scholarly journals Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1341
Author(s):  
Irene Daprà ◽  
Giambattista Scarpi
Keyword(s):  
Power Series ◽  
Newtonian Fluid ◽  
Constant Pressure ◽  
Rock Fracture ◽  
Momentum Equation ◽  
Constitutive Law ◽  
Mean Flow ◽  
Logarithmic Model ◽  
The Past ◽  
The Mean

The purpose of this work is to study the motion of a non-Newtonian fluid in a rock fracture, generated by a constant pressure gradient to which a pulsating component is superposed. The momentum equation is faced analytically by adopting a logarithmic constitutive law; the velocity is expressed as a power series of the amplitude of the pulsating component, up to the second order, easily usable for numerical calculations. The results obtained are compared with those provided in the past by the authors, using a three-parameter Williamson model. The comparison highlights that the value of the mean flow rate in a period differs by less than 10% even if the velocity profiles look quite different.

Turbulent planar wakes under pressure gradient conditions

2017 ◽  
Vol 830 ◽  
Author(s):  
Sina Shamsoddin ◽  
Fernando Porté-Agel
Keyword(s):  
Pressure Gradient ◽  
Maximum Velocity ◽  
Wind Farms ◽  
Parameter Tuning ◽  
Momentum Equation ◽  
Mean Flow ◽  
Self Similarity ◽  
High Lift ◽  
Velocity Deficit ◽  
The Mean

Accurate prediction of the spatial evolution of turbulent wake flows under pressure gradient conditions is required in some engineering applications such as the design of high-lift devices and wind farms over topography. In this paper, we aim to develop an analytical model to predict the evolution of a turbulent planar wake under an arbitrary pressure gradient condition. The model is based on the cross-stream integration of the streamwise momentum equation and uses the self-similarity of the mean flow. We have also made an experimentally supported assumption that the ratio of the maximum velocity deficit to the wake width is independent of the imposed pressure gradient. The asymptotic response of the wake to the pressure gradient is also investigated. After its derivation, the model is successfully validated against experimental data by comparing the evolution of the wake width and maximum velocity deficit. The inputs of the model are the imposed pressure gradient and the wake width under zero pressure gradient. The model does not require any parameter tuning and is deemed to be practical, computationally fast, accurate enough, and therefore useful for the scientific and engineering communities.

scholarly journals Comments on “A Combined Derivation of the Integrated and Vertically Resolved, Coupled Wave–Current Equations”

2017 ◽  
Vol 47 (9) ◽  
pp. 2377-2385 ◽  
Author(s):  
Fabrice Ardhuin ◽  
Nobuhiro Suzuki ◽  
James C. McWilliams ◽  
Hidenori Aiki
Keyword(s):  
Vertical Integration ◽  
Order Term ◽  
Momentum Equation ◽  
Total Momentum ◽  
Leading Order ◽  
Mean Flow ◽  
Wave Forcing ◽  
The Mean ◽  
New Formulation ◽  
Wave Momentum

AbstractSeveral equivalent equations for the evolution of the wave-averaged current momentum have been proposed, implemented, and used. In contrast, the equation for the total momentum, which is the sum of the current and wave momenta, has not been widely used because it requires a less practical wave forcing. In an update on previous derivations, Mellor proposed a new formulation of the wave forcing for the total momentum equation. Here, the authors show that this derivation misses a leading-order term that has a zero depth-integrated value. Corrected for this omission, the wave forcing is equivalent to that in the first paper by Mellor. When this wave forcing effect on the currents is approximated it leads to an inconsistency. This study finally repeats and clarifies that the vertical integration of several various forms of the current-only momentum equations are consistent with the known depth-integrated equations for the mean flow momentum obtained by subtracting the wave momentum equation from the total momentum equation. Several other claims in prior Mellor manuscripts are discussed.

A physical model of the turbulent boundary layer consonant with mean momentum balance structure

2007 ◽  
Vol 365 (1852) ◽  
pp. 823-840 ◽  
Author(s):  
Joe Klewicki ◽  
Paul Fife ◽  
Tie Wei ◽  
Pat McMurtry
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Physical Model ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Dynamical Structure ◽  
Mean Flow ◽  
Structure And Dynamics ◽  
The Mean ◽  
Balance Structure

Recent studies by the present authors have empirically and analytically explored the properties and scaling behaviours of the Reynolds averaged momentum equation as applied to wall-bounded flows. The results from these efforts have yielded new perspectives regarding mean flow structure and dynamics, and thus provide a context for describing flow physics. A physical model of the turbulent boundary layer is constructed such that it is consonant with the dynamical structure of the mean momentum balance, while embracing independent experimental results relating, for example, to the statistical properties of the vorticity field and the coherent motions known to exist. For comparison, the prevalent, well-established, physical model of the boundary layer is briefly reviewed. The differences and similarities between the present and the established models are clarified and their implications discussed.

On the diffusion of momentum and mass by internal gravity waves

1976 ◽  
Vol 77 (4) ◽  
pp. 789-823 ◽  
Author(s):  
Peter Mtfller
Keyword(s):  
Wave Field ◽  
Gravity Waves ◽  
General Circulation ◽  
Viscosity Coefficient ◽  
Internal Gravity Waves ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Mean Flow ◽  
Vertical Diffusion ◽  
The Mean

The interaction between short internal gravity waves and a larger-scale mean flow in the ocean is analysed in the Wkbj approximation. The wave field determines the radiation-stress term in the momentum equation of the mean flow and a similar term in the buoyancy equation. The mean flow affects the propagation characteristics of the wave field. This cross-coupling is treated as a small perturbation. When relaxation effects within the wave field are considered, the mean flow induces a modulation of the wave field which is a linear functional of the spatial gradients of the mean current velocity. The effect that this modulation itself has on the mean flow can be reduced to the addition of diffusion terms to the equations for the mass and momentum balance of the mean flow. However, there is no vertical diffusion of mass and other passive properties. The diffusion coefficients depend on the frequency spectrum and the relaxation time of the internal-wave field and can be evaluated analytically. The vertical viscosity coefficient is found to be vv [ape ] 4 x 103cm2/s and exceeds values typically used in models of the general circulation by at least two orders of magnitude.

The neutral curves for periodic perturbations of finite amplitude of plane Poiseuille flow

1969 ◽  
Vol 39 (3) ◽  
pp. 629-639 ◽  
Author(s):  
C. L. Pekeris ◽  
B. Shkoller
Keyword(s):  
Power Series ◽  
Perturbation Method ◽  
Poiseuille Flow ◽  
Finite Amplitude ◽  
Neutral Curve ◽  
Plane Poiseuille Flow ◽  
Mean Flow ◽  
Periodic Perturbations ◽  
Neutral Curves ◽  
The Mean

It is shown that there exist undamped solutions for perturbations of finite amplitude of plane Poiseuille flow, which are periodic in the direction of the axis of the channel. The shift in the ‘neutral curve’ as a function of the amplitude λ* of the disturbance is shown in figure 2. The solution is obtained by a perturbation method in which the eigenfunctions and the eigenvalue c are expanded in power series of the amplitude λ, as shown in (14), (15), (16) and (17). Near the neutral curve for a finite amplitude disturbance, the curvature of the mean flow shows a tendency to become negative (figure 5).

Scrub typhus (Orientia tsutsugamushi), A rapidly spreading epidemic in Chennai - A standalone lab experience

2016 ◽  
Vol 5 (09) ◽  
pp. 4896
Author(s):  
Sripriya C.S.* ◽  
Shanthi B. ◽  
Arockia Doss S. ◽  
Antonie Raj I. ◽  
Mohana Priya
Keyword(s):  
Scrub Typhus ◽  
Clinical Symptoms ◽  
Clinical Manifestations ◽  
Febrile Illness ◽  
Orientia Tsutsugamushi ◽  
The Past ◽  
Igm Elisa ◽  
The Mean ◽  
Specific Symptoms ◽  
Symptoms And Signs

Scrub typhus (Orientia tsutsugamushi), is a strict intracellular bacterium which is reported to be a recent threat to parts of southern India. There is re-emergence of scrub typhus during the past few years in Chennai. Scrub typhus is an acute febrile illness which generally causes non-specific symptoms and signs. The clinical manifestations of this disease range from sub-clinical disease to organ failure to fatal disease. This study documents our laboratory experience in diagnosis of scrub typhus in patients with fever and suspected clinical symptoms of scrub typhus infection for a period of two years from April 2014 to April 2016 using immunochromatography and IgM ELISA methods. The study was conducted on 648 patients out of whom 188 patients were found to be positive for scrub typhus. Results also showed that pediatric (0 -12 years) and young adults (20 – 39 years) were more exposed to scrub typhus infection and female patients were more infected compared to male. The study also showed that the rate of infection was higher between September to February which also suggested that the infection rate is proportional to the climatic condition. Statistical analysis showed that the mean age of the patients in this study was 37.6, standard deviation was 18.97, CV % was 50.45. 

Simple explicit model of liquid mean flow in region above axial impeller

1985 ◽  
Vol 50 (11) ◽  
pp. 2396-2410
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Vortex Flow ◽  
Flow Model ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flat Bottom ◽  
Proposed Model ◽  
Minimum Number ◽  
The Mean ◽  
Model Equations ◽  
Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

scholarly journals Technical note: Inherent benchmark or not? Comparing Nash–Sutcliffe and Kling–Gupta efficiency scores

2019 ◽  
Vol 23 (10) ◽  
pp. 4323-4331 ◽  
Author(s):  
Wouter J. M. Knoben ◽  
Jim E. Freer ◽  
Ross A. Woods
Keyword(s):  
Time Series ◽  
Coefficient Of Variation ◽  
Ad Hoc ◽  
Model Performance ◽  
Technical Note ◽  
Mean Flow ◽  
Model Adequacy ◽  
Robust Model ◽  
The Mean ◽  
Adequacy Assessment

Abstract. A traditional metric used in hydrology to summarize model performance is the Nash–Sutcliffe efficiency (NSE). Increasingly an alternative metric, the Kling–Gupta efficiency (KGE), is used instead. When NSE is used, NSE = 0 corresponds to using the mean flow as a benchmark predictor. The same reasoning is applied in various studies that use KGE as a metric: negative KGE values are viewed as bad model performance, and only positive values are seen as good model performance. Here we show that using the mean flow as a predictor does not result in KGE = 0, but instead KGE =1-√2≈-0.41. Thus, KGE values greater than −0.41 indicate that a model improves upon the mean flow benchmark – even if the model's KGE value is negative. NSE and KGE values cannot be directly compared, because their relationship is non-unique and depends in part on the coefficient of variation of the observed time series. Therefore, modellers who use the KGE metric should not let their understanding of NSE values guide them in interpreting KGE values and instead develop new understanding based on the constitutive parts of the KGE metric and the explicit use of benchmark values to compare KGE scores against. More generally, a strong case can be made for moving away from ad hoc use of aggregated efficiency metrics and towards a framework based on purpose-dependent evaluation metrics and benchmarks that allows for more robust model adequacy assessment.

scholarly journals Experimental study on the mean flow characteristics of a supersonic multiple jet configuration

2021 ◽  
Vol 108 ◽  
pp. 106377
Author(s):  
Mohammed Faheem ◽  
Aqib Khan ◽  
Rakesh Kumar ◽  
Sher Afghan Khan ◽  
Waqar Asrar ◽  
...  
Keyword(s):  
Experimental Study ◽  
Flow Characteristics ◽  
Mean Flow ◽  
The Mean
Sign in / Sign up

Export Citation Format

Share Document