Mesh Reynolds Number Research Articles

Non-explicit large eddy simulations of turbulent channel flows from [formula omitted] up to [formula omitted

This numerical study based on high-order finite-difference schemes presents LES-NWR (Large Eddy Simulation with near-wall resolution) of turbulent channel flows up to Reτ=5200 using non-explicit approaches for which numerical dissipation is introduced via the discretisation of viscous terms of the Navier-Stokes equations. These models are cheaper than explicit LES models as no extra terms are needed in the equations to account for the contribution of the unresolved scales. The Approximate Deconvolution Method with Relaxation Term (ADM-RT) approach is also assessed and the present LES data are compared with reference Direct Numerical Simulations (DNS) data for first and second order moments as well as for the turbulent kinetic energy budget. Even if the viscous sublayer is not resolved, the proposed non-explicit LES approaches are in excellent agreement with the reference DNS data and to a certain extent with the ADM-RT model, for a fraction of the cost of the DNS. The proposed non-explicit models, for which the possibility to locally adjust the added numerical dissipation is investigated, are straightforward to implement and come with a negligible additional computational cost while the ADM-RT model is 30% more expensive than the non-explicit models.The parameters of the models are defined before the simulations and no modifications of the parameters are needed when the Reynolds number and the mesh resolution are changed. It is shown that a modulation of the magnitude of the numerical dissipation in time and in space is not necessarily needed, at least for the mesh resolutions and Reynolds numbers considered in the present study. The main conclusion is that non-explicit models can replace advantageously explicit models when high-order finite-difference methods are used. They can generate accurate LES-NWR of turbulent channel flows over a wide range of Reynolds numbers at a fraction of a cost of DNS.

Investigation on aerodynamic performance of luxury cruise ship

Due to the high superstructures and complex configurations of luxury cruise ships, the impacts of wind loads on the ships must be analyzed during design. In this study, the aerodynamic performance of a Vista-class cruise ship was investigated through wind tunnel measurements, empirical formulae and numerical calculations. Wind tunnel experiments were conducted in a simulated atmospheric boundary layer wind field, and the measured data exhibited reliable wind load characteristics of the cruise ship. Three empirical formulae were employed to estimate the wind loads on the cruise ship. The comparison between the estimated results and the experimental data indicated that the general characteristics of the wind loads on generic ship types summarized by empirical formulae were not consistent with those on the Vista-class cruise ship. Numerical simulations based on the Reynolds-averaged Navier-Stokes (RANS) equations were performed under the same conditions as those of the wind tunnel experiments. Mesh independence and Reynolds number independence analyses were carried out. The numerical results of the wind loads matched well with the experimental data. Valuable flow field details captured by the numerical calculations were also extracted to analyze the flow characteristics around the cruise ship. The results demonstrated that the Vista-class cruise ship is a typical blunt body. The wind loads on the cruise ship were sensitive to the Reynolds number. The reversed-flow zones around the ship were primarily distributed over the front/back sides of the ship, the top deck, and the ship's leeward side. These reversed-flow zones were mostly induced by the flow separation at the corners of the bow and aft decks and the sharp edges of the top deck. The analysis of the flow characteristics around the ship can provide guidance for future optimization of the aerodynamic performance of the Vista-class cruise ship.

Integral invariants and decay of temporally developing grid turbulence

We present a study of a large-scale energy spectrum and integral invariants in temporally developing grid turbulence at mesh Reynolds numbers of ReM = 10 000 and 20 000 by employing direct numerical simulations (DNSs) in a periodic box. The simulations are initialized with a velocity field that approximates the wakes induced by the bars of conventional square grids. The turbulence statistics obtained in the temporal DNS agree well with those of the previous experiments in both the production and decay regions. The temporally developing grid turbulence also has a so-called non-equilibrium region, which is consistent with its spatially developing counterpart, where the normalized dissipation rate of turbulence kinetic energy (TKE), Cε, increases as the turbulence decays. The decay exponent n of TKE is n = 1.22 at ReM = 20 000 and n = 1.35 at ReM = 10 000, which are close to the values for the Saffman turbulence [i.e., 6/5 for ReM = 20 000 and 6(1 + p)/5 ≈ 1.36 for ReM = 10 000 with p ≈ 0.13 obtained by Cε ∼ tp at large t]. The longitudinal integral length scale and the TKE dissipation rate also exhibit temporal evolutions consistent with the Saffman turbulence for both ReM. The Saffman integral directly evaluated in the grid turbulence tends to be time-independent after the turbulence evolves for about 200 times of characteristic time scale defined by mesh size divided by the mean velocity of a fluid passing the grid. A direct evaluation of the TKE spectrum E(k) shows that E(k) ≈ Lk2/4π2 is valid for a finite range of low wavenumbers.

Adaptive filtering for the simulation of turbulent flows with lattice Boltzmann methods

This paper presents an extension of a Large Eddy Simulation based approach in the framework of Lattice Boltzmann Methods. An extended filter technique is introduced based on selective viscosity filters. In contrast to previous approaches we omit adjusting parameters, a technique frequently used in literature to achieve good fit with turbulence benchmarks. Such parameters have to be adapted manually for different Reynolds numbers and grid resolutions. The new filter approach is based on a time dependent coupling between resolved scales and a phase averaged strain-rate. We demonstrate that our method is able to recover turbulent statistics of the Taylor–Green vortex benchmark, representing Homogeneous Isotropic Turbulence for varying mesh resolutions and Reynolds numbers. Beyond that, we show the applicability to wall-bounded turbulence represented by the turbulent channel flow at friction Reynolds numbers Reτ=180,Reτ=395 and Reτ=590. A spectral viscosity analysis is performed in order to demonstrate the methods ability to adapt the numerical dissipation according to the mesh resolution.

Decay of grid turbulence in superfluid helium-4: Mesh dependence

Temporal decay of grid turbulence is experimentally studied in superfluid 4He in a large square channel. The second sound attenuation method is used to measure the turbulent vortex line density (L) with a phase locked tracking technique to minimize frequency shift effects induced by temperature fluctuations. Two different grids (0.8 mm and 3.0 mm mesh) are pulled to generate turbulence. Different power laws for decaying behavior are predicted by a theory. According to this theory, L should decay as t−11/10 when the length scale of energy containing eddies grows from the grid mesh size to the size of the channel. At later time, after the energy containing eddy size becomes comparable to the channel, L should follow t−3/2. Our recent experimental data exhibit evidence for t−11/10 during the early time and t−2 instead of t−3/2 for later time. Moreover, a consistent bump/plateau feature is prominent between the two decay regimes for smaller (0.8 mm) grid mesh holes but absent with a grid mesh hole of 3.0 mm. This implies that in the large channel different types of turbulence are generated, depending on mesh hole size (mesh Reynolds number) compared to channel Reynolds number.

Scale-adaptive subgrid-scale modelling for large-eddy simulation of turbulent flows

The proportionality between the subgrid-scale (SGS) drain rate of kinetic energy and the viscous dissipation rate of the resolved motions is studied a priori by filtering a given fully resolved field and evaluating a generic form of the hypothesized energy spectrum. The ratio of the SGS drain to the resolved dissipation, on which a balance condition for the SGS dissipation across an arbitrary grid scale is founded, is shown to be independent of the turbulence Reynolds number, and can be described by a function in terms of the averaged mesh Reynolds number. Such a balance condition can serve as a physical constraint in the SGS modeling to account for the scale effects of the model coefficient(s). Scale-adaptive dynamic Smagorinsky-Lilly model and mixed nonlinear model are formulated for large-eddy simulation of transitional and/or turbulent flows in such a way that the constraint is satisfied. The newly proposed scale-adaptive dynamic SGS models are validated in simulations of homogeneous isotropic turbulence and turbulent channel flow, and prove to be superior over traditional dynamic SGS models.

On the stability analysis of the PISO algorithm on collocated grids

Abstract A Fourier stability analysis is performed on the standard PISO algorithm for collocated grids. The amplification matrices of the sequence are obtained for one-dimensional and two-dimensional incompressible flow problems and the error amplification is studied for different numerical conditions (i.e. mesh-Reynolds number, Courant number, number of PISO corrections). Stability features are also analyzed for steady state conditions and the performance is compared against the SIMPLE-family algorithms. The effect of the mesh orientation and aspect ratio on two-dimensional flow problems are also investigated. It is found that a grid with a higher refinement in one direction can produce an unstable behavior for small mesh-Reynolds numbers, while stability is ensured for the same conditions with a uniformly refined grid in both directions. The first situation can be corrected by enforcing the coupling between pressure and velocity through more PISO corrections.

Stability Condition for Single-Relaxation Time Isothermal Lattice Boltzmann Formulation

In this present research, the Lattice Boltzmann method has been used to determine the stability condition of the single relaxation time. The range of Reynolds number is 100,400 and 1000. Meanwhile, the range of mesh size is varying between 31 to 251. The results show that the increase in both mesh size and Reynolds number give an effect on deviation percentages. The deviation percentages for all mesh and Reynolds number also presented.

On grid-generated turbulence in the near- and far field regions

AbstractUsing a conventional bi-planar turbulence-generating grid, we confirm the recent findings (Valente & Vassilicos,Phys. Rev. Lett., vol. 108, 2012, art. 214503) that show there is a turbulence decay region close to the generating grid that departs from the ‘classical’ turbulence decay (Comte-Bellot & Corrsin,J. Fluid Mech., vol. 25, 1966, pp. 657–682). In this ‘near-field’ region, the turbulence energy decays more rapidly than in the far-field and it exhibits unusual scaling properties. Based on the velocity decay laws, we show that for our conventional grid, the near-field extends from$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x/M \sim 6$to$x/M \sim 12$where$x$is the downstream distance from the grid and$M$is the mesh size. This corresponds to$1.1 \le x/x* \le 2.3$where$x*$is the wake interaction length scale (Mazellier & Vassilicos,Phys. Fluids, vol. 22, 2010, art. 075101). However, other statistics (velocity derivatives and length-scale ratios) indicate that the extent of the initial period depends on the grid mesh Reynolds number,$R_M$, extending further for higher values of$R_M$. In the near-field the turbulence approaches isotropy both at the large and small scales but there still is inhomogeneity in the derivative statistics. The derivative skewness also departs from values observed at comparable Reynolds numbers in the far-field decay region, and in other turbulent flows at comparable Reynolds numbers. Two values of$R_M$were studied:$42 \times 10^3$and$76 \times 10^3$.

Oscillating-grid experiments in water and superfluid helium.

Passing a fluid through a grid is a well-known mechanism used to study the properties of turbulence. Oscillating a horizontal grid vertically in a tank has also been used extensively and is considered to be a source of almost homogenous isotropic turbulence. When the oscillating grid is turned on a turbulent flow is induced. A front translates into the experimental tank, behind which the flow is highly turbulent. Long predicted that the growth of such a front would grow diffusively as the square root of time (i.e., d ∼ sqrt[t]) and Dickinson and Long presented experimental evidence for the diffusive result at a low mesh Reynolds number of 555. This paper revisits these experiments and attempts a set of two models for the advancing front in both square and round tanks. We do not observe significant differences between runs in square and round tanks. The experiments in water reach mesh Reynolds numbers of order 30000. Using some data from superfluid helium experiments we are able to explore mesh Reynolds numbers to about 43000. We find the power law for the advancing front decreases weakly with the mesh Reynolds number. Using a very long tank we find that the turbulent front stops completely at a certain depth and attempt a simple explanation for that behavior. We study the propagation of the turbulent front into tubes of different diameters inserted into the main tank. We show that these tubes exclude wavelengths much larger than the tube diameter. We explore the variation of the position of the steady-state boundary H on tube diameter D and find that H = cD with c ∼ 2. We suggest this may be explained by saturation of the energy-containing length scale ℓ(e). We also report on the effect of plugging up just one hole of the grid. Finally, we recall some earlier oscillating grid experiments in superfluid (4)He in the light of the present results.

A study on effects of temporally varying/ fluctuating noises on statistical profiles measured by means of PLIF method (Development of prediction formulas of the effects, and validation by high-Sc-number scalar mixing layer in grid turbulence)

In planar laser induced fluorescence (PLIF) measurement, temporally varying and fluctuating noises affect measured statistical profiles, significantly. In this study, the former φ is caused by a ratio of temporally varying quantum yield φ between measurement and reference images, and the latter sβI is mainly due to temporal fluctuations of a ratio of camera sensitively β and a ratio of incident laser I to excite a fluorescent dye, where sβI ≡ βI - 1. These noises can significantly affect statistical profiles of fluctuating concentration field. The aim of this study is to develop predictive formulas for the effects on fundamental statistical profiles. The effects of φ and sβI are reconstructed to mean of φ, αT/2, mean of sβI, SβI and intensity of fluctuation of sβI, <e2>, where α is rate of temporal change of φ, T is required time of the experiment, SβI = <sβI>, e = sβI, sβI = SβI + sβI and <> denotes ensemble average. Then, we show a series of the formulas to predict the effects on mean scalar, intensity of scalar fluctuation, 3rd-order statistics and 4th-order statistics of scalar fluctuation. The predictive formulas are validated by using experimental results of high-Sc-number scalar mixing layer in grid-generated turbulence measured by PLIF method, where the mesh Reynolds number was 2,500 and the Schmidt number was about 2,100, respectively. The effects of <e2> is analytically found to be the most significant among αT, SβI and <e2> by expanding the predictive formulas. In fact, the profile of <c2> is significantly affected by variation of <e2>. The predictive formulas can be used as formulas to correct the profiles when given values of the three parameter are appropriate.

On invariants in grid turbulence at moderate Reynolds numbers

AbstractThe decay characteristics and invariants of grid turbulence were investigated by means of laboratory experiments conducted in a wind tunnel. A turbulence-generating grid was installed at the entrance of the test section for generating nearly isotropic turbulence. Five grids (square bars of mesh sizes $M= 15$, 25 and 50 mm and cylindrical bars of mesh sizes $M= 10$ and 25 mm) were used. The solidity of all grids is $\sigma = 0. 36$. The instantaneous streamwise and vertical (cross-stream) velocities were measured by hot-wire anemometry. The mesh Reynolds numbers were adjusted to $R{e}_{M} = 6700$, 9600, 16 000 and 33 000. The Reynolds numbers based on the Taylor microscale $R{e}_{\lambda } $ in the decay region ranged from 27 to 112. In each case, the result shows that the decay exponent of turbulence intensity is close to the theoretical value of ${- }6/ 5$ (for the $M= 10~\mathrm{mm} $ grid, ${- }6(1+ p)/ 5\sim - 1. 32$) for Saffman turbulence. Here, $p$ is the power of the dimensionless energy dissipation coefficient, $A(t)\sim {t}^{p} $. Furthermore, each case shows that streamwise variations in the integral length scales, ${L}_{uu} $ and ${L}_{vv} $, and the Taylor microscale $\lambda $ grow according to ${L}_{uu} \sim 2{L}_{vv} \propto {(x/ M- {x}_{0} / M)}^{2/ 5} $ (for the $M= 10~\mathrm{mm} $ grid, ${L}_{uu} \propto {(x/ M- {x}_{0} / M)}^{2(1+ p)/ 5} \sim {(x/ M- {x}_{0} / M)}^{0. 44} $) and $\lambda \propto {(x/ M- {x}_{0} / M)}^{1/ 2} $, respectively, at $x/ M\gt 40{\unicode{x2013}} 60$ (depending on the experimental conditions, including grid geometry), where $x$ is the streamwise distance from the grid and ${x}_{0} $ is the virtual origin. We demonstrated that in the decay region of grid turbulence, ${ u}_{\mathit{rms}}^{2} { L}_{uu}^{3} $ and ${ v}_{\mathit{rms}}^{2} { L}_{vv}^{3} $, which correspond to Saffman’s integral, are constant for all grids and examined $R{e}_{M} $ values. However, ${ u}_{\mathit{rms}}^{2} { L}_{uu}^{5} $ and ${ v}_{\mathit{rms}}^{2} { L}_{vv}^{5} $, which correspond to Loitsianskii’s integral, and ${ u}_{\mathit{rms}}^{2} { L}_{uu}^{2} $ and ${ v}_{\mathit{rms}}^{2} { L}_{vv}^{2} $, which correspond to the complete self-similarity of energy spectrum and $\langle {\boldsymbol{u}}^{2} \rangle \sim {t}^{- 1} $, are not constant. Consequently, we conclude that grid turbulence is a type of Saffman turbulence for the examined $R{e}_{M} $ range of 6700–33 000 ($R{e}_{\lambda } = 27{\unicode{x2013}} 112$) regardless of grid geometry.

Fractal analysis of turbulent mixing in fractal-generated turbulence by planar laser-induced fluorescence

The fractal geometry of turbulent mixing of high-Schmidt-number scalars in multiscale, fractal-generated turbulence (FGT) is experimentally investigated. The difference between the fractal geometry in FGT and that in classical grid turbulence (CGT) generated by a biplane, single-scale grid is also investigated. Nondimensional concentration fields are measured by a planar laser-induced fluorescence technique whose accuracy has recently been improved by our research group, and the fractal dimensions are calculated by using the box-counting method. The mesh Reynolds number is 2500 for both CGT and FGT. The Schmidt number is about 2100. It is found that the threshold width ΔCth, when applying the box-counting method, does not affect the evaluation of the fractal dimension at large scales; therefore, the fractal dimensions at large scales have been investigated in this study. The results show that the fractal dimension in FGT is larger than that in CGT. In addition, the fractal dimension in FGT monotonically increases with the onset of time (or with the downstream direction), whereas that in CGT is almost constant with time. The investigation of the number of counted boxes in a unit area, together with the above results, suggests that turbulent mixing is more enhanced in FGT from the viewpoints of fractal geometry and expansion of the mixing interface.

S053023 格子乱流の減衰特性における初期条件の影響([S053-02]渦流れのダイナミクス(2))

The decay characteristics of grid turbulence were investigated by means of laboratory experiments conducted in a wind tunnel. A turbulence-generating grid was installed at the entrance of the test section for generating nearly isotropic turbulence. Five grids(square bars of mesh size M= 15, 25 and 50 mm and cylindrical bars of mesh size M= 10 and 25mm) were used. The solidity of all grids is σ=0.36. The instantaneous streamwise and vertical velocities were measured by hot wire anemometry. The mesh Reynolds numbers were adjusted to Re_M = 6,700, 9,600, 16,000 and 33,000. In each case, the result shows that the decay exponent of turbulent intensity is close to the theoretical value of -6/5 for Saffman turbulence. Furthermore, each case shows that streamwise variations in the integral length scales L_<uu> and L_<vv> and the Taylor microscale X grow according to L_<uu>〜2L_<vv>∝(x/M-x_0/M)^<2/5> and λ∝(x/M-x_0/M)<1/2>, respectively, at x/M > 40-60(depending on the experimental conditions, including grid geometry), where x is the streamwise distance from the grid and x_0 is the virtual origin. We demonstrated that in the decay region of grid turbulence, u_<r.m.s>^2L_<uu>^3 and v_<r.m.s>^2L_<vv>^3., which correspond to Saffman's integral, are constant for all grids and examined Re_M values. Consequently, we conclude that grid turbulence is a type of Saffman turbulence for the examined Re_M range of 6,700-33,000 regardless of grid geometry.

Leray-α Regularization of the Smagorinsky-Closed Filtered Equations for Turbulent Jets at High Reynolds Numbers

The article reports on blending of the Leray-α regularization with the conventional Smagorinsky subgrid-scale closure as an option for large-eddy-simulation of turbulent flows at very high Reynolds number on coarse meshes. The model has been tested in the self-similar far-field region of a jet at a range of Reynolds numbers spanning over two decades (4×103, 4×104 and 4×105) on two very coarse meshes of 2×105 and 3×104 mesh cells. The results are compared with the well-resolved DNS for \(Re_D=4\times 10^3\) on 15 million cells and experimental data for higher Re numbers. While the pure Leray-α can fail badly at high Re numbers on very coarse meshes, a blending of the two strategies by adding a small amount of extra-dissipation performs well even at a huge jet Reynolds number of \(Re_D=4\times 10^5\) on a very coarse mesh (2×105 cells), despite the ratio of the typical mesh spacing to the Kolmogorov length exceeding 300. It is found that the main prerequisite for successful LES, both for the classic Smagorinsky and the blended Leray-α/Smagorinsky model, is to resolve the shear-length \(L_s=\sqrt{\varepsilon/{\cal S}^3}\) (where \({\cal S}\) is the shear-rate modulus), defined by the constraint Δ/Ls < 1, where Δ is the typical mesh-cell size. For the mixed Leray-α/Smagorinsky model the regularization parameter should also be related to the shear-length rather than the local mesh size or Reynolds number, for which we propose a guide criterion α = 0.15÷0.3 Ls.

On Invariants in Energy Decay Region in Grid Turbulence

Decaying characteristics of grid turbulence are investigated by means of the laboratory experiments using a wind tunnel. Turbulence-generating grids are installed at the entrance to the test section to generate nearly isotropic turbulence. Four grids (mesh size M = 10, 15, 25 and 50 mm) are used. Instantaneous streamwise velocity is measured by a hot wire anemometer. The mesh Reynolds numbers are adjusted to ReM = 6,700, 9,600, 16,000 and 33,000. In this study, decaying characteristics and invariants of grid turbulence for four grid sizes and ReM are mainly investigated. The result for each case shows that the decay exponent of turbulent intensity is close to a theoretical value of -6/5 for Saffman turbulence. Each case also shows that streamwise variation of integral length scale Luu and Taylor microscale λ grow as Luu ∝ (x/M - x0/M)2/5 and λ ∝(x/M - x0/M)1/2 at (x/M - x0/M) > 50, where x0 is the virtual origin. Consequently, it is concluded that in the decaying region of grid turbulence, u2r.m.sL3uu, which corresponds to Saffman's integral, are constant for all grids and ReM examined. However, u2r.m.sL5uu, which corresponds to Loitsianskii's integral, is not constant.

An Alternative HSS Preconditioner for the Unsteady Incompressible Navier‐Stokes Equations in Rotation Form

We study the preconditioned iterative method for the unsteady Navier‐Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew‐Hermitian preconditioner to the Krylov subspace‐iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, Reynolds numbers, time step, and algorithm parameters. The preconditioner is efficient and easy to apply for the unsteady Oseen problems in rotation form.

Effects of Freestream Turbulence on an Axisymmetric CO2 Turbulent Jet Diffusion Field

Effects of freestream turbulence on an axisymmetric CO2 turbulent jet diffusion field is experimentally investigated. The composite probe consisting of two concentration-sensitive I-type hot-wires is used for the simultaneous measurement of instantaneous axial velocity and concentration. To measure grid turbulence without the jet, I- and X-type hot wire probes are used. The fractal square grid is used to generate freestream turbulence. The Taylor Reynolds number is Reλ = 80 - 160. The results are compared with previous measurements in which weak freestream turbulence at Reλ-35 is generated by the classical biplane grid (regular grid). For both flows, the mesh Reynolds number based on the grid mesh size M and freestream speed U0 is 6,000 and the jet Reynolds number based on the diameter d (= 3 mm) of jet exit and relative velocity between freestream and exit velocity, UJ-U0, is 5,000. The results show that profiles of normalized mean velocity and concentration in the CO2 jet do not change at the present Reλ in the freestream flow, while growth of half widths of mean velocity and mean concentration, turbulent intensity, turbulent mass flux and eddy diffusivity in the CO2 jet are significantly increased under the effect of strong freestream turbulence. The eddy diffusivity in the CO2 jet becomes approximately three times of that in the regular grid turbulence.

Direct numerical simulation of turbulent mixing in regular and fractal grid turbulence

Turbulent mixing in regular and fractal grid turbulence is investigated in this work by using direct numerical simulation (DNS). Two types of turbulence-generating grids are used: a biplane square grid (regular grid) and a square fractal grid. The thickness ratios tr of the fractal grids are set at 5.0 and 8.5. The grid solidity is maintained at σ=0.36 for all the grids. The mesh Reynolds number, ReM=U0Meff/ν, is set at 2500 for all cases, where U0 is the cross-sectionally averaged mean velocity; Meff, the effective mesh size; and ν, the kinematic viscosity. The grids are numerically generated using the immersed boundary method at 4Meff downstream of the entrance to the computational domain. The computational domain size normalized by Meff is 64×8×8 in the streamwise, vertical and spanwise directions for the regular grid and 64×16×16 for the fractal grids. Scalar mixing layers that initially have a step profile develop downstream of the grids. The Prandtl number is set at Pr=0.71 considering the heat transfer in air flow. Instantaneous temperature fields, instantaneous fluctuating temperature fields and fundamental turbulent statistics are presented. The results show that turbulent mixing is more strongly enhanced in fractal grid turbulence than in regular grid turbulence for the same ReM. In fractal grid turbulence, turbulent mixing is more strongly enhanced at tr=8.5 than at tr=5.0.

High-Schmidt-number scalar transfer in regular and fractal grid turbulence

Turbulent mixing of high-Schmidt-number passive scalars in regular and fractal grid turbulence is experimentally investigated using a water channel. A turbulence-generating grid is installed at the entrance of the test section, which is 1.5 m in length and 0.1 m×0.1 m in cross section. Two types of grids are used: one is a regular grid consisting of square-mesh and biplane constructions, and the other is a square-type fractal grid, which was first investigated by Hurst and Vassilicos (2007 Phys. Fluids 19 035103) and Seoud and Vassilicos (2007 Phys. Fluids 19 105108). The two grids have the same solidity of 0.36. The Reynolds number based on the mesh size, ReM=U0Meff/ν, is 2500 in both flows, where U0 is the cross-sectionally averaged mean velocity, Meff is the effective mesh size and ν is the kinematic viscosity. A fluorescent dye (rhodamine B) is homogeneously premixed only in the lower stream and therefore the scalar mixing layers with an initial step profile develop downstream of the grids. The Schmidt number of the dye is O(103). The time-resolved particle image velocimetry and the planar laser-induced fluorescence techniques are used to measure the velocity and concentration fields. The results show that the turbulent mixing in fractal grid turbulence is more strongly enhanced than that in regular grid turbulence for the same mesh Reynolds number ReM. The profile of instantaneous scalar dissipation shows that scalar dissipation takes place locally even in the far downstream region at x/Meff=120 in fractal grid turbulence.