Spatiotemporal representation of the dynamic modes in turbulent cavity flows

Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) were used to extract the coherent structures in turbulent cavity flows. The spatiotemporal representation of the modes was achieved by performing the circular convolution of a change of basis on the data sequence, wherein the transformation function was extracted from the POD or DMD. The spatiotemporal representation of the modes provided significant insight into the evolutionary behavior of the structures. Self-sustained oscillations arise in turbulent cavity flows due to unsteady separation at the leading edge. The turbulent cavity flow at Re_D = 12,000 and a length to depth ratio L/D = 2 was analyzed. The dynamic modes extracted from the data clarified the presence of self-sustained oscillations. The spatiotemporal representation of the POD and DMD modes that caused self-sustained oscillations revealed the prevalent dynamics and evolutionary behavior of the coherent structures from their formation at the leading edge to their impingement at the trailing edge. A local minimum in the mode amplitude representing the energy contributions to the flow was observed upon the impingement of coherent structure at the trailing edge. The modal energy associated with the periodic formation of organized coherent structures followed by their dissipation upon impingement revealed the oscillatory behavior over time.     

The flow field around a micropillar confined in a microchannel

The flow field over a low aspect ratio (AR) circular pillar (L/D = 1.5) in a microchannel was studied experimentally. Microparticle image velocimetry (μPIV) was employed to quantify flow parameters such as flow field, spanwise vorticity, and turbulent kinetic energy (TKE) in the microchannel. Flow regimes of cylinder-diameter-based Reynolds number at 100 ⩽ Re_D ⩽ 700 (i.e., steady, transition from quasi-steady to unsteady, and unsteady flow) were elucidated at the microscale. In addition, active flow control (AFC), via a steady control jet (issued from the pillar itself in the downstream direction), was implemented to induce favorable disturbances to the flow in order to alter the flow field, promote turbulence, and increase mixing. Together with passive flow control (i.e., a circular pillar), turbulent kinetic energy was significantly increased in a controllable manner throughout the flow field.     

Influence of wall proximity on characteristics of wake behind a square cylinder: PIV measurements and POD analysis

Influence of wall proximity on characteristics of the wake behind a two-dimensional square cylinder was experimentally studied in the present work. A low-speed recirculation water channel was established for the experiment; the Reynolds number based on the free-stream velocity and cylinder width (D) was kept at Re_D = 2250. Four cases with different gap width, e.g., G/D = 0.1, 0.2, 0.4 and 0.8, were chosen for comparison. Two experimental techniques, e.g., the standard PIV with high image-density CCD camera and TR-PIV with a high-speed camera were employed in measuring the wake field, enabling a comprehensive view of the time-averaged wake pattern at high spatial resolution and the instantaneous flow field at high temporal resolution, respectively. For the four cases, the difference in spatial characteristics of the wake in the vicinity of the plane wall was analyzed in terms of the time-averaged quantities measured by the standard PIV, e.g., the streamline pattern, the vector field, the streamwise velocity fluctuation intensity and the reverse-flow intermittency. The proper orthogonal decomposition (POD) method was extensively used to decompose the TR-PIV measurements, giving a close-up view of the energetic POD modes buried in the wake. The low-order flow model of the wake at G/D = 0.8 and 0.4 was constructed by using the linear combination of the first two POD modes and the time-mean flow field, which reflected well the vortex shedding process in the sense of the phase-dependent patterns. The intermittent appearance of the weakly separated region near the wall was found at G/D = 0.4. On going from G/D = 0.8 to 0.4, the remarkable variation of the instantaneous wake in the longitudinal direction confirmed that the wall constraint stretches the vortices in the plane of the wall and transfers the energy to the longitudinal component at the expense of the lateral one.     

Periodic flow boiling in a non-uniformly heated microchannel heat sink

Hydrodynamic and thermal characteristics of flow boiling in a non-uniformly heated microchannel were studied. Experiments were performed with a single microchannel and a series of microheaters to study the microscale boiling of water under axially non-uniform heat input conditions. A simultaneous real time visualization of the flow pattern was performed with the measurement of experimental parameters. Tests were performed over a mass flux of 309.8 kg/m² s, and heat flux of 200–600 kW/m². Test results showed different fluctuations of heated wall temperature, pressure drop, and mass flux with variations of the heat input along the flow direction. The unique periodic flow boiling in a single microchannel was observed at all heat flux conditions except for the increasing heat input distribution case which is the nearly uniform effective heat input distribution condition. The instability is correlated with flow pattern transition. For the nearly uniform effective heating condition, no fluctuation of the wall temperature, pressure drop, or mass flux was observed. We can relieve the instability by increasing total heat input along the flow direction and predict the instability using the transition criteria and flow pattern map.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 10³ based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.     

LES of the flow around several cuboids in a row

This paper presents Large Eddy Simulations (LES) of flow around a four-vehicle platoon when one of the platoon members was forced to undergo in-line oscillations. The LES were made at the Reynolds number of 10⁵ based on the height of the vehicles. Combinations of two different frequencies corresponding to non-dimensional frequencies at the Strouhal numbers St₁ = 0.025 and St₂ = 0.013 and two oscillation amplitudes were used in this study. The methodology was validated by comparisons with data from previous experimental investigations. In order to highlight the dynamic effects, comparisons were made with steady results on a single vehicle and on a four-vehicle platoon. Large differences were found in the flow structures between quasi-steady and dynamic results. Furthermore, the behavior of the drag coefficient of the upstream neighbor of the oscillating model was investigated.     

Hydrodynamic forces on a rotating sphere

The wake dynamics of a rotating sphere with prescribed rotation axis angles are quantitatively analysed by carrying out numerical simulations at Reynolds numbers of Re = 100, 250 and 300, non-dimensional rotational rates Ω¹ = 0–1 and rotation axis angles α = 0, π/6, π/3 and π/2 measured from the free stream axis. These parameters are the same as those in an earlier study (Poon et al., 2010, Int. J. Heat Fluid Flow) where the instantaneous flow structures were discussed qualitatively. This study extends the findings of the earlier study by employing phase diagrams (C_Lx, C_Ly) and (C_D, C_L) to provide a quantitative analysis of the time-dependent behaviour of the flow structures. At Re = 300 and Ω¹ = 0.05, the phase diagrams (C_Lx, C_Ly) show ‘saw tooth’ patterns for both α = 0 and π/6. The ‘saw tooth’ pattern indicates that the flow structures comprise a higher frequency oscillation component at a Reynolds number of 300 which is not observed until Re ≈ 800 for a stationary sphere. This ‘saw tooth’ pattern disappears as Ω¹ increases. The employment of the phase diagrams also reveals that different flow structures induce different oscillation amplitudes on both lateral force coefficients. With the exception of the vortices formed from a shear layer instability, all other flow regimes show larger fluctuations in C_L than C_D.     

Low Reynolds number flow over a square cylinder with a detached flat plate

A numerical study of the alteration of a square cylinder wake using a detached downstream thin flat plate is presented. The wake is generated by a uniform flow of Reynolds number 150 based on the side length of the cylinder, D. The sensitivity of the near wake structure to the downstream position of the plate is investigated by varying the gap distance (G) along the wake centerline in the range 0 ⩽ G ⩽ 7D for a constant plate length of L = D. A critical gap distance is observed to occur at G_c ≈ 2.3D that indicates the existence of two flow regimes. Regime I is characterised by vortex formation occurring downstream of the gap while for regime II, formation occurs within the gap. By varying the plate length and gap distance, a condition is found where significant unsteady total lift reduction can occur. The root mean square lift reduction is limited by an unsteady stall process on the plate.     

Two-phase pressure drop and flow visualization of FC-72 in a silicon microchannel heat sink

The rapid development of two-phase microfluidic devices has triggered the demand for a detailed understanding of the flow characteristics inside microchannel heat sinks to advance the cooling process of micro-electronics. The present study focuses on the experimental investigation of pressure drop characteristics and flow visualization of a two-phase flow in a silicon microchannel heat sink. The microchannel heat sink consists of a rectangular silicon chip in which 45 rectangular microchannels were chemically etched with a depth of 276 μm, width of 225 μm, and a length of 16 mm. Experiments are carried out for mass fluxes ranging from 341 to 531 kg/m² s and heat fluxes from 60.4 to 130.6 kW/m² using FC-72 as the working fluid. Bubble growth and flow regimes are observed using high speed visualization. Three major flow regimes are identified: bubbly, slug, and annular. The frictional two-phase pressure drop increases with exit quality for a constant mass flux. An assessment of various pressure drop correlations reported in the literature is conducted for validation. A new general correlation is developed to predict the two-phase pressure drop in microchannel heat sinks for five different refrigerants. The experimental pressure drops for laminar-liquid laminar-vapor and laminar-liquid turbulent-vapor flow conditions are predicted by the new correlation with mean absolute errors of 10.4% and 14.5%, respectively.     

Two-phase flow regime assignment based on wavelet features of a capacitance signal

In this work, a new method is proposed to determine the two-phase flow regime based on the capacitance trace of the flow. The experimental data set contains 123 capacitance traces measured for a horizontal tube with an inner diameter of 8 mm. The tested refrigerant is R134a. The mass flux is varied between 200 and 500 kg/m² s and the vapour quality x is varied between 0 and 1. For each capacitance signal the wavelet variance is estimated based on the maximum overlap wavelet transform of the signal. The used wavelet function is a D8 wavelet of the Daubechies family. A feature space is generated based on the wavelet variance values associated with frequencies below 100 Hz. Principal component analysis and linear discriminant analysis are subsequently applied to this raw feature space, after which the Fuzzy c-means clustering algorithm is used to divide the feature space into clusters corresponding to different flow regimes. The resulting flow regime assignment shows a good agreement with a visual classification of the data set based on flow visualisations. Finally, the classification was performed based on variable training data to show the robustness of the method.     

Flow pattern characterization for R-245fa in minichannels: Optical measurement technique and experimental results

An optical measurement method using image processing for two-phase flow pattern characterization in minichannel is developed. The bubble frequency, the percentage of small bubbles as well as their velocity are measured. A high-speed high-definition video camera is used to measure these parameters and to identify the flow regimes and their transitions. The tests are performed in a 3.0 mm glass channel using saturated R-245fa at 60 °C (4.6 bar). The mass velocity is ranging from 100 to 1500 kg/m² s, the heat flux is varying from 10 to 90 kW/m² and the inlet vapor quality from 0 to 1. Four flow patterns (bubbly flow, bubbly–slug flow, slug flow and annular flow) are recognized. The comparison between the present experimental intermittent/annular transition lines and five transition lines from macroscale and microscale flow pattern maps available in the literature is presented. Finally, the influence of the flow pattern on the heat transfer coefficient is highlighted.     

Characterisation of gas-liquid two-phase flow in minichannels with co-flowing fluid injection inside the channel,part I: unified mapping of flow regimes

Present research highlights the potential of apparatuses with integrated minichannel packings to intensify gas-liquid-solid contacting. Especially an operation of these devices within the Taylor flow regime gained extraordinary attention due to its excellent heat and mass transfer and the segmented flow characteristics. However, criteria for flow regime transitions are mainly developed from water-similar fluids and are contradictory which hinders uniform flow regime prediction.This work presents a systematic analysis of adiabatic gas-liquid downflow in a square minichannel of 1.0 mm hydraulic diameter. In the mixing zone located within the flow channel, gas was injected into the co-flowing liquid by so-called capillary injectors with variable inner diameter (0.184, 0.317, 0.490 mm). Experiments were conducted using water, water-glycerol, and water-ethanol mixtures to cover a broad range of material properties. The gas and liquid superficial velocities were varied between 9.81·10^-4…2.72 m/s and 1.7·10⁻⁴…0.80 m/s, respectively. Taylor flow, Taylor-annular flow, annular flow, churn flow, and bubbly flow were observed. Using the Pi-theorem, 8 significant dimensionless groups dictating the flow transition were identified, namely u_{G, s}/u_{L, s}, Re_G, Re_L, We_G, We_L, Θ*, d_{In, CI}/d_h, and d_{Ou, CI}/d_h. Based on more than 1500 experimental data, criteria for the regime transitions of Taylor flow are provided. The derived flow regime map shows good agreement for all applied liquids and for the two larger injector geometries.     

Simulation of a valveless pump with an elastic tube

A valveless pump consisting of a pumping chamber with an elastic tube was simulated using an immersed boundary (IB) method. The interaction between the motion of the elastic tube and the pumping chamber generated a net flow toward the outlet throughout a full cycle of the pump. The net flow rate of the valveless pump was examined by varying the stretching coefficient (ϕ), bending coefficient (γ), the aspect ratio (l/d) of the elastic tube, and the frequency (f) of the pumping chamber. As the stretching and bending coefficients of the elastic tube increased, the net flow through the valveless pump decreased. Elastic tubes with aspect ratios in the range of 2 ⩽ l/d ⩽ 3 generated a higher flow rate than that generated for tubes with aspect rations of l/d = 1 or 4. As the frequency of the pumping chamber increased, the net flow rate of the pump for l/d = 2 increased. However, the net flow rate for l/d = 3 was nonlinearly related to the pumping frequency due to the complexity of the wave motions. Snapshots of the fluid velocity vectors and the wave motions of the elastic tube were examined over one cycle of the pump to gain a better understanding of the mechanism underlying the valveless pump. The relationship between the average gap in the elastic tube and the average flow rate of the pump was analyzed. A smaller gap in the elastic tube during the expansion mode and a wider gap in the elastic tube during the contraction mode played a dominant role in generating a high average flow rate in the pump, regardless of the stretching coefficient (ϕ), the aspect ratio (l/d) of the elastic tube, or the pumping frequency of the pumping chamber (f).     

Lattice Boltzmann simulation of the convective heat transfer from a stream-wise oscillating circular cylinder

In this paper, we studied the convective heat transfer from a stream-wise oscillating circular cylinder. Two dimensional numerical simulations are conducted at Re = 100–200, A = 0.1–0.4 and F = f_o/f_s = 0.2–3.0 with the aid of the lattice Boltzmann method. In particular, detailed attentions are paid on the extensive numerical results elucidating the influence of oscillation frequency, oscillation amplitude and Reynolds number on the time-average and RMS value of the Nusselt number. Over the ranges of conditions considered herein, the heat transfer characteristics are observed to be influenced in an intricate manner by the value of the oscillation frequency (F), oscillation amplitude (A) and Reynolds number (Re). Firstly, the heat transfer is enhanced when the cylinder oscillates stream-wise with small amplitude and low frequency, while it will be reduced by large amplitude and high frequency. Secondly, the average Nusselt number (Nu (ave)) decreases against the increasing value of oscillation frequency, while the RMS value of the Nusselt number, Nu (RMS), displays an opposite trend. Third, we obtained a similar frequency effect on the heat transfer over the range of Reynolds numbers investigated in this paper. In addition, detailed analyses on phase portraits, energy spectrum are also made.     

Spatially resolved wall temperature measurements during flow boiling in microchannels

Spatial and temporal variations of channel wall temperature during flow boiling microchannel flows using infrared thermography are presented and analyzed. In particular, the top channel wall temperature in a branching microchannel silicon heat sink is measured non-intrusively. Using this technique, time-averaged temperature measurements, with a spatial resolution of 10 μm, are presented over an 18 mm × 18 mm area of the heat sink. Also presented, within a specific sub-region of the heat sink, are intensity maps that are recorded at a rate of 120 frames per second. Time series data at selected point locations in this sub-region are analyzed for their frequency content, and dominant temperature fluctuations are extracted using proper orthogonal decomposition.Results at low-vapor-quality boiling condition indicate that temperatures can be determined from recorded radiation intensities with a temperature uncertainty varying from 0.9 °C at 25 °C to 1.0 °C at 125 °C. The time series data indicate periodic wall temperature fluctuations of approximately 2 °C that are attributed to the passage of vapor slugs. A dominant band of frequencies around 2–4 Hz is suggested by the frequency analysis. Proper orthogonal decomposition results indicate that first six orthogonal modes account for approximately 90% of the variance in temperature. The first mode reconstruction accounts for temporal variations in the dataset in the sub-region analyzed; however the magnitude of fluctuations and spatial variations in temperature are not accurately captured. A reconstruction using the first 25 modes is considered sufficient to capture both the temporal and spatial variations in the data.     

Atomistic simulation of crystallization of a polyethylene melt in steady uniaxial extension

We present simulation results of flow-induced crystallization of a dense polymeric liquid subjected to a strong uniaxial elongational flow using a rigorous nonequilibrium Monte Carlo method. A distinct transition between the liquid and the crystalline phases occurred at critical values of flow strength, with an abrupt, discontinuous transition of the overall chain conformation. The flow-induced crystalline phase matched quantitatively the experimental X-ray diffraction data of the real crystals remarkably well, including the sharp Bragg peaks at small wavenumbers, k < 1.5 Å^?1, indicating the existence of a global long-range ordering. We also found that the enthalpy change (ΔH = 225 J/g) during the phase transition was quantitatively very similar to the experimental heat of fusion (276 J/g) of polyethylene crystals under quiescent conditions. Furthermore, a detailed analysis of the configuration-based temperature provided a sound microscopic physical origin for the effective enhancement of the crystallization (or melting) temperature that has been observed in experiments. Simulation results also allow for the deduction of potential nonequilibrium expressions for thermodynamic quantities, such as temperature and heat capacity.     

Oil mist transport process in a long pipeline on turbulent flow transition region

Internal gas velocity fluctuations and their effects on the mist diffusion process were examined in a long horizontal pipe to understand oil mist transportation, particularly in the laminar-to-turbulent flow transition region. Three hot-wire anemometers and aerosol concentration monitors were used to deduce these effects as the two-phase mist flow gradually developed in the stream-wise direction. We found significant axial mist diffusion at Reynolds numbers (Re) < 1000 because of passive scalar transport by Poiseuille flow. However, this diffusion was restricted by the non-zero inertia of the mist at a Stokes number, O(10⁻⁵), relying on the Brownian motion of the mist. At Re > 2400, a sharp mist waveform was maintained by a turbulent flow with active radial mixing. New data were obtained within the range of 1000 < Re < 2400, which cannot be explained by interpolation between the above-mentioned two states. The mist concentration displays multiple temporal peaks at Re < 2000 owing to perturbations of localized turbulence as well as radial anisotropy as being conveyed more than 2000-diameters in distance. This behavior is caused by intermittent disturbances induced by the pipe wall roughness, which sharply distorts the wall-aligned laminar mist layer left by parabolic axial stretching of local laminar flow.