Effect of Pressure Fluctuation at Nozzle Exit on Flapping Phenomena in a Two-Dimensional Jet

2011 ◽  
Author(s):  
Yuichi Shoji ◽  
Osamu Terashima ◽  
Yasuhiko Sakai ◽  
Kouji Nagata
Keyword(s):  
Pressure Fluctuation ◽  
Velocity Fluctuation ◽  
Streamwise Velocity ◽  
Measured Data ◽  
The Self ◽  
Pressure Probe ◽  
Two Dimensional ◽  
Hot Wire ◽  
Ensemble Averaging ◽  
Streamwise Velocity Fluctuation

The flapping motion of the flow is one of the coherent structures in a two-dimensional turbulent jet. In past studies, the flapping phenomenon indicated that a pair of fluid lumps with the positive and negative streamwise velocity fluctuation exists on the opposite sides of the jet centerline, and the signs of the velocity fluctuation for those fluid lumps change alternately as the time advances. Additionally, it is known that the vortices at the jet exit are arranged symmetrically to the jet centerline and gradually become the alternate arrangement, and in the self-preserving region, the flapping phenomenon can be observed. However, the reason why the flapping phenomenon arises is not cleared yet. In this study, in order to clarify the influence of the velocity and pressure fluctuation on the arising of the flapping phenomenon, the characteristics of the velocity and pressure at near the jet exit are investigated. The measurements of the flapping phenomenon, the characteristics of the velocity and pressure at near the jet exit are conducted by using combined probe composed of an X-type hot-wire probe and a pressure probe, and at the same time, the measurements of streamwise velocity fluctuations at the two points in the self-preserving region are performed to determine the time when the flapping phenomenon is arising. The measured data are analyzed statistically by ensemble-averaging technique and conditional-sampling technique on the basis of the intermittency function for the flapping/non-flapping decision. The intermittency function is obtained by applying the wavelet transform analysis to the measured data by two I-type hot wire probes placed at the opposite side of the jet centerline in the self-preserving region. Measured and analyzed results show that the RMS value of the streamwise velocity fluctuation at the jet exit is clearly different according to whether flapping phenomenon arises or not. On the other hand, the RMS value of the pressure fluctuation at the jet exit is not influenced by the arising of the flapping phenomenon. In addition, the possibility that the arising of the strong negative pressure fluctuation at near the jet exit has an important role in the flapping phenomenon is shown.

scholarly journals A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers

2018 ◽  
Vol 842 ◽  
pp. 354-380 ◽  
Author(s):  
Xiang I. A. Yang ◽  
Mahdi Abkar
Keyword(s):  
Velocity Fluctuation ◽  
Passive Scalar ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Ensemble Averaging ◽  
Outer Length ◽  
Passive Scalars ◽  
Streamwise Velocity Fluctuation ◽  
Wall Bounded Flows ◽  
High Reynolds

The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, ‘a fully developed passive scalar’ refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the ‘HRAP formalism’ is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence:$u=\sum _{i=1}^{N_{z}}a_{i}$, where the instantaneous streamwise velocity fluctuation at a generic wall-normal location$z$is modelled as a sum of additive contributions from wall-attached eddies ($a_{i}$) and the number of addends is$N_{z}\sim \log (\unicode[STIX]{x1D6FF}/z)$. The HRAP model admits generalized logarithmic scalings including$\langle \unicode[STIX]{x1D719}^{2}\rangle \sim \log (\unicode[STIX]{x1D6FF}/z)$,$\langle \unicode[STIX]{x1D719}(x)\unicode[STIX]{x1D719}(x+r_{x})\rangle \sim \log (\unicode[STIX]{x1D6FF}/r_{x})$,$\langle (\unicode[STIX]{x1D719}(x)-\unicode[STIX]{x1D719}(x+r_{x}))^{2}\rangle \sim \log (r_{x}/z)$, where$\unicode[STIX]{x1D719}$is the streamwise velocity fluctuation,$\unicode[STIX]{x1D6FF}$is an outer length scale,$r_{x}$is the two-point displacement in the streamwise direction and$\langle \cdot \rangle$denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for$\unicode[STIX]{x1D719}$being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.

scholarly journals Experimental investigations of the turbulent/non-turbulent interface over surface with spanwise heterogeneity

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Yanguang Long ◽  
Jinjun Wang ◽  
Chong Pan
Keyword(s):  
Boundary Layer ◽  
Velocity Fluctuation ◽  
Large Scale ◽  
Dynamic Properties ◽  
Sampling Rate ◽  
Water Channel ◽  
Streamwise Velocity ◽  
Plane Boundary ◽  
Streamwise Velocity Fluctuation ◽  
Secondary Vortices

The sharp but irregular interface that separates the instantaneous turbulent and irrotational flows is termed as the turbulent/non-turbulent interface (TNTI). TNTI can be widely observed in various types of flow, such as turbulent boundary layers, jets and combustion flame fronts. Due to its importance on the intermittency and entrainment process, TNTI has been widely explored in its geometry and dynamic properties (da Silva et al., 2014). Most of the studies focus on the TNTIs in smooth plane boundary layer, while few investigate the effects of wall shapes. However, the wall conditions in many engineering applications are complex and heterogeneous, which will induce large-scale heterogeneity (Barros and Christensen, 2014) and require further investigations. To shed new light on the intermittency and entrainment above complex surfaces, the TNTI over spanwise heterogeneity are investigated here with time-resolved stereoscopic PIV (TR-SPIV). The model and TR-SPIV experimental set-up are shown in Fig. 1. The experiments are conducted in the low-speed water channel at Beijing University of Aeronautics and Astronautics. The spanwise distance S between two adjacent ridges is S/(δ) = 1.35, where (δ) is the spanwise-averaged boundary layer thickness. This spanwise distance is selected to induced strong secondary vortices (Vanderwel and Ganapathisubramani, 2015; Wangsawijaya et al., 2020). The Reynolds number based on the streamwise location x is Rex = 7.2×105. The field of view is around 2S×1.8S, and is captured by two CMOS cameras (2048×2048 pixel) with sampling rate as 500Hz. The averaged resolution is about 8 pixels per Kolmogorov scale (calculated at y/(δ) = 0.6), which is high enough for TNTI-related research (Borrell and Jimenez, 2016). The ´TNTI is detected by the magnitude of local enstrophy ω2/2, and the threshold is selected to be the value where changing the threshold has the smallest influence on the TNTI-mean-height (Watanabe et al., 2018). The time-mean velocity and TNTI location are present in Fig.2(a). A pair of counter-rotating largescale secondary vortices (SVs) are induced over the ridge-type roughness. At the position where SVs induce upwash flow, a low-momentum pathway (LMP) can be observed, while the time-mean height of TNTI (yI) is brought higher. As a contrast, where downwash flow induces high-momentum pathway (HMP), (yI) is lower. TNTI properties are further discussed from two aspect. The geometry properties are firstly investigated. The fractal dimension of the TNTI keeps as 2.3 along the spanwise direction. This value is consistent with the result over smooth plate (Borrell and Jimenez, 2016; Wu et al., 2020) and riblets plates(Cui et al., 2019),´ which indicates that the wall shapes do not influence the multiscale properties of the TNTI. The streamwise wavelength of the TNTI (λI) is further obtained by calculating the streamwise pre-multiplied spectrum of the TNTI. It is found that at each spanwise location, λI is identical to the wavelength of streamwise velocity fluctuation at the TNTI mean height. This shows that the large-scale fluctuation of TNTI is controlled by the large-scale streamwise velocity fluctuation structures. Secondly, the p.d.f. of TNTI instantaneous height is investigated, as shown in Fig. 2(b). It can be observed that the p.d.f. of TNTI height above LMP shows a negative skewness, while the p.d.f. above HMP skews positively. A closer look at instantaneous structures shows that the skewness is attributed to the different probability of Q2/Q4 events in LMP and HMP.

Structure of Low-Speed Streaks in Drag Reducing Flow With Polymer Solution Blown From the Channel Wall

2011 ◽  
Author(s):  
Hening Xu ◽  
Shota Ishitsuka ◽  
Masaaki Motozawa ◽  
Kaoru Iwamoto ◽  
Hirotomo Ando ◽  
...  
Keyword(s):  
Polymer Solution ◽  
Buffer Layer ◽  
Velocity Fluctuation ◽  
Channel Wall ◽  
Streamwise Velocity ◽  
Low Speed ◽  
Blowing Ratio ◽  
Image Velocimetry ◽  
Streamwise Velocity Fluctuation ◽  
Low Speed Streaks

For the investigation of turbulent structure in drag reducing flow with polymer solution blown from the channel wall (wall blowing), instantaneous velocity field has been precisely measured in the x-z plane at different locations along the wall-normal direction via Particle Image Velocimetry (PIV). Polymer solutions with 25 ppm and 100 ppm of weight concentration were tested at a blowing ratio of 1.2×10−4 and at 20000 of Reynolds number. About 5% and 11% of drag reduction (DR) rate was obtained, respectively. As a result of this experiment, turbulent statistic data showed that the Root Mean Square (RMS) of streamwise velocity fluctuation increased and RMS of spanwise velocity fluctuation was suppressed comparing with water flow. We found that these low-speed streaks became relatively regular in the buffer layer, including an increase of both length and width, which indicated a depression of turbulence by polymer diffused in the buffer layer.

Irrotational fluctuations near a turbulent boundary layer

1967 ◽  
Vol 27 (2) ◽  
pp. 209-230 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Fluctuation ◽  
Velocity Fluctuation ◽  
Low Frequency ◽  
Two Dimensional ◽  
Frequency Range ◽  
Fluctuation Spectrum ◽  
One Dimensional ◽  
Irrotational Field

A verification of some of the predictions of the theory of Phillips (1955) is presented, and the relation between one-dimensional and two-dimensional wavenumber spectra is discussed. The convection velocity of the irrotational field deduced from measurements of the frequency spectrum alone appears to be about 0.9U1in the frequency range carrying most of the energy. It follows that the pressure-fluctuation spectrum is proportional to the velocity-fluctuation spectrum and varies as ω2at low frequency. The discrepancy between this result and measurements of wall-pressure spectra is plausibly attributed to extraneous sound.

scholarly journals Two-dimensional energy spectra in high-Reynolds-number turbulent boundary layers

2017 ◽  
Vol 826 ◽  
Author(s):  
Dileep Chandran ◽  
Rio Baidya ◽  
Jason P. Monty ◽  
Ivan Marusic
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Spatial Spectrum ◽  
Two Dimensional ◽  
Hot Wire ◽  
Self Similarity ◽  
Low Reynolds Numbers ◽  
High Reynolds

Here, we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity ($u$) in a high-Reynolds-number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26 000. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise ($\unicode[STIX]{x1D706}_{x}$) and spanwise ($\unicode[STIX]{x1D706}_{y}$) length scales to the streamwise variance at a given wall height ($z$). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows$\unicode[STIX]{x1D706}_{y}/z\sim (\unicode[STIX]{x1D706}_{x}/z)^{1/2}$behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship ($\unicode[STIX]{x1D706}_{y}\sim \unicode[STIX]{x1D706}_{x}$), as required for self-similarity and predicted by the attached eddy hypothesis.

scholarly journals Circular quiver gauge theories, isomonodromic deformations and $$W_N$$ fermions on the torus

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Pavlo Gavrylenko ◽  
Alessandro Tanzini
Keyword(s):  
Integrable System ◽  
Gauge Theories ◽  
The Self ◽  
Free Fermion ◽  
Two Dimensional ◽  
Isomonodromic Deformation ◽  
Specific Time ◽  
Dimensional Torus ◽  
Isomonodromic Deformations ◽  
Deformation Problem

AbstractWe study the relation between class $$\mathcal {S}$$ S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two-dimensional torus with punctures. Turning on the self-dual $$\Omega $$ Ω -background corresponds to a deautonomization of the Seiberg–Witten integrable system which implies a specific time dependence in its Hamiltonians. We show that the corresponding $$\tau $$ τ -function is proportional to the dual gauge theory partition function, the proportionality factor being a nontrivial function of the solution of the deautonomized Seiberg–Witten integrable system. This is obtained by mapping the isomonodromic deformation problem to $$W_N$$ W N free fermion correlators on the torus.

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