected by compressibility for the range of $R_{{\it\lambda}}$ and $M_{t}$ investigated.

Download Full-text