scholarly journals Transient energy growth of channel flow with cross-flow

2019 ◽  
Vol 286 ◽  
pp. 07008
Author(s):  
J. Benyza ◽  
M. Lamine ◽  
A. Hifdi
Keyword(s):  
Flow Rate ◽  
Initial Conditions ◽  
Cross Flow ◽  
High Sensitivity ◽  
Maximum Growth ◽  
Growth Function ◽  
High Energy ◽  
Optimal Perturbation ◽  
Energy Growth ◽  
Transient Energy

The effect of a uniform cross flow (injection/ suction) on the transient energy growth of a plane Poiseuille flow is investigated. Non-modal linear stability analysis is carried out to determine the two-dimensional optimal perturbations for maximum growth. The linearized Navier-Stockes equations are reduced to a modified Orr Sommerfeld equation that is solved numerically using a Chebychev collocation spectral method. Our study is focused on the response to external excitations and initial conditions by examining the energy growth function G(t) and the pseudo-spectrum. Results show that, the transient energy of the optimal perturbation grows rapidly at short times and decline slowly at long times when the cross-flow rate is low or strong. In addition, the maximum energy growth is very pronounced in low injection rate than that of the strong one. For the intermediate cross-flow rate, the transient energy growth of the perturbation, is only possible at the long times with a very high-energy gain. Analysis of the pseudo-spectrum show that the non-normal character of the modified Orr-Sommerfeld operator tends to a high sensitivity of pseudo-spectra structures.

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

2019 ◽  
Vol 878 ◽  
pp. 190-220 ◽  
Author(s):  
Francesca M. Sogaro ◽  
Peter J. Schmid ◽  
Aimee S. Morgans
Keyword(s):  
Time Domain ◽  
Time Scale ◽  
Initial Conditions ◽  
Normal Modes ◽  
Time Domain Analysis ◽  
Normal Behaviour ◽  
Optimal Perturbation ◽  
Acoustic Modes ◽  
Energy Growth ◽  
The Time Domain

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.

scholarly journals On the longitudinal optimal perturbations to inviscid plane shear flow: formal solution and asymptotic approximation

2013 ◽  
Vol 737 ◽  
pp. 387-411 ◽  
Author(s):  
C. Arratia ◽  
J.-M. Chomaz
Keyword(s):  
Shear Flow ◽  
Initial Conditions ◽  
Formal Solution ◽  
Base Flow ◽  
Flow Profile ◽  
Plane Shear ◽  
Optimal Perturbation ◽  
Energy Growth ◽  
Perturbation Problem ◽  
New Formulation

AbstractWe study the longitudinal linear optimal perturbations (which maximize the energy gain up to a prescribed time $T$) to inviscid parallel shear flow, which present unbounded energy growth due to the lift-up mechanism. Using the phase invariance with respect to time, we show that for an arbitrary base flow profile and optimization time, the computation of the optimal longitudinal perturbation reduces to the resolution of a single one-dimensional eigenvalue problem valid for all times. The optimal perturbation and its amplification are then derived from the lowest eigenvalue and its associated eigenfunction, while the remainder of the infinite set of eigenfunctions provides an orthogonal base for decomposing the evolution of arbitrary perturbations. With this new formulation we obtain, asymptotically for large spanwise wavenumber ${k}_{z} , $ a prediction of the optimal gain and the localization of inviscid optimal perturbations for the two main classes of parallel flows: free shear flow with an inflectional velocity profile, and wall-bounded flow with maximum shear at the wall. We show that the inviscid optimal perturbations are localized around the point of maximum shear in a region with a width scaling like ${ k}_{z}^{- 1/ 2} $ for free shear flow, and like ${ k}_{z}^{- 2/ 3} $ for wall-bounded shear flows. This new derivation uses the stationarity of the base flow to transform the optimization of initial conditions in phase space into the optimization of a temporal phase along each trajectory, and an optimization among all trajectories labelled by their intersection with a codimension-1 subspace. The optimization of the time phase directly imposes that the initial and final energy growth rates of the optimal perturbation should be equal. This result requires only time invariance of the base flow, and is therefore valid for any linear optimal perturbation problem with stationary base flow.

Observation of surface morphology by reflection electron holography

1989 ◽  
Vol 47 ◽  
pp. 536-537
Author(s):  
N. Osakabe ◽  
J. Endo ◽  
T. Matsuda ◽  
A. Tonomura
Keyword(s):  
Phase Shift ◽  
Surface Morphology ◽  
High Sensitivity ◽  
High Energy ◽  
Path Difference ◽  
Transmission Mode ◽  
Electron Holography ◽  
Dynamical Process ◽  
High Vertical Resolution ◽  
Amplification Technique

Progress in microscopy such as STM and TEM-TED has revealed surface structures in atomic dimension. REM has been used for the observation of surface dynamical process and surface morphology. Recently developed reflection electron holography, which employes REM optics to measure the phase shift of reflected electron, has been proved to be effective for the observation of surface morphology in high vertical resolution ≃ 0.01 Å.The key to the high sensitivity of the method is best shown by comparing the phase shift generation by surface topography with that in transmission mode. Difference in refractive index between vacuum and material Vo/2E≃10-4 owes the phase shift in transmission mode as shownn Fig. 1( a). While geometrical path difference is created in reflection mode( Fig. 1(b) ), which is measured interferometrically using high energy electron beam of wavelength ≃0.01 Å. Together with the phase amplification technique , the vertivcal resolution is expected to be ≤0.01 Å in an ideal case.

High-sensitivity external modulator data link for high-energy particle detector diagnostics

1993 ◽  
Author(s):  
Kent G. McCammon ◽  
Mark E. Lowry ◽  
Yuan-Hann Chang ◽  
Paul J. Parker ◽  
Bolek Wyslouch ◽  
...  
Keyword(s):  
High Sensitivity ◽  
High Energy ◽  
High Energy Particle ◽  
Particle Detector ◽  
Energy Particle ◽  
Data Link

Heat and Mass Transfer to Air in a Cross Flow Heat Exchanger with Surface Deluge Cooling

2016 ◽  
Vol 24 (01) ◽  
pp. 1650002 ◽  
Author(s):  
Andrea Diani ◽  
Luisa Rossetto ◽  
Roberto Dall’Olio ◽  
Daniele De Zen ◽  
Filippo Masetto
Keyword(s):  
Heat Exchanger ◽  
Heat Flow ◽  
Flow Rate ◽  
Data Center ◽  
Heat Dissipation ◽  
Cross Flow ◽  
Critical Conditions ◽  
Heat Flow Rate ◽  
External Temperature ◽  
Flow Heat

Cross flow heat exchangers, when applied to cool data center rooms, use external air (process air) to cool the air stream coming from the data center room (primary air). However, an air–air heat exchanger is not enough to cope with extreme high heat loads in critical conditions (high external temperature). Therefore, water can be sprayed in the process air to increase the heat dissipation capability (wet mode). Water evaporates, and the heat flow rate is transferred to the process air as sensible and latent heat. This paper proposes an analytical approach to predict the behavior of a cross flow heat exchanger in wet mode. The theoretical results are then compared to experimental tests carried out on a real machine in wet mode conditions. Comparisons are given in terms of calculated versus experimental heat flow rate and evaporated water mass flow rate, showing a good match between theoretical and experimental values.

Growth of vortical disturbances entrained in the entrance region of a circular pipe

2021 ◽  
Vol 932 ◽  
Author(s):  
Pierre Ricco ◽  
Claudia Alvarenga
Keyword(s):  
Reynolds Number ◽  
Initial Conditions ◽  
Maximum Growth ◽  
Streamwise Velocity ◽  
Velocity Profiles ◽  
Boundary Region ◽  
Base Flow ◽  
Entrance Region ◽  
Circular Pipe ◽  
Large Reynolds Number

The development and growth of unsteady three-dimensional vortical disturbances entrained in the entry region of a circular pipe is investigated by asymptotic and numerical methods for Reynolds numbers between $1000$ and $10\,000$ , based on the pipe radius and the bulk velocity. Near the pipe mouth, composite asymptotic solutions describe the dynamics of the oncoming disturbances, revealing how these disturbances are altered by the viscous layer attached to the pipe wall. The perturbation velocity profiles near the pipe mouth are employed as rigorous initial conditions for the boundary-region equations, which describe the flow in the limit of low frequency and large Reynolds number. The disturbance flow is initially primarily present within the base-flow boundary layer in the form of streamwise-elongated vortical structures, i.e. the streamwise velocity component displays an intense algebraic growth, while the cross-flow velocity components decay. Farther downstream the disturbance flow occupies the whole pipe, although the base flow is mostly inviscid in the core. The transient growth and subsequent viscous decay are confined in the entrance region, i.e. where the base flow has not reached the fully developed Poiseuille profile. Increasing the Reynolds number and decreasing the frequency causes more intense perturbations, whereas small azimuthal wavelengths and radial characteristic length scales intensify the viscous dissipation of the disturbance. The azimuthal wavelength that causes the maximum growth is found. The velocity profiles are compared successfully with available experimental data and the theoretical results are helpful to interpret the only direct numerical dataset of a disturbed pipe-entry flow.

scholarly journals Microfiltration with periodic gas backwashing as an alternative technique for increasing permeate flux

2018 ◽  
Vol 72 (2) ◽  
pp. 59-68
Author(s):  
Tijana Urosevic ◽  
Dragan Povrenovic ◽  
Predrag Vukosavljevic ◽  
Ivan Urosevic
Keyword(s):  
Steady State ◽  
Flow Rate ◽  
Driving Force ◽  
Fruit Juice ◽  
Cross Flow ◽  
Fruit Juices ◽  
Transmembrane Pressure ◽  
Permeate Flux ◽  
Cross Flow Filtration ◽  
Flow Filtration

In this paper, the influence of operating parameters (transmembrane pressure, temperature, the flow rate of retentate) on the cross - flow microfiltration of synthetic fruit juice and periodic backwashing with air was examined. In the experiments, the Kerasep W5 ceramic membrane with a separation limit of 0.2 ?m was used. The results of experiments in which different transmembrane pressures were used showed that stationary fluxes, at stationary conditions, after 60 minutes, have similar values. So, it can be concluded that the value of the driving force is irrelevant at steady state conditions. However, until the steady state conditions are established, a positive effect of the increase in the driving force is opposed to the negative effect of the increased polarization resistance, as a result of the driving force increase. Thus, the optimal transmembrane pressure was determined amounting to 2 bars. The optimum temperature of the process of clearing the fruit juices by microfiltration is reported as 55?C. Higher temperatures are not used due to a degrading effect on the chemical composition of the juice and a long microfiltration process. With an increase in the temperature of retentate from 22?C to 55?C, the permeate flux increased up to 60%. Increasing the flow rate of retentate reduces the thickness of the formed layer on the surface of the membrane. Due to limitations of the experimental setup and the large surface area of the membrane, the specific velocity of the retentate was low, so that the effects of cross-flow filtration were absent. The use of cross-flow filtration is one of the main requirements for increasing permeate flux, but in the present case it was in overall insufficient, so we have applied periodic air backwashing for improving fruit juice flux during membrane clarification. With this technique, the deposited layer on the membrane is lifted and the permeate flux is maintained at high levels preventing establishment of the steady state in the low flux zone. The time spent for the periodic backwashing was low as compared to the benefits of the increase in the collected permeate quantity. In all experiments with periodic backwashing with air, the collected permeate quantity is higher for up to 72.5 % as compared to experiments without backwashing. By increasing the backwashing duration, the flux increase is up to 5 %, which can be significant for microfiltration at industrial scale. Therefore, this technique is certainly recommended for microfiltration in the production of fruit juices.

scholarly journals Data assimilation method in flood forecasting for Red river system using high performent computer

2015 ◽  
Vol 37 (1) ◽  
pp. 29-42
Author(s):  
Nguyen Thanh Don ◽  
Nguyen Van Que ◽  
Tran Quang Hung ◽  
Nguyen Hong Phong
Keyword(s):  
Data Assimilation ◽  
Flow Rate ◽  
New Technologies ◽  
Weather Forecasting ◽  
Initial Conditions ◽  
River System ◽  
Red River ◽  
Time Dependent ◽  
Complex Case ◽  
Flood Model

Around the world, the data assimilation framework has been reported to be of great interest for weather forecasting, oceanography modeling and for shallow water flows particularly for flood model. For flood model this method is a power full tool to identify time-independent parameters (e.g. Manning coefficients and initial conditions) and time-dependent parameters (e.g. inflow). This paper demonstrates the efficiency of the method to identify time-dependent parameter: inflow discharge with a real complex case Red River. Firstly, we briefly discuss about current methods for determining flow rate which encompasses the new technologies, then present the ability to recover flow rate of this method. For the case of very long time series, a temporal strategy with time overlapping is suggested to decrease the amount of memory required. In addition, some different aspects of data assimilation are covered from this case.

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