Adjoint sensitivity and optimal perturbations of the low-speed jet in cross-flow

2019 ◽  
Vol 877 ◽  
pp. 330-372
Author(s):  
Marc A. Regan ◽  
Krishnan Mahesh
Keyword(s):  
Shear Layer ◽  
Time Horizon ◽  
Cross Flow ◽  
Adjoint Equations ◽  
Low Speed ◽  
Time Horizons ◽  
Jet In Cross Flow ◽  
Jet Nozzle ◽  
The Cross ◽  
Short Time

The tri-global stability and sensitivity of the low-speed jet in cross-flow are studied using the adjoint equations and finite-time horizon optimal disturbance analysis at Reynolds number $Re=2000$, based on the average velocity at the jet exit, the jet nozzle exit diameter and the kinematic viscosity of the jet, for two jet-to-cross-flow velocity ratios $R=2$ and $4$. A novel capability is developed on unstructured grids and parallel platforms for this purpose. Asymmetric modes are more important to the overall dynamics at $R=4$, suggesting increased sensitivity to experimental asymmetries at higher $R$. Low-frequency modes show a connection to wake vortices. Adjoint modes show that the upstream shear layer is most sensitive to perturbations along the upstream side of the jet nozzle. Lower frequency downstream modes are sensitive in the cross-flow boundary layer. For $R=2$, optimal analysis reveals that for short time horizons, asymmetric perturbations dominate and grow along the counter-rotating vortex pair observed in the cross-section. However, as the time horizon increases, large transient growth is observed along the upstream shear layer. When $R=4$, the optimal perturbations for short time scales grow along the downstream shear layer. For long time horizons, they become hybrid modes that grow along both the upstream and downstream shear layers.

Effect of operational modes on the removal of a synthetic organic chemical by powdered activated carbon during ultrafiltration

2001 ◽  
Vol 1 (5-6) ◽  
pp. 39-47
Author(s):  
Y. Matsui ◽  
A. Yuasa ◽  
F. Colas
Keyword(s):  
Activated Carbon ◽  
Cross Flow ◽  
Powdered Activated Carbon ◽  
Organic Chemical ◽  
Filtration Cycle ◽  
Dead End ◽  
Synthetic Organic Chemical ◽  
The Cross ◽  
Short Time ◽  
Operational Modes

The effects of operational modes on the removal of a synthetic organic chemical (SOC) in natural water by powdered activated carbon (PAC) during ultrafiltration (UF) were studied, through model simulations and experiments. The removal percentage of the trace SOC was independent of its influent concentration for a given PAC dose. The minimum PAC dosage required to achieve a desired effluent concentration could quickly be optimized from the C/C0 plot as a function of the PAC dosage. The cross-flow operation was not advantageous over the dead-end regarding the SOC removal. Added PAC was re-circulated as a suspension in the UF loop for only a short time even under the cross-flow velocity of gt; 1.0 m/s. The cross-flow condition did not contribute much to the suspending of PAC. The pulse PAC addition at the beginning of a filtration cycle resulted in somewhat better SOC removal than the continuous PAC addition. The increased NOM loading on PAC which was dosed in a pulse and stayed longer in the UF loop could possibly further decrease the adsorption rate.

Secondary instability of cross-flow vortices in Falkner–Skan–Cooke boundary layers

1998 ◽  
Vol 368 ◽  
pp. 339-357 ◽  
Author(s):  
MARKUS HÖGBERG ◽  
DAN HENNINGSON
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Boundary Layers ◽  
Growth Rates ◽  
High Frequency ◽  
Cross Flow ◽  
Low Frequency ◽  
Secondary Instability ◽  
The Cross ◽  
Flow Vortex

Linear eigenvalue calculations and spatial direct numerical simulations (DNS) of disturbance growth in Falkner–Skan–Cooke (FSC) boundary layers have been performed. The growth rates of the small-amplitude disturbances obtained from the DNS calculations show differences compared to linear local theory, i.e. non-parallel effects are present. With higher amplitude initial disturbances in the DNS calculations, saturated cross-flow vortices are obtained. In these vortices strong shear layers appear. When a small random disturbance is added to a saturated cross-flow vortex, a low-frequency mode is found located at the bottom shear layer of the cross-flow vortex and a high-frequency secondary instability is found at the upper shear layer of the cross-flow vortex. The growth rates of the secondary instabilities are found from detailed analysis of simulations of single-frequency disturbances. The low-frequency disturbance is amplified throughout the domain, but with a lower growth rate than the high-frequency disturbance, which is amplified only once the cross-flow vortices have started to saturate. The high-frequency disturbance has a growth rate that is considerably higher than the growth rates for the primary instabilities, and it is conjectured that the onset of the high-frequency instability is well correlated with the start of transition.

To Invest or Insure?

2008 ◽  
Vol 41 (7) ◽  
pp. 971-1000 ◽  
Author(s):  
Joseph Wright
Keyword(s):  
Developing Countries ◽  
Foreign Aid ◽  
Time Horizon ◽  
Positive Impact ◽  
Aid Effectiveness ◽  
Time Horizons ◽  
Positive Growth ◽  
Long Time ◽  
Short Time ◽  
Negative Growth

In this article, the author argues that the time horizon a dictator faces affects his incentives over the use of aid in three ways. First, dictators have a greater incentive to invest in public goods when they have a long time horizon. Second, dictators with short time horizons often face the threat of challengers to the regime; this leads them to forgo investment and instead consume state resources in two forms that harm growth: repression and private pay-offs to political opponents. Third, dictators with short time horizons have a strong incentive to secure personal wealth as a form of insurance in case the regime falls. Using panel data on dictatorships in 71 developing countries from 1961 to 2001, the author finds that time horizons have a positive impact on aid effectiveness: Foreign aid is associated with positive growth when dictators face long time horizons and negative growth when time horizons are short.

scholarly journals Low Speed Wind Tunnel Flow Diagnostics and Benchmark Cases for Thermal Fluids CFD Validation Efforts

2020 ◽  
Author(s):  
Paul Kristo ◽  
Saniya Sohail ◽  
Ryan S. Read ◽  
Mark L. Kimber
Keyword(s):  
Wind Tunnel ◽  
Cross Sections ◽  
Cross Flow ◽  
Reynolds Stresses ◽  
Cfd Validation ◽  
University Of Pittsburgh ◽  
Low Speed ◽  
Thermal Fluids ◽  
Jet In Cross Flow ◽  
Flow Past A Cylinder

A low speed, closed loop wind tunnel at Texas A&M University is presented for the study of turbulent mixing produced by a variety of flows types. Anticipated experiments range from canonical “unit flows” to more complex combinations of flows and geometries. Originally located at the University of Pittsburgh, the facility has since been re-located to the Thermal Hydraulics Verification and Validation (THVV) laboratory at Texas A&M University. The tunnel has undergone considerable modification and updated diagnostics prompting renewed interest in flow quality assessment. This includes a thorough mapping of the tunnel inlet velocity profile provided by Particle Image Velocimetry (PIV) measurements. Additional temperature and gage pressure measurements complete the assessment of system capabilities. These preliminary diagnostics yield empirically determined boundary conditions and fluid property correlations necessary for Computational Fluid Dynamics (CFD) model validation. The article concludes with the presentation of two unit flow types, including flow past a cylinder, with three distinct cross sections, and a single round jet in cross flow at three velocity ratios. The unit flows serve as initial benchmarks for THVV simulation efforts. Key validation metrics are presented for each benchmark including ensemble averaged velocities, Reynolds stresses, and proper orthogonal decomposition (POD) eigenvectors.

scholarly journals Time is money. Waiting costs explain why selection favors steeper time discounting in deprived environments.

2019 ◽  
Author(s):  
Hugo Mell ◽  
Nicolas Baumard ◽  
Jean-Baptiste André
Keyword(s):  
Time Horizon ◽  
Behavioural Syndrome ◽  
Muscular Tissue ◽  
Risk Averse ◽  
Time Discounting ◽  
Time Horizons ◽  
Per Se ◽  
Short Time ◽  
Evolutionarily Stable

Individuals exposed to deprivation tend to show a characteristic behavioural syndrome suggestive of a short time horizon. This pattern has traditionally been attributed to the intrinsically higher unpredictability of deprived environments, which renders waiting for long term rewards more risky (i.e. collection risks are high). In the current paper, based on a simple dynamic life history model, we show that a significant portion of individuals’ propensity to discount future rewards might have a completely distinct origin. Upon collecting a resource, individuals have the opportunity to accumulate “capital” (e.g. grow muscular tissue, build a protective shelter, buy a car, etc.), which eventually increases their productivity and/or their chances of survival. As a result, delaying the collection of a resource creates an opportunity cost in the sense that during the waiting time, the benefits otherwise generated by the increment in capital are lost. These forgone benefits are independent of collection risks and constitute waiting costs per se. Using optimal control theory we show that these costs can lead to the evolution of short time horizons even in the complete absence of collection risks. Moreover, assuming diminishing returns to capital, we show that the evolutionarily stable time horizon increases with the amount of capital already owned by individuals. When individuals possess little capital, they have a lot of room to improve their productivity and/or survival, hence they should be impatient to collect resources; that is, their time horizon should be short. On the contrary, when individuals already possess a lot of capital, the benefits of further accumulation are plateauing, hence patience becomes a more profitable strategy and individuals should lengthen their time horizon. This means that individuals get more patient as they age and that people in deprivation, who still have important productive and survival needs that can be satisfied, should have a shorter time horizon. Moreover, beyond time horizon, our model shows that people with little capital should also be more risk averse than the more privileged. Taken together, these results lead us to interpret the behavioral constellation of deprivation in a new way.

Bifurcation and stability analysis of a jet in cross-flow: onset of global instability at a low velocity ratio

2012 ◽  
Vol 696 ◽  
pp. 94-121 ◽  
Author(s):  
Miloš Ilak ◽  
Philipp Schlatter ◽  
Shervin Bagheri ◽  
Dan S. Henningson
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Initial Growth ◽  
Low Velocity ◽  
Hairpin Vortices ◽  
Jet In Cross Flow ◽  
Periodic Behaviour ◽  
Set Up

AbstractWe study direct numerical simulations (DNS) of a jet in cross-flow at low values of the jet-to-cross-flow velocity ratio$R$. We observe that, as the ratio$R$increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi-periodic behaviour, before finally becoming turbulent, as seen in the simulation of Bagheriet al. (J. Fluid. Mech., vol. 624, 2009b, pp. 33–44). The value of$R$at which the first bifurcation occurs for our numerical set-up is found, and shedding of hairpin vortices characteristic of a shear layer instability is observed. We focus on this first bifurcation, and find that a global linear stability analysis predicts well the frequency and initial growth rate of the nonlinear DNS at the critical value of$R$and that good qualitative predictions about the dynamics can still be made at slightly higher values of$R$where multiple unstable eigenmodes are present. In addition, we compute the adjoint global eigenmodes, and find that the overlap of the direct and the adjoint eigenmode, also known as a ‘wavemaker’, provides evidence that the source of the first instability lies in the shear layer just downstream of the jet.

Before I Die

GeroPsych ◽  
2018 ◽  
Vol 31 (3) ◽  
pp. 151-162 ◽  
Author(s):  
Qiao Chu ◽  
Daniel Grühn ◽  
Ashley M. Holland
Keyword(s):  
End Of Life ◽  
Psychosocial Development ◽  
Time Horizon ◽  
Development Theory ◽  
Life Stages ◽  
Socioemotional Selectivity Theory ◽  
Socioemotional Selectivity ◽  
Time Horizons

Abstract. We investigated the effects of time horizon and age on the socioemotional motives underlying individual’s bucket-list goals. Participants were randomly assigned to one of three time-horizon conditions to make a bucket list: (1) an open-ended time horizon (Study 1 & 2), (2) a 6-month horizon (i.e., “Imagine you have 6 months to live”; Study 1 & 2), and (3) a 1-week horizon (Study 2). Goal motives were coded based on socioemotional selectivity theory and psychosocial development theory. Results indicated that time horizon and age produced unique effects on bucket-list goal motives. Extending past findings on people’s motives considering the end of life, the findings suggest that different time horizons and life stages trigger different motives.

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