On the onset of high-Reynolds-number grid-generated wind tunnel turbulence

Abstract

Using an active grid devised by Makita (1991), shearless decaying turbulence is studied for the Taylor-microscale Reynolds number, Rλ, varying from 50 to 473 in a small (40 × 40 cm2 cross-section) wind tunnel. The turbulence generator consists of grid bars with triangular wings that rotate and flap in a random way. The value of Rλ is determined by the mean speed of the air (varied from 3 to 14 m s–1) as it passes the rotating grid, and to a lesser extent by the randomness and rotation rate of the grid bars. Our main findings are as follows. A weak, not particularly well-defined scaling range (i.e. a power-law dependence of both the longitudinal (u) and transverse (v) spectra, F11(k1) and F22(k1) respectively, on wavenumber k1) first appears at Rλ ∼ 50, with a slope, n1, (for the u spectrum) of approximately 1.3. As Rλ was increased, n1 increased rapidly until Rλ ∼ 200 where n ∼ 1.5. From there on the increase in n1 was slow, and even by Rλ = 473 it was still significantly below the Kolmogorov value of 1.67. Over the entire range, 50 [les ] Rλ [les ] 473, the data were well described by the empirical fit: $n_1 = \frac{5}{3}(1-3.15R_\lambda^{-2/3})$. Using a modified form of the Kolmogorov similarity law: F11(k1) = C1*ε2/3k1–5/3(k 1η)5/3–n1 where ε is the turbulence energy dissipation rate and η is the Kolmogorov microscale, we determined a linear dependence between n1 and C1*: C1* = 4.5 – 2.4n1. Thus for n1 = 5/3 (which extrapolation of our results suggests will occur in this flow for Rλ ∼ 104), C1* = 0.5, the accepted high-Reynolds-number value of the Kolmogorov constant. Analysis of the p.d.f. of velocity differences Δu(r) and Δv(r) where r is an inertial subrange interval, conditional dissipation, and other statistics showed that there was a qualitative difference between the turbulence for Rλ < 100 (which we call weak turbulence) and that for Rλ > 200 (strong turbulence). For the latter, the p.d.f.s of Δu(r) and Δv(r) had super Gaussian tails and the dissipation (both of the u and v components) conditioned on Δu(r) and Δv(r) was a strong function of the velocity difference. For Rλ < 100, p.d.f.s of Δu(r) and Δv(r) were Gaussian and conditional dissipation statistics were weak. Our results for Rλ > 200 are consistent with the predictions of the Kolmogorov refined similarity hypothesis (and make a distinction between the dynamical and kinematical contributions to the conditional statistics). They have much in common with similar statistics done in shear flows at much higher Rλ, with which they are compared.

The inertial subrange in turbulent pipe flow: centreline

“…Here the constant, µ of K62, (1.3) is replaced by the empirical function, (4.4). Figures 6 (a,b) show spectra with inner and outer scalings indicated by (4.3) and (4.5) respectively: there are identifiable plateaux with both inner and outer scaling at the three highest Reynolds numbers, with an ordinate value of about 0.73, very close to the Mydlarski & Warhaft (1996) value. However, this is not the self-similar value of about 0.55 (see figure 2) and the difference is presumably due to the empirical function.…”

“…Figure 7. Second-order (n = 2) moments, compensated using Mydlarski & Warhaft (1996) function (4.4). Same data as figure 5.…”

“…Dual studies are limited, notable exceptions in shear flows being Saddoughi & Veeravalli (1994); Mydlarski & Warhaft (1996), among others. Many of the ambiguities associated with the definition of the −5/3 inertial subrange law might be clarified by appeal to a unifying physical process.…”

Effect of background turbulence on an axisymmetric turbulent jet

“…The optimal parameters were found to be (µ on , σ on ) = (12 , 4) s, and (µ off , σ off ) = (108 , 36) s. On average, 10% of the pumps were on at a time. In the second algorithm, the state of a pump changed if a random number (between 0 and 1) that was generated every 0.4 seconds (for each pump) was greater than a certain threshold (0.98) (Mydlarski and Warhaft, 1996). Between these two algorithms, the flow produced using the first algorithm was superior, most notably because of its lower mean flow (at 110 cm downstream of the RJA, <U>/u rms < 15% for the first algorithm, while <U>/u rms was up to 50% for the second one).…”

The Century of Turbulence Theory: The Main Achievements and Unsolved Problems

“…The authors applied to the considered by them problem hypotheses of the same type as those used in the papers [97,98] for the evaluation of velocity profiles in turbulent pipe, channel and boundary-layer flows. Obtained in [123] results proved to be in good agreement with the experimental results by Mydlarski and Warhaft [124] relating to spectral measurements in the isotropic turbulent flow produced in a relatively small wind tunnel by an 'active grid' generating intensive turbulent fluctuations. The data by Mydlarski and War haft corresponded to a limited range of not too large Reynolds numbers; therefore even the existence here of the intermediate range of wave numbers k where E n (k) °= k" a , a>0, was somewhat unexpected.…”