Proper orthogonal decomposition of the flow in geometries containing a narrow gap

Geometries containing a narrow gap are characterized by strong quasi-periodical flow oscillations in the narrow gap region. The above mentioned phenomena are of inherently unstable nature and, even if no conclusive theoretical study on the subject has been published, the evidence shown to this point suggests that the oscillations are connected to interactions between eddy structures of turbulent flows on opposite sides of the gap. These coherent structures travel in the direction of homogeneous turbulence, in a fashion that strongly recalls a vortex street. Analogous behaviours have been observed for arrays of arbitrarily shaped channels, within certain range of the geometric parameters. A modelling for these phenomena is at least problematic to achieve since they are turbulence driven. This work aims to address the use of Proper Orthogonal Decomposition (POD) to reduce the Navier–Stokes equations to a set of ordinary differential equations and better understand the dynamics underlying these oscillations. Both experimental and numerical data are used to carry out the POD.     

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES) method at a Reynolds number Re = 8 500. The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric. The proper orthogonal decomposition(POD) analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1% of the turbulent kinetic energy, and hence their impact on the wake dynamics is studied. The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point. The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction. In addition, the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.     

槽道内涡波流场的POD分析

对槽道内涡波流场的瞬态速度矢量场进行了2DPIV测量实验,将2DPIV测量的矢量场数据进行POD分析,根据POD分解的各阶模态的能量比确定了表征涡波流场主导结构的前15阶模态。结果表明,POD分解的前15阶模态发现槽道内涡波流场是由槽道壁面剪切层诱导的涡列以及伴随的波状主流组成;流场中大尺度的涡旋发展为涡对,对波状主流的脉动频率产生影响;根据涡波流场中的驻点和鞍点,获取了流场的大尺度涡对、平均流场以及Helmholtz涡环等明显特征;最后根据POD分解的前15阶模态对槽道内涡波流场进行重组,重组流场表征了槽道内层流状态下波状主流的形态和涡旋共存的涡波结构以及驻点和鞍点的位置处涡旋的变化等主要特征,有效地剔除了PIV测量流场中的随机信息,保留了PIV测量流场的主导特征。     

Nonlinear dynamics of cycle-to-cycle variations in a lean-burn natural gas engine with a non-uniform pre-mixture

Nonlinear Dynamics - The Hopf bifurcation behavior is an important issue for the nonlinear dynamic analysis of gas foil bearing (GFB)-rotor systems. However, there is a lack of detailed study on...     

Developing laminar flow in the inlet length of a smooth pipe

The laminar flow phenomena in the inlet (entrance) region of circular pipe are investigated experimentally. New curves of friction factor versus Reynolds number, for various entry lengths, are obtained and compared with the standard curve for fully developed laminar flow. The relationship between the viscous friction, the energy loss due to the lengthwise rate of change of the kinetic energy coefficient and the total energy loss is investigated. The continuous variation of the velocity profile is analysed by using the concept of a non-Newtonian liquid whose shear sensitivity varies continuously along the pipe.Nomenclature A cross-sectional area - kinetic energy correction coefficient - D pipe diameter - boundary thickness - increment - f measured friction factor as defined by Darcy's law - f _k component of f due to change in kinetic energy only - f _v component of f due to viscous head loss only - f _L friction factor as computed from Langhaar's theory - g gravitational acceleration - h head loss - H _k component of h due to change in kinetic energy - H _v component of h due to viscous friction - K, n constants in the power law =K(dU/dr) ⁿ - v kinematic viscosity - viscosity - L length - L _e entry length - L _d developing (inlet) length - N _R Reynolds number - P pressure - Q volume discharge - r distance from the centre line of the pipe towards the wall - r ₀ radius - pressure - shear stress - U velocity - U _m mean velocity - U _c centre-line (maximum) velocity - x ₁ axial distance from entrance to the first pressure tapping point - x ₂ axial distance from entrance to the second pressure tapping point - Z dimensionless number=L/r ₀ - dimensionless number=Z/N _R     

Analysis of misfires in a direct injection engine using proper orthogonal decomposition

Previous work demonstrated that the occasional misfired and partially burned cycles (MF) in a stratified-charge, spark-ignited direct injection engine always achieved an early flame kernel, but failed to reach and inflame the fuel in the bottom of the piston bowl. This conclusion was derived from intra-cycle crank angle resolved velocity and fuel concentration images that were recorded simultaneously using high-speed particle image velocimetry and planar laser-induced fluorescence. In this study, both ensemble average analysis, conditionally sampled on either MF or Well Burned (WB) cycles and proper orthogonal decomposition (POD) are applied separately to the velocity and fuel distributions. POD of the velocity and fuel distributions near the spark plug were performed, and the mode energy and structure of the modes are compared. This analysis is used to assess the similarity and differences between the MF and the WB cycles and to identify physical insight gained by POD. The POD modes were determined from the combined set of 200 WB and 37 MF cycles to create two sets of 237 orthogonal modes, one set for the velocity, V, and one for the equivalence ratio, ε. Then, conditionally sampled averages of the POD coefficients could be used to quantify the extent to which each mode contributed to the MFs. Also, the probability density functions of the coefficients quantified the cyclic variability of each mode’s contribution. The application of proper orthogonal decomposition to velocity and equivalence ratio images was useful in identifying and analyzing the differences in flow and mixture conditions at the time of spark between well-burning and misfiring cycles. However, POD results alone were not sufficient to identify which of the cycles were misfiring cycles, and additional information was required for conditional sampling.     

Proper orthogonal decomposition of wall-pressure fluctuations under the constrained wake of a square cylinder

The proper orthogonal decomposition (POD) analysis of the wall-pressure fluctuations below the constrained wake of a two-dimensional square cylinder in proximity to a plane wall was made on two systems, i.e., G/D = 0.25 and 0.5, which corresponds to the wakes with and without suppression of the vortex shedding, respectively. Here, G is the gap distance and D is the width of the square cylinder. Synchronized measurements of wall-pressure fluctuations were made using a microphone array. For the system G/D = 0.5, the first two energetic modes contribute 34.7% and 23.4% to the total fluctuation energy, respectively; however, the fluctuation energy corresponding to the third mode are relatively small and less than 10%. This sharp variation in eigenvalue is due to the presence and dominance of the Karman-like vortex shedding. However, for the system G/D = 0.25, the considerable reduction in the eigenvalues of the first several modes is due to the suppression of the Karman-like vortex shedding. The spatial wavy pattern of the first several energetic eigenmodes was shown to be a good reflection of convective vortices superimposed in the wakes. The spectra of the POD coefficients determined the frequency of the dominant structures. Based on the coherence of the POD coefficients, an effective method of determining the number of POD modes for reconstruction of the low-order wall-pressure field was proposed. Accordingly, the low-order wall-pressure fluctuations in the systems G/D = 0.5 and 0.25 were reconstructed by using the first four and five POD modes, respectively. The coherence and cross-correlation analysis of the reconstructed wall-pressure fluctuations, which excluded the influence of the small-scale structures and background ‘noise’, gave an insight view of the footprints of the dominant flow structures, which otherwise could not be effectively captured by using the original wall-pressure fluctuations.     

Analytic solutions of incompressible laminar flow in the inlet region of a pipe

The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.     

Direct numerical simulation of the flow in the intake pipe of an internal combustion engine

The incompressible flow in the intake pipe of a laboratory-scale internal combustion engine at Reynolds numbers corresponding to realistic operating conditions was studied with the help of direct numerical simulations. The mass flow through the curved pipe remained constant and the valve was held fixed at its halfway-open position, as is typically done in steady flow engine test bench experiments for the optimization of the intake manifold. The flow features were identified as the flow evolves in the curved intake pipe and interacts with the cylindrical valve stem. The sensitivity of the flow development on the velocity profile imposed at the inflow boundary was assessed. It was found that the flow can become turbulent very quickly depending on the inflow profile imposed at the pipe inlet, even though no additional noise was added to mimic turbulent velocity fluctuations. The transition to turbulence results from competing and interacting instability mechanisms both at the inner curved part of the intake pipe and at the valve stem wake. Azimuthal variations in the local mass flow exiting the intake pipe were identified, in agreement with previously reported measurement results, which are known to play an important role in the charging motion inside the cylinder of an internal combustion engine.     

Creeping flow analysis of an integrated microfluidic device for rheometry

This paper analyzes flow of a power-law fluid in a microfluidic device for the purpose of discovering an algorithm for rheometry. Previous investigations have shown that measurement of the velocity field or the pressure field and the inlet flow rate in a microfluidic T-junction allow determination of rheological parameters uniquely. However, the range of shear induced within the flow domain was limited by the constant pressure drop applied across the micro-device. To avoid this control restriction and further develop our inverse technique, a constant flow rate system was investigated. With this configuration, the flow rate can be set appropriately to achieve a desired shear range and the rheological parameters can be inferred from the measurement of mean pressure at the inlet and at the junction. By assuming creeping flow conditions and the existence of a Hagen-Poiseuille-like law for the relationship between the pressure drop and the volumetric flow rate, the analysis produces an algorithm that is self-consistent (demonstrates the Hagen-Poiseuille law) and permits the inference of the power-law parameters from the ratio of any two field variables measured over a region (averaged), the pressure drop, and the volumetric flow rate.     

Capillary-driven flow analysis of a micro-grooved pipe

Solar energy provides significant opportunities to the power needs. The pipes with micro-grooves etched in the inner wall have been widely taken on the absorber receiver in the parabolic trough and cooling systems for solar thermal absorbers because this sort of pipes improves heat transfer. To support parabolic trough design in solar energy application systems, this study developed a capillary-driven two-phase flow model. The study further examines the influences caused by different micro-grooves, fluids, temperatures, radiuses and widths of groove. Our study concludes that (1) the triangular-microgroove has better influence of the liquid front position than semicircular-microgroove. (2) Water has better influence of liquid front position than ethanol and benzene. (3) The saturated temperature is indirectly proportional to the liquid front position. (4) The length of liquid front position is longer if value of radius is higher. (5) The width of groove does not significantly affect on the liquid front position and velocity. In addition, the proposed mathematical modeling is solved more correctly as compared to previous research. From our results, a good design of the micro-groove pipe can be achieved.     

Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

This paper presents reduced order modelling (ROM) in fluid–structure interaction (FSI). The ROM via the proper orthogonal decomposition (POD) method has been chosen, due to its efficiency in the domain of fluid mechanics. POD-ROM is based on a low-order dynamical system obtained by projecting the nonlinear Navier–Stokes equations on a smaller number of POD modes. These POD modes are spatial and temporally independent. In FSI, the fluid and structure domains are moving, owing to which the POD method cannot be applied directly to reduce the equations of each domain. This article proposes to compute the POD modes for a global velocity field (fluid and solid), and then to construct a low-order dynamical system. The structure domain can be decomposed as a rigid domain, with a finite number of degrees of freedom. This low-order dynamical system is obtained by using a multiphase method similar to the fictitious domain method. This multiphase method extends the Navier–Stokes equations to the solid domain by using a penalisation method and a Lagrangian multiplier. By projecting these equations on the POD modes obtained for the global velocity field, a nonlinear low-order dynamical system is obtained and tested on a case of high Reynolds number.     

Pathline analysis of traveling wavy blowing and suction control in turbulent pipe flow for drag reduction

Skin friction drag is much greater in turbulent flows as compared with that in laminar flows. It is well known that traveling wave control can be used to achieve a large drag reduction. In the present study, a direct numerical simulation of a turbulent pipe flow was performed to clarify the mechanism of the drag reduction caused by the traveling wave control. The flow induced by the control was evaluated using pathline analysis. Near the wall, a “closed flow” was formed, wherein the injected particles return to the wall owing to the suction flow. The random component of Reynolds shear stress was perfectly suppressed in the closed flow, which suggests that there was no turbulence. The controlled flow was categorized into four patterns, and each flow characteristic and drag reduction effect was discussed. When the closing rate is high, the drag decreases, while when the closing rate is low, i.e., when the injected particles are released into the main flow, the turbulence is maintained. If the thickness of the layer suppressing turbulence is insufficient, a significant effect in terms of the drag reduction cannot be expected. The large drag reduction owing to the traveling wave control can be attributed to the elimination of turbulence in the region near the wall.     

Effect of pipe diameter on flow patterns for air-water flow in horizontal pipes

New results are presented on interfacial patterns observed for air and water flowing in horizontal 2.54 and 9.53 cm pipelines close to atmospheric conditions. This work differs from previous studies in that measurements of pressure fluctuations at two locations separated in the streamwise direction are used to detect slugs. The liquid flow needed to initiate slugs at low gas velocities is strongly affected by pipe diameter and appears to depend on a linear instability. At high gas velocities the transition is approximately independent of pipe diameter and is explained by a nonlinear mechanism associated with the coalescence of roll waves. The initiation of slugs in the annular flow regime is determined to occur at much lower liquid flows than had been reported by previous investigators. The transition from stratified to annular flow is different in smaller-diameter pipes than in larger pipes because wave wetting plays a more important role.     

Effect of injection on the flow in the inlet region of a channel

Momentum and energy integrals are used to study the effect of injection on the flow in the inlet region of a channel, taking into account the loss of energy due to viscous dissipation in the boundary layer. Analytical expressions for boundary layer development and inlet region pressure distribution are presented. A comparison of the results of the present analysis is made with earlier studies.     

Effect of inlet subcooling on two-phase flow oscillations in a vertical boiling channel

In this work, results of experimental research to investigate the effects of heat transfer augmentation and inlet subcooling on two-phase flow instabilities are presented. For this purpose, a simple set-up was designed and built. The effect of inlet subcooling was investigated using different heat transfer surfaces and inlet temperatures at constant heat input of 415 W. Freon-11 has been used as the test fluid, and the experiments were carried out for six heater tubes having different heat transfer surfaces. Inlet temperatures were in the range of –9.8°C to 38°C. The results indicate that, in the range of present experiments, the system becomes more stable, that it's instability boundary moves into lower mass flow rates, with increase in the inlet subcooling. However, the amplitudes and the periods of the oscillations increase with increase in the inlet subcooling. For some of the tested surfaces there was a particular inlet subcooling, above and below which the system's stability decreased.

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Der Einfluß der Eintrittsunterkühlung auf die Oszillationen einer Zwei-Phasen-Strömung in einem senkrechten Siede-Kanal

Zusammenfassung In dieser Arbeit werden die Ergebnisse einer experimentellen Untersuchung des Einflusses von Verbesserungen der Wärmeübertragung und der Eintrittsunterkühlung auf Instabilitäten der Zweiphasenströmung dargestellt. Zu diesem Zweck wurde ein einfacher Aufbau konstruiert und aufgebaut. Der Einfluß der Eintrittsunterkühlung wurde unter Benutzung verschiedener Wärmeübertragungsoberflächen und Eintrittstemperaturen bei einer konstanten Wärmezufuhr von 415 W untersucht. Als Testfluid wurde Freon-11 benutzt. Die Experimente wurden für sechs Heizrohre mit verschiedenen Wärmeübertragungsoberflächen durchgeführt. Die Eintrittstemperaturen lagen in diesem Bereich von –9.8°C bis 38°C. Die Ergebnisse zeigen, daß in dem Bereich der vorliegenden Untersuchungen das System mit einem Ansteigen der Eintrittsunterkühlung stabiler wird und daß dessen Instabilitätsgrenze sich zu niedrigeren Massenstromdichten bewegt. Die Amplituden und Perioden der Schwingungen steigen mit Zunahme der Eintrittsunterkühlung an. Für einige der getesteten Oberflächen existierte eine bestimmte Eintrittsunterkühlung, über bzw. unter welcher die Stabilität des Systems abnahm.