Drinking water distribution networks such as South East Water Ltd. (SEWL), Melbourne Water, Sydney Water, etc. are supposed to transport only dissolved matter rather than a few visible particles. However, it is almost impossible to make the drinking water free from suspended solid particles. The ability to determine the origins of these particles varies between different water supply systems, with possible sources being from catchment, treatment processes, biofilm growth within the water supply pipes, and corrosion products. Improvement of our understanding of the complex hydrodynamic behavior of suspended and/or deposited particles involved in these distribution pipe networks requires mathematical and physical models. Computational Fluid Dynamics (CFD) along with analytical turbulent model is one of the most popular mathematical techniques, which has the ability to predict the behavior of complex flows for such multiphase flow applications. This study has been completed mainly in two steps. A CFD investigation was carried out to predict the hydrodynamic behavior of turbid particle flowing through a horizontal pipe networks including loop consist of bends and straight pipes. Furthermore, an extended analytical model was re-developed for the liquid-solid system to look at the similar behavior of the solid particles flowing in a turbulent field. These two parallel studies will provide better understandings about the turbidity spikes movements in the distribution networks. A comprehensive CFD investigation was carried out for particle deposition in a horizontal pipe loop consisting of four 900 bends in a turbulent flow field. A satisfactory agreement was established with the experimental data as validation. This was a steady state multi-particle problem, which helped to understand the deposition characteristics for different particle sizes and densities at upstream and downstream sides of the bends as well as its circumference. Particle concentration was seen high at the bottom wall in the pipe flow before entering the bends, but for the downstream of bend the deposition was not seen high at the bottom as seen in upstream of bend rather inner side of the bend wall (600 skewed from bottom). The larger particles clearly showed deposition near the bottom of the wall except downstream. As expected, the smaller particles showed less tendency of deposition and this was more pronounced at higher velocity. Due to the high stream line curvature and associated centrifugal force acting on the fluid at different depths the particles became well mixed and resulted in homogeneous distribution near the bend regions. The hydrodynamic behavior of particles flowing in a turbulent unsteady state flowing through a horizontal pipe was also studied to compare with the drinking water distribution networks data. In this numerical simulation six different flow-profiles and particle-load profiles were used to compute particles deposition and re-entrainment into the systems and to identify the conditions of the deposition and suspension mechanisms. Results showed that after a certain length of pipe and period of time after downward velocity gradient, when the velocity was constants over time, the shear stress was sufficiently high enough to cause the particle deposition on and roll along the bottom wall of pipe wall and created a secondary group of particle peak (called kink). Finally, an extended analytical Turbulent Diffusion Model for liquid-solid phase was developed following an existing gas-liquid turbulence model. This turbulent diffusion model was then compared with the results of the CFD investigation making use of the same boundary conditions. The comparison established good agreement between these two models. The influence of velocity on the particle size distribution was dominant over the influence of the superficial liquid velocity, which was also explained by using the new parameter, velocity ratio. This velocity ratio was defined as the ratio between the free flight and gravitational velocity. Due to some inevitable assumptions used in the analytical model, the results showed typically less deposition as compared with the CFD investigation.

The high cost of energy has resulted in a renewed interest in the study of reducing skin-friction drag in aeronautical applications. Laminar Flow Control (LFC) refers to any technique which alters the basic-state flow-field to delay transition from laminar to turbulent flow. Achieving fully laminar flow over a civilian transport wing will significantly reduce drag and fuel costs while increasing range and performance. Boundary-layer suction has proven to be an effective means of achieving laminar flow over an aircraft wing as demonstrated with the Northrop X-21 program; however, even with the savings in fuel, the high manufacturing and maintenance costs have discouraged the use of this technology. Recent work using threedimensional (3-D) spanwise-periodic distributed roughness elements (DREs) has shown great promise as a means of controlling the crossflow instability responsible for transition over a swept wing without the need for a complex suction system. The Texas A

The intensive research on sediment transport indicates a need of an appropriate equation for predicting the total sediment load in rivers to manage reservoirs, operate dam and design in-stream hydraulic structures. None of the available equations in sediment transport has gained universal acceptance for predicting the total sediment transport rate. These facts indicate the need of a general formula to represent all these formula for predicting the sediment transport rate. The first goal of this dissertation is to find a unified total sediment transport equation for all rivers. On the other hand, scour around hydraulic structures such as spur dikes and bridge piers can be a serious problem that weakens structural stability. An investigation on the turbulent flow field and turbulence distribution around such hydraulic structures is essential to understand the mechanism of local scour and to determine which turbulence properties affect the local sediment transport. In addition, a universal turbulent model that is valid for all cases of turbulent flow in open channels does not exist. This dissertation thoroughly examined the turbulent flow field and turbulence distribution around a series of three dikes. The goal is to determine the significant turbulent properties for predicting the local sediment transport rate and to identify the appropriate turbulence model for simulating turbulent flow field around the dikes.To develop a general unified total load equation, this study evaluates 31 commonly used formulae for predicting the total sediment load. This study attributes the deviations of calculated results from different formulae to the stochastic properties of bed shear stresses and assumes that the bed shear stress satisfies the log- normal distribution. At any given bed shear stress, Monte Carlo simulation is applied to each equation, and a set of bed shear stresses are randomly generated. Total sediment load generated from each Monte Carlo realization of all the equations are assembled to represent the samples of total sediment load predicted from all the equations. The statistical properties of the resultant total sediment loads (e.g. standard deviation, mean) at each given bed shear stress are calculated. Then, a unified total sediment load equation is obtained based on the mean value from all the equations. The results showed the mean of all the equations is a power function of dimensionless bed shear stress. Reasonable agreements with measurements demonstrate that the unified equation is more accurate than any individual equation for predicting the total sediment load.An experimental study and numerical simulation of the flow field and local scour around a series of spur dikes is performed in a fixed flat bed and scoured bed condition. A micro-Acoustic Doppler Velocimeter (ADV) is used to measure the instantaneous velocity field in all the three spatial directions and the measured velocity profiles are used to calculate the turbulence properties. Results show that the local scour develops around the first dike. Turbulence intensity together with the mean velocity in the vertical direction measured at the flat bed closely correlates to the scour depth. In addition, the maximum bed shear stress, occurring at the tip of the second dike in the three-dike series, does not correspond to the maximum scour. Large bed load transport due to bed shear stress may not initiate bed scouring, but turbulence bursts (e.g. sweeps and ejections) will entrain sediment from bed surface and develop the local scour.A three-dimensional numerical model FLOW-3D is used to simulate the turbulent flow field around a series of spur dikes in flat and scoured bed. This study examines Prandtl's mixing length model, one equation model, standard two-equation model, Renormalization-Group (RNG) model, and Large Eddy Simulations (LES) turbulence model. The Prandtl's mixing length model and one equation model are not applicable to flow field around dikes. Results of mean flow field by using the standard two-equation model, and RNG turbulence model are close to the experimental data, however the simulated turbulence properties from different turbulent model deviate considerably. The calculated results from different turbulence models show that the RNG model best predicts the mean flow field for this series of spur dikes. None of the turbulence closure models can predict accurate results of turbulence properties, such as turbulence kinetic energy. Based on those results, this study recommends the use of RNG model for simulating mean flow field around dikes. Further improvements of FLOW-3D model is needed for predicting turbulence properties near this series of spur dikes under various flow conditions.

Η παρούσα διπλωματική εργασία ασχολείται με την ανάλυση της τυρβώδους ροής σε ορθογωνικό, ανοικτό αγωγό τριών διαστάσεων, στον οποίον ενυπάρχουν εμπόδια της μορφής προβόλων (groynes). Τέτοιου είδους κατασκευές χρησιμοποιούνται σε πάρα πολλούς ποταμούς ώστε να διατηρείται η επιθυμητή διατομή και το επιθυμητό βάθος ροής αλλά και να αποφεύγεται η διάβρωση των οχθών σε έντονα πλημμυρικά φαινόμενα. Για την επίλυση του προβλήματος αξιοποιήθηκαν οι εξισώσεις RANS, ενώ για το κλείσιμο της τύρβης χρησιμοποιήθηκε το μοντέλο δύο εξισώσεων και το μοντέλο . Η διαχείριση της ελεύθερης επιφάνειας έγινε με την μέθοδο Volume of Fluid (VOF), ενώ η αριθμητική επίλυση βασίστηκε στην μέθοδο των πεπερασμένων όγκων και πραγματοποιήθηκε με τον εμπορικό κώδικα FLUENT 6.1.2. Για την ροή στον υπό εξέταση αγωγό θεωρήθηκε αριθμός Reynolds , ύψος τραχύτητας τοιχωμάτων και κλίση πυθμένα . Για λόγους ελέγχου της ακρίβειας της αριθμητικής μεθόδου που χρησιμοποιήθηκε, αρχικά επιλύθηκε η περίπτωση τρισδιάστατου καναλιού ορθογωνικής διατομής χωρίς προβόλους και τα αποτελέσματα που προέκυψαν συγκρίθηκαν με αναλυτικά αποτελέσματα δισδιάστατης ροής (κατακόρυφο επίπεδο) υπεράνω επίπεδου πυθμένα. Τα αποτελέσματα βρέθηκαν σε καλή συμφωνία μεταξύ τους, γεγονός που επιβεβαίωσε την καταλληλότητα της μεθόδου. Για το τρισδιάστατο πρόβλημα με τους εγκάρσιους προβόλους, η ανάλυση έδειξε ότι το διάμηκες προφίλ της ελεύθερης επιφάνειας παρουσιάζει τοπική ταπείνωση στην θέση των προβόλων, ενώ η κατανομή των διατμητικών τάσεων παρουσιάζει μια σημαντική αύξηση στο μέτωπο των προβόλων και μια μείωση κατάντη των προβόλων στον πυθμένα και στο πλαϊνό τοίχωμα συγκριτικά με τις τιμές της διατμητικής τάσης στο κανάλι χωρίς τα εμπόδια. Επιπροσθέτως, παρατηρήθηκε η δημιουργία μιας περιοχής ανακυκλοφορίας της ροής κατάντη κάθε προβόλου. Η επανακόλληση της ροής κατάντη των προβόλων υπολογίστηκε ότι συμβαίνει σε μια απόσταση 11-19 φορές το μήκος του προβόλου πλησίον του πυθμένα ενώ πλησίον της ελεύθερης επιφάνειας αυτή η απόσταση ισούται με 6-7 φορές το μήκος του προβόλου ανάλογα με τον αριθμό και την απόσταση που απέχουν οι πρόβολοι μεταξύ τους. Αξίζει να σημειωθεί επίσης ότι οι τάσεις στο πλαϊνό τοίχωμα και στον πυθμένα στην περιοχή κατάντη των προβόλων παρουσίασαν μειωμένη κατά απόλυτο τιμή συγκριτικά με την περίπτωση του καναλιού χωρίς τα εμπόδια, γεγονός που συνηγορεί στη χρησιμοποίηση των προβόλων για προστασία διάβρωσης του ακτής. / This thesis deals with the analysis of turbulent flow in rectangular, three-dimensional open channel, in which inherent cantilever barriers (groynes). Such structures are used in many rivers to maintain the desired cross section and the desired depth of flow and to avoid corrosion of the banks to intense flooding.

Made available in DSpace on 2016-12-12T20:25:11Z (GMT). No. of bitstreams: 1 Daniel Giovani Possamai.pdf: 5728163 bytes, checksum: fa0767d89c96a437378f4ccb89802dc7 (MD5) Previous issue date: 2013-07-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The main objective of the present work is the numerical simulation of an incompressible, isothermal turbulent flow inside a timber dry kiln using the commercial software ANSYS CFX®. The physical study aims at assessing the dry kiln aerodynamics by determining the velocity distribution inside the kiln for different operating conditions. In the study of the flow topology inside the dry kiln, the analysis is focused mainly on the evaluation of the influence of the (i) width of the inlet plenum and (ii) flow velocity at its entrance. The simulations show that the plenum width has a direct influence on the velocity distribution in the kiln. This parameter directly affects the location and size of the vortex generated just after the plenum entrance corner. Moreover, the variation of the inlet velocity imposes no significant differences in the flow topology inside the kiln. Finally, it is worth to emphasize that to significantly improve flow uniformity in the channels across the stack height it is necessary to find alternatives able to reduce or eliminate the vortex generated at the entrance of the inlet plenum . / O presente trabalho teve por objetivo principal a análise de um escoamento turbulento incompressível e isotérmico no interior de um secador de madeira utilizando uma metodologia numérica baseada no programa comercial ANSYS CFX®. O estudo físico realizado consistiu em avaliar a aerodinâmica do secador, a saber: determinar a distribuição de velocidades no interior do dispositivo em diferentes condições de operação. No estudo da topologia do escoamento no interior do secador de madeira, a análise foi focada, principalmente, na avaliação da influência dos seguintes parâmetros: (i) largura do canal vertical de entrada, plenum e (ii) velocidade do escoamento na entrada. De acordo com os resultados obtidos, a largura do plenum tem influência direta na distribuição de velocidades no interior do secador. Este parâmetro está diretamente relacionado à localização e tamanho do vórtice gerado após a quina de entrada. Por outro lado, a variação da velocidade de entrada não apresentou diferenças significativas na topologia do escoamento no interior do secador. Por fim, vale salientar que para se obter ganhos significativos na uniformidade do escoamento nos canais faz-se necessário encontrar alternativas que minimizem o vórtice gerado na quina de entrada do secador.

Experimental investigations of liquid helium flows Selected turbulent flows of He II, the superfluid phase of liquid 4 He, are inves- tigated experimentally. The second sound attenuation technique is employed to directly probe the tangle of quantized vortices, thin topological defects within the superfluid, while relatively small particles made of solid hydrogen are dispersed in He II to visualize the overall flow of the liquid via the particle tracking ve- locimetry. Considering the known particle-vortex interaction mechanisms, steady thermal counterflow in a square channel is investigated. Significant inhomogene- ity of the vortex tangle density along the channel height (near the flow-generating heater) is shown to develop. The means of energy transport in turbulent flows of He II are found strikingly different from those taking place in turbulent flows of viscous fluids. Moreover, individual particles in counterflow are observed to intermittently switch between two distinct motion regimes along their trajecto- ries. The regimes are identified and qualitatively described. Steady counterflow jets in He II are realized and the spatial arrangement of the underlying vortex tangle is explored. Finally, macroscopic vortex rings are thermally generated and observed in He II. A method for tracking their...

Made available in DSpace on 2014-10-09T12:41:29Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:03:20Z (GMT). No. of bitstreams: 0 / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

Made available in DSpace on 2014-10-09T12:41:29Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:03:20Z (GMT). No. of bitstreams: 0 / Circuitos de convecção natural ou sistemas de circulação natural são empregados em diversas áreas da engenharia. Reatores nucleares refrigerados a água utilizam circuitos de circulação natural como método passivo de seguranca. Em situações críticas, sem qualquer controle externo, o sistema permanece em segurança por suas próprias características de funcionamento (intrinsecamente seguro). O trabalho proposto consiste em estudar numericamente o circuito de circulação natural de água, localizado no Instituto de Pesquisas Energéticas e Nucleares / Comissão Nacional de Energia Nuclear em São Paulo, por meio do uso de modelos matemáticos, objetivando determinar o padrão do escoamento em condições sem mudança de fase líquido-vapor. A comparação dos resultados de temperatura obtidos por cada um dos modelos de turbulência aos pontos instrumentados no circuito experimental, na condição transitória, revelou desvios significativos nas respostas do modelo de zero equação. Desvios intermediário foram observados nos modelos de transporte da viscosidade turbulenta (EVTE), k - ω, SST e SSG e resultados melhores foram vericados nos modelos k - ε e DES (com significativa superioridade do primeiro modelo). / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

The presence of vegetation in open channel flow has a significant influence on flow resistance, turbulence structures and sediment transport. This study will evaluate flow resistance and scale velocity profile in depth limited flow conditions, specifically investigating the impact of vegetation on the flow resistance under submerged flow conditions. The resistance induced by vegetation in open channel flows has been interpreted differently in literature, largely due to different definitions of friction factors or drag coefficients and the different Reynolds numbers. The methods utilized in this study are based on analytical and numerical models to investigate the effects of vegetation presence on flow resistance in open channel flows. The performing strategy approach was applied by three-dimensional computational fluid dynamics (CFD) simulations, using artificial cylinders for the velocity profile. This is to estimate the average flow velocity and resistance coefficients for flexible vegetation, which results in more accurate flow rate predictions, particularly for the case of low Reynolds number. This thesis shows different formulas from previous studies under certain conditions for a length scale metric, which normalises velocity profiles of depth limited open channel flows with submerged vegetation, using both calculated and simulated model work. It considers the submerged vegetation case in shallow flows, when the flow depth remains no greater than twice the vegetation height. The proposed scaling has been compared and developed upon work that have been influenced by logarithmic and power laws to present velocity profiles, in order to illustrate the variety of flow and vegetation configurations.

In comparison to the flow in a rigid channel, there is a multi-fold reduction in the transition Reynolds number for the flow in a micro channel when one of the walls is made sufficiently soft, due to a dynamical instability induced by the fluid-wall coupling. The flow after transition is characterized using Particle Image Velocimetry (PIV) in the x − y plane where x is the stream-wise direction and y is the cross-stream co-ordinate along the small dimension of the channel of height 0.2 − 0.3mm. For the two different soft walls of shear modulus 18 kPa and 2.19 kPaused here, the transition Reynolds number is about 250 and 330 respectively. The deformation of the microchannel due to the applied pressure gradient is measured in the experiments, and is used to predict the laminar mean velocity profiles for comparison with the experimental results. The mean velocity profiles in the microchannel are in quantitative agreement with those predicted for the laminar flow before transition, but are flatter near the centerline and have higher gradients at the wall after transition. The flow after transition is characterized by a mean velocity profile that is flatter at the center and steeper at the walls in comparison to that for a laminar flow. The root mean square of the stream-wise fluctuating velocity shows the characteristic sharp increase from the wall and a maximum close to the wall, as observed in turbulent flows in rigid-walled channels. However, the profile is asymmetric with a significantly higher maximum close to the soft wall in comparison to that close to the hard wall, and the Reynolds stress is found to be non-zero at the soft wall, indicating that there is a stress exerted by fluid velocity fluctuations on the wall. The turbulent energy production profile has a maximum at the soft wall, in contrast to the flow at a rigid surface where the turbulent energy production is zero at the wall (due to the zero Reynolds stress). The maximum of the root mean square of the velocity fluctuations and the Reynolds stress (divided by the fluid density) in the soft-walled microchannel for Reynolds numbers in the range 250-400, when scaled by suitable powers of the maximum velocity, are comparable to those in a rigid channel at Reynolds numbers in the range 5000-20000. The near-wall velocity profile shows no evidence of a viscous sub-layer for (yv∗/ν) as low as 2, but there is a logarithmic layer for (yv∗/ν) up to about 30, where the von Karman constants are very deferent from those for a rigid-walled channel. Here, v∗ is the friction velocity, ν is the kinematic viscosity and y is the distance from the soft surface. . The surface of the soft wall in contact with the fluid is marked with dye spots to monitor the deformation and motion along the fluid-wall interface. The measured displacement of the surface in the stream-wise direction, which is of the order of 5 − 12µm, is consistent with that calculated on the basis of linear elasticity. Low-frequency oscillations in the displacement of the surface are observed after transition in both the stream-wise and span-wise directions, indicating that the turbulent velocity fluctuations are dynamically coupled to motion in the solid. Modification of soft-wall turbulence in a micro channel due to the addition of small amounts of polymer The modification of soft-wall turbulence in a microchannel due to the addition of small amounts of polymer is experimentally studied using Particle Image Velocimetry (PIV) to measure the mean and the fluctuating velocities. The micro channels are of rectangular cross-section with height about 160 µm, width about 1.5 mm and length about 3 cm, with three walls made of hard Poly-dimethylsiloxane (PDMS) gel, and one wall made of soft PDMS gel with an elasticity modulus of about 18 kPa. A dynamical instabilty of the laminar flow due to the fluid-wall coupling, and a transition to turbulence, is observed at a Reynolds number of about 290 for the flow of pure water in the soft-walled microchannel (Verma and Kumaran, J. Fluid Mech., 727, 407-455, 2013). Solutions of polyacrylamide of molecular weight 5 × 106 and mass fraction up to 50 ppm, and of molecular weight 4 × 104 and mass fraction up to 1500 ppm, are used in the experiments. In all cases, the solutions are in the dilute limit be-low the critical concentration where the interactions between polymer molecules become important. The modification of the fluid viscosity due to addition of polymer molecules is small; the viscosity of the solutions with the highest polymer concentration exceed those for pure water by about 10% for the polymer with molecular weight 5 × 106, and by about 5% for the polymer with molecular weight 4 × 104. Two distinct types of flow modifications below and above a threshold mass fraction for the polymer, cTHRESHOLD , which is about 1 ppm for the polyacrylamide with molecular weight 5 × 106, and about 500 ppm for the polyacrylamide with molecular weight 4 × 104. As the polymer mass fraction increases up to the threshold value, there is no change in the transition Reynolds number, but there is significant turbulence attenuation the root mean square velocities in the stream wise and cross-stream directions decrease by a factor of 2, and the Reynolds stress decreases by a factor of 4 in comparison to that for pure water. When the polymer concentration increases beyond the threshold value, there is a decrease in the decrease in the transition Reynolds number by nearly one order of magnitude, and a further decrease in the intensity of the turbulent fluctuations. The lowest transition Reynolds number of about 35 for the solution of polyacrylamide with molecular weight 5 × 106 and mass fraction 50 ppm. For the polymer solutions with the highest concentrations, the fluctuating velocities in the stream wise and cross-stream direction are lower by a factor of 5, and the Reynolds stress is lower by a factor of 10, in comparison to pure water. Despite the significant turbulence attenuation, a sharp increase in the intensity of the fluctuating velocities is evident at transition for all polymer concentrations. Transitions to deferent kinds of turbulence in a channel with soft walls The flow in a rectangular channel with walls made of soft polyacrylamide gel is studied to examine the effect of soft walls on transition and turbulence. The width of the channel is much larger than the height, so that the flow can be considered approximately two-dimensional, the wall thickness is much larger than the channel height (smallest dimension), the bottom wall is fixed to a substrate and the top wall is unrestrained. The fluid velocity is measured using Particle Image Velocimetry, while the wall motion is studied by embedding beads in the soft wall, and measuring the time-variation of the displacement both parallel and perpendicular to the surface. As the Reynolds number increases, two different flow regimes are observed in sequence. The first is the ‘soft-wall turbulence’ resulting from a dynamical instability of the base flow due to the fluid-wall coupling. The flow in this case exhibits many of the features of the turbulent flow in a rigid channel, including the departure of the velocity profile from the parabolic profile, and the near-wall maxima in the stream-wise root mean square fluctuating velocity. However, there are also significant differences. The turbulence intensities, when scaled by suitable powers of the mean velocity, are much larger than those after the hard-wall laminar-turbulent transition at a Reynolds number of about 1000. The Reynolds stress profiles do not decrease to zero at the walls, indicating that the wall motion plays a role in the generation of turbulent fluctuations. There is no evidence of a viscous sub-layer close to the wall to within the experimental resolution. The mean velocity profile does satisfy a logarithmic law close to the surface within a region between 2-30 wall units from the surface, but the von Karman constants are very different from those for the hard-wall turbulence. The wall displacement measurements indicate that there is no observable motion perpendicular to the surface, but displacement fluctuations parallel to the surface are observed after transition, coinciding with the onset of velocity fluctuations in the fluid. The fluid velocity fluctuations are symmetric about the center line of the channel, and they show relatively little downstream variation after a flow development length of about 5 cm. As the Reynolds number is further increased, there is a second ‘wall flutter’ transition, which involves visible downstream traveling waves in the top (unrestrained) wall alone. Wall displacement fluctuations of low frequency (less than about 500 rad/s) are observed both parallel and perpendicular to the wall. The mean velocity profiles and turbulence intensities are asymmetric, with much larger turbulence intensities near the top wall. There is no evident logarithmic profile close to either the top or bottom wall. Fluctuations are initiated at the entrance of the test section, and the fluctuation intensities decrease with downstream distance, the fluctuation intensities first rapidly increase and then decrease as the Reynolds number is increased. For a channel with relatively small height (0.6 mm), the transition Reynolds number for the soft-wall instability is lower the hard-wall transition Reynolds number of about 1000, and the laminar flow becomes unstable to the soft-wall instability leading to soft-wall turbulence and then to wall flutter as the Reynolds number is increased. For a channel with relatively large height (1.8 mm), the transition Reynolds number for the soft-wall instability is higher than 1000, the flow first undergoes the hard-wall laminar-turbulent transition at a Reynolds number of about 1000, the turbulent flow undergoes the soft-wall transition leading to soft-wall turbulence, and then to wall flutter.