Unsteady forcing of turbulence by a randomly actuated impeller array

We investigate the unsteady forcing of turbulent flow in a well-stirred reactor using opposing arrays of pitched-blade impellers which randomly and independently reverse rotation. We systematically explore the dependence of the large-scale motions and the homogeneity and isotropy of the turbulence upon the forcing. We identify three dimensionless control parameters: the source fraction (the fraction of time spent in clockwise motion), the dimensionless forcing period and an impeller Reynolds number. We find the timescale of unsteady motion corresponds to the forcing period T, the average period of impeller reversal, independently of the impeller angular speed $$\varOmega$$ Ω and source fraction. As in jet-stirred tanks, unsteady forcing substantially increases the unsteady kinetic energy, energy dissipation, integral length scale and Taylor microscale Reynolds number ($$R_\lambda$$ R λ ) and improves the homogeneity and isotropy of the flow, provided the source fraction is chosen optimally and the forcing period is sufficiently large ($$\varOmega T > 10^3$$ Ω T > 10 3 ); impeller Reynolds number has a relatively small influence. The forcing period must be matched to angular speed: decreasing the forcing period below this threshold results in a less intense, more inhomogeneous turbulent flow. Spectra of two-point velocity increments demonstrate that unsteady energy injection is dominated by axial shear generated across impellers and becomes less prominent at smaller scales. However, even at $$R_\lambda \approx 354$$ R λ ≈ 354 , the signature of this unsteady forcing can still be detected in near-dissipation-range statistics. These observations provide insight into optimisation of forcing and the mechanism of energy transfer when using unsteady forcing to generate turbulence in confined vessels. Graphical abstract

Analysis of thermally stratified radiative flow of Sutterby fluid with mixed convection

In this attempt, we investigate the mixed convection in Sutterby fluid flow based on boundary layer approximation. Heat transport analysis is composed of stratification and thermal radiative phenomena. The system of non-linear PDEs is transformed into coupled ODEs. Convergent series approximations are evaluated via homotopic technique. Influence of various pertinent parameters is sketched and graphically analyzed. It is found that horizontal velocity increments for higher mixed convection parameter. The radiation parameter has a similar relation with temperature whereas the stratification parameter shows opposite behavior for temperature field.

Scale-dependent anisotropy, energy transfer and intermittency in bubble-laden turbulent flows

Data from direct numerical simulations of disperse bubbly flows in a vertical channel are used to study the effect of the bubbles on the carrier-phase turbulence. We developed a new method, based on an extension of the barycentric map approach, that allows us to quantify and visualize the anisotropy and componentiality of the flow at any scale. Using this we found that the bubbles significantly enhance anisotropy in the flow at all scales compared with the unladen case, and that for some bubble cases, very strong anisotropy persists down to the smallest scales of the flow. The strongest anisotropy observed was for the cases involving small bubbles. Concerning the energy transfer among the scales of the flow, our results indicate that for the bubble-laden cases, the energy transfer is from large to small scales, just as for the unladen case. However, there is evidence of an upscale transfer when considering the transfer of energy associated with particular components of the velocity field. Although the direction of the energy transfer is the same with and without the bubbles, the behaviour of the energy transfer is significantly modified by the bubbles, suggesting that the bubbles play a strong role in altering the activity of the nonlinear term in the flow. The skewness of the velocity increments also reveals a strong effect of the bubbles on the flow, changing both its sign and magnitude compared with the single-phase case. We also consider the normalized forms of the fourth-order structure functions, and the results reveal that the introduction of bubbles into the flow strongly enhances intermittency in the dissipation range, but suppresses it at larger scales. This strong enhancement of the dissipation-scale intermittency has significant implications for understanding how the bubbles might modify the mixing properties of turbulent flows.

Design Optimization and Parameter Analysis of a Hybrid Rocket Motor-Powered Small LEO Launch Vehicle

In this paper, the effects of different grain shapes of a hybrid rocket motor (HRM) and different payload mass/orbit heights on the design of small launch vehicles (SLVs) are systematically discussed. An integrated overall design model for the hybrid rocket motor-powered small launch vehicle (HPSLV) is established, and two groups of three-stage SLVs capable of sending small payloads to the low earth orbit (LEO) are designed and optimized. In the first group, the SLVs with different grain shapes and different numbers of chambers in HRMs at the 1st and the 2nd stages are optimized and analyzed. In the second group, the SLVs capable of sending different payload mass to different orbit heights are optimized and analyzed. Pareto graphs of the design results show that the design of HRM at the 1st stage has the greatest impact on the take-off mass, total velocity increment, and maximum axial overload of the SLV. Self-organizing maps show that the take-off mass, maximum diameter, overall length, and velocity increment of the SLVs have the same variation tendency. For the 1-chamber HRM at the 1st stage, the wheel-shaped grain is better than circle-shaped and star-shaped grains in terms of reducing the total mass and length of the SLV, and the 4-chamber parallel HRM has more advantages over all 1-chamber designs for the same reason. The theoretical velocity increments are calculated by the Tsiolkovsky formula, and the actual velocity increments are obtained based on the trajectory simulation data. The results indicate that the HPSLV has a regular distribution in terms of the ratio of theoretical (actual) velocity increments at three different stages, and the estimated distribution ratio is around 1 : 1.55 : 1.69 (1 : 1.9 : 2.39), which can provide some reference for future development of HPSLV.

Generalized Description of Intermittency in Turbulence via Stochastic Methods

We present a generalized picture of intermittency in turbulence that is based on the theory of stochastic processes. To this end, we rely on the experimentally and numerically verified finding by R. Friedrich and J. Peinke [Phys. Rev. Lett. 78, 863 (1997)] that allows for an interpretation of the turbulent energy cascade as a Markov process of velocity increments in scale. It is explicitly shown that phenomenological models of turbulence, which are characterized by scaling exponents ζn of velocity increment structure functions, can be reproduced by the Kramers–Moyal expansion of the velocity increment probability density function that is associated with a Markov process. We compare the different sets of Kramers–Moyal coefficients of each phenomenology and deduce that an accurate description of intermittency should take into account an infinite number of coefficients. This is demonstrated in more detail for the case of Burgers turbulence that exhibits pronounced intermittency effects. Moreover, the influence of nonlocality on Kramers–Moyal coefficients is investigated by direct numerical simulations of a generalized Burgers equation. Depending on the balance between nonlinearity and nonlocality, we encounter different intermittency behavior that ranges from self-similarity (purely nonlocal case) to intermittent behavior (intermediate case that agrees with Yakhot’s mean field theory [Phys. Rev. E 63 026307 (2001)]) to shock-like behavior (purely nonlinear Burgers case).

A Comparison of Incremental Running Field and Treadmill Tests in Young Soccer Players

The purpose of this study was to compare the incremental running tests performed by young soccer players on a treadmill (Tr) and in the field (FTcod: 100 m change of direction and FTcir: 100 m circle). Nineteen players (average age 17.4 ± 1.1 years; body height 172.0 ± 5.7 cm; body mass 68.9 ± 6.7 kg) volunteered to perform incremental Tr , FTcod and FTcir running tests. In all three tests, players ran for 3 min at 8, 10, 12 and 14 km∙h-1 and were given a 1 min rest interval between subsequent stages. Blood lactate concentrations (La-) were measured at 1 min rest intervals and the heart rate (HR) responses of players were recorded during the tests. After a 5 min recovery period, the second part of the test started; players ran at 15 km∙h-1 with velocity increments of 1 km∙h-1 every 1 min until exhaustion. This part was performed to determine maximum HR, maximum La- and the players’ final velocities. The results showed that players had significantly lower La- (F = 6.93, p = 0.07, η2 = 0.46, 95%CI(TR-FTcir) = -1.91/-0.34, 95%CI(TR-FTcod) = -1.59/-0.05) and HR (F = 9.08, p = 0.02, η2 = 0.53, 95%CI(TR-FTcir) = -6.98/-1.68, 95%CI(TR-FTcod) = -7.19/1.08) responses in the Tr test than in the FTcir and FTcod tests at 14 km∙h-1. It was also found that players completed the Tr test (F = 58.22, p = 0.00, η2 = 0.87) at higher final running velocities than the FTcir (95%CI(TR-FTcir) = 1.67/2.78) and FTcod (95%CI(TR-FTcod) = 1.69/2.85) tests. In conclusion, when coaches or sports scientists plan to train at higher running velocities or according to the final velocity in the test, it is advisable to carry out testing in the circumstances under which training will be carried out (in the field or on a treadmill).

Wind turbine load dynamics in the context of turbulence intermittency

The importance of a high-order statistical feature of wind, which is neglected in common wind models, is investigated: non-Gaussian distributed wind velocity increments related to the intermittency of turbulence and their impact on wind turbine dynamics and fatigue loads are the focus. Gaussian and non-Gaussian synthetic wind fields obtained from a continuous-time random walk model are compared and fed to a common aero-servo-elastic model of a wind turbine employing blade element momentum (BEM) aerodynamics. It is discussed why and how the effect of the non-Gaussian increment statistics has to be isolated. This is achieved by assuring that both types feature equivalent probability density functions, spectral properties and coherence, which makes them indistinguishable based on wind characterizations of common design guidelines. Due to limitations in the wind field genesis, idealized spatial correlations are considered. Three examples with idealized; differently sized wind structures are presented. A comparison between the resulting wind turbine loads is made. For the largest wind structure sizes, differences in the fatigue loads between intermittent and Gaussian are observed. These are potentially relevant in a wind turbine certification context. Subsequently, the dependency of this intermittency effect on the field's spatial variation is discussed. Towards very small structured fields, the effect vanishes.

Wind turbine load dynamics in the context of turbulence intermittency

The importance of a high order statistical feature of wind, which is neglected in common wind models, is investigated: Non-Gaussian distributed wind velocity increments related to the intermittency of turbulence and their impact on wind turbines dynamics and fatigue loads are in the focus. Two types of synthetic wind fields obtained from a Continuous-Time-Random Walk model are compared and fed to a common Blade-Element/Momentum theory based aero-servo-elastic wind turbine model. It is discussed why and how the effect of the non-Gaussian increment statistics has to be isolated. This is achieved by assuring that both types feature equivalent probability density functions, spectral properties and coherence, which makes them indistinguishable based on wind characterizations of common design guidelines. Due to limitations in the wind field genesis idealized spatial correlations are considered. Three examples with idealized, differently sized wind structures are presented. A comparison between the resulting wind turbine loads is made. For the largest wind structure sizes differences in the fatigue loads between intermittent and Gaussian are observed. These are potentially relevant in a wind turbine certification context. Subsequently, the dependency of this intermittency effect on the field's spatial variation is discussed. Towards very small structured fields the effect vanishes.

A tool for determining maximum sustained swimming ability of selected inland fish species in an Afrotropic ecozone

Critical swimming speed (Ucrit) predicts the maximum sustained swimming velocity that various fish species are able to sustain for prolonged periods. The objective of this study was to determine the Ucrit of Afrotropic ecozone fish, determine oxygen consumption at Ucrit and relate the resulting optimum flow requirements to effective movement through fishways under South African flow conditions. The selected fish species were Coptodon rendalli, Tilapia sparrmanii, Pseudocrenilabrus philander, Oreochromis mossambicus and Enteromius trimaculatus. Ucrit and oxygen consumption (MO2) were measured in a swim respirometer at 5-min intervals, at increasing velocity increments of 0.5 cm·s−1 until volitional exhaustion. No significant differences were seen in the Ucrit values between C. rendalli, T. sparrmanii and P. philander, but all species significantly differed from O. mossambicus and E. trimaculatus, which had the highest Ucrit (17.6 ± 1.5 bl·s−1 and 18.2 ± 2.8 bl·s−1). Size plays an important role in the swimming performance of fish, with larger fish able to sustain a greater velocity, which was specifically true for O. mossambicus in this study. Additionally, smaller fish consumed more oxygen during swimming and therefore used more energy, experiencing relative physiological strain. Based on these data, flow respirometry was shown to be a useful tool to determining prolonged swimming abilities of South African fish species, and can help inform the structure and flow rates of culverts and fishways.