Gas Waterhammer

2007 ◽  
Author(s):  
Hugh Goyder
Keyword(s):  
Acoustic Waves ◽  
Safety Valve ◽  
Initial Conditions ◽  
Assessment Process ◽  
High Frequencies ◽  
Lack Of Information ◽  
Process Plant ◽  
Pressure Relief Valves ◽  
Support Conditions ◽  
Set Up

Gas process plant includes pressure relief valves, or pressure safety valves, which enable vessels containing high pressure gas to be emptied quickly into a relief main which takes the gas to a flair stack. The pressure safety valve opens suddenly and sets up acoustic waves, in the manner of a waterhammer, that propagate backwards and forwards in pipework until a steady flow is obtained. Such acoustic waves may set up large forces in pipework that may cause damage. Consequently, an assessment process is required that includes the forces generated by the gas and the resultant stresses in the pipework. One particular problem, investigated here, is the initial conditions for the acoustic waves as the pressure safety valve lifts. The main difficulty with an assessment is the near impossibility of modelling the pipe dynamics adequately. This difficulty is due to the lack of information available concerning pipework support systems and the need to model pipework vibration to high frequencies. A conservative method for assessment based on looking at extremes of support conditions is proposed.

scholarly journals On Kaufmann's theory of the impact of the pianoforte hammer

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
Keyword(s):  
Initial Conditions ◽  
Practical Importance ◽  
Prima Facie ◽  
Point Of View ◽  
Infinite Length ◽  
Modes Of Vibration ◽  
Rigorous Treatment ◽  
The Subject ◽  
Set Up ◽  
The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

scholarly journals USE OF SCALED SEMIVARIOGRAMS IN THE PLANNING SAMPLE OF SOIL CHEMICAL PROPERTIES IN SOUTHERN AMAZONAS, BRAZIL

2015 ◽  
Vol 39 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Ivanildo Amorim de Oliveira ◽  
Milton César Costa Campos ◽  
José Marques Junior ◽  
Renato Eleotério de Aquino ◽  
Daniel de Bortoli Teixeira ◽  
...  
Keyword(s):  
Chemical Properties ◽  
Spherical Model ◽  
Exponential Model ◽  
Soil Samples ◽  
Soil Chemical Properties ◽  
Sampling Density ◽  
Sugarcane Crop ◽  
Lack Of Information ◽  
Set Up ◽  
Almost All

The lack of information concerning the variability of soil properties has been a major concern of researchers in the Amazon region. Thus, the aim of this study was to evaluate the spatial variability of soil chemical properties and determine minimal sampling density to characterize the variability of these properties in five environments located in the south of the State of Amazonas, Brazil. The five environments were archaeological dark earth (ADE), forest, pasture land, agroforestry operation, and sugarcane crop. Regular 70 × 70 m mesh grids were set up in these areas, with 64 sample points spaced at 10 m distance. Soil samples were collected at the 0.0-0.1 m depth. The chemical properties of pH in water, OM, P, K, Ca, Mg, H+Al, SB, CEC, and V were determined at these points. Data were analyzed by descriptive and geostatistical analyses. A large part of the data analyzed showed spatial dependence. Chemical properties were best fitted to the spherical model in almost all the environments evaluated, except for the sugarcane field with a better fit to the exponential model. ADE and sugarcane areas had greater heterogeneity of soil chemical properties, showing a greater range and higher sampling density; however, forest and agroforestry areas had less variability of chemical properties.

Modeling and prediction for the oxidation efficiency of magnesium sulfite in aeration tank of magnesium-based seawater exhaust gas clean system

2017 ◽  
Vol 233 (1) ◽  
pp. 164-173
Author(s):  
Quan Liu ◽  
Yimin Zhu ◽  
Tie Li ◽  
Xiaojia Tang ◽  
Weifeng Liu ◽  
...  
Keyword(s):  
Flow Field ◽  
Initial Conditions ◽  
Negative Impact ◽  
Fluid Model ◽  
Aeration Tank ◽  
Exhaust Gas ◽  
Clean System ◽  
Physics Modeling ◽  
Set Up ◽  
Oxidation Efficiency

In magnesium-based seawater exhaust gas clean system, the desulfurization by-product, magnesium sulfite (MgSO3), has a negative impact on the ecological environment, which needs to be treated to make harmless. Due to the limited space on board, the aeration oxidation method is used to convert it to magnesium sulfate. Because of the variable size, shape and flow field of aeration tank, it is difficult and expensive to design and verify the oxidation efficiency of the aeration tank by experimental method. In this work, in order to predict the oxidation efficiency accurately, RFlow, a computational fluid dynamics software, was used to analyze the flow field and MgSO3 oxidation reaction in aeration tank. The subdomain technology was adopted for physics modeling and mesh generation of the aeration tank, and the total number of meshes was 285,000. The multi-phase flow field model was set up using the multi-fluid model and dispersive k-ε turbulence model. Under the given initial conditions, the predicted oxidation efficiency was 94.2%. Compared with the results of the actual ship test, the prediction model for MgSO3 oxidation efficiency of the aeration tank is reliable.

scholarly journals Laboratory-based surveillance for Cryptosporidium in France, 2006–2009

2010 ◽  
Vol 15 (33) ◽  
Author(s):  
Collective The ANOFEL Cryptosporidium National Network
Keyword(s):  
Seasonal Pattern ◽  
Late Summer ◽  
Epidemiological Data ◽  
University Hospitals ◽  
National Network ◽  
Lack Of Information ◽  
Health Authorities ◽  
Public Health Authorities ◽  
Set Up ◽  
Voluntary Basis

In 2002, the French Food Safety Agency drew attention to the lack of information on the prevalence of human cryptosporidiosis in the country. Two years later, the ANOFEL Cryptosporidium National Network (ACNN) was set up to provide public health authorities with data on the incidence and epidemiology of human cryptosporidiosis in France. Constituted on a voluntary basis, ACNN includes 38 hospital parasitology laboratories (mainly in university hospitals). Each laboratory is engaged to notify new cases of confirmed human cryptosporidiosis, store specimens (e.g. stools, duodenal aspirates or biopsies) and related clinical and epidemiological data, using datasheet forms. From January 2006 to December 2009, 407 cryptosporidiosis cases were notified in France and 364 specimens were collected. Of the notified cases, 74 were children under four years of age, accounting for 18.2%. HIV-infected and immunocompetent patients represented 38.6% (n=157) and 28% (n=114) of cases, respectively. A marked seasonal pattern was observed each year, with increased number of cases in mid to late summer and the beginning of autumn. Genotyping of 345 isolates from 310 patients identified C. parvum in 168 (54.2%) cases, C. hominis in 113 (36.4%) and other species in 29 (9.4%), including C. felis (n=15), C. meleagridis (n=4), C. canis (n=4), Cryptosporidium chipmunk genotype (n=1), Cryptosporidium rabbit genotype (n=1) and new Cryptosporidium genotypes (n=4). These data represent the first multisite report of laboratory-confirmed cases of cryptosporidiosis in France.

Effects of inertia and stratification in incompressible ideal fluids: pressure imbalances by rigid confinement

2013 ◽  
Vol 726 ◽  
pp. 404-438 ◽  
Author(s):  
R. Camassa ◽  
S. Chen ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni
Keyword(s):  
Euler Equations ◽  
Initial Conditions ◽  
Numerical Algorithms ◽  
Wave Dispersion ◽  
Variable Density ◽  
Density Variation ◽  
Fluid Inertia ◽  
Time Dynamics ◽  
Long Wave ◽  
Set Up

AbstractConsequences of density stratification are studied for an ideal (Euler) incompressible fluid, confined to move under gravity between rigid lids but otherwise free to move along horizontal directions. Initial conditions that generate horizontal pressure imbalances in a laterally unbounded domain are examined. The aim is to show analytically the existence of classes of initial data for which total horizontal momentum evolves in time, even though only vertical forces act on the fluid in this set-up. A simple class of such initial conditions, leading to momentum evolution, is identified by systematic asymptotic expansions of the governing inhomogeneous Euler equations in the small-density-variation limit. These results for Euler equations are compared and confirmed with long-wave asymptotic models, which can handle arbitrary density variations and provide closed-form mathematical expressions for limiting cases. In particular, the role of wave dispersion arising from the fluid inertia is captured by the long-wave models, even for short-time dynamics emanating from initial conditions outside the models’ asymptotic range of validity. These results are compared with direct numerical simulations for variable-density Euler fluids, which further validate the numerical algorithms and the analysis.

scholarly journals The non-modal onset of the tearing instability

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
D. MacTaggart
Keyword(s):  
Initial Conditions ◽  
Linear Equations ◽  
Initial Perturbation ◽  
Transient Growth ◽  
Tearing Mode ◽  
Eigenvalue Spectrum ◽  
Tearing Instability ◽  
Set Up ◽  
Solution Behaviour ◽  
Physical Quantities

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number$S$increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the$L_{2}$-norm, for the classical set-up of current sheets unstable to the TI, scales as$O(S^{1/4})$on time scales of$O(S^{1/4})$for$S\gg 1$. This behaviour is much faster than the time scale$O(S^{1/2})$when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

Role of initial condition and parametric uncertainty in a severe hailstorm forecast

2021 ◽  
Author(s):  
Patrick Kuntze ◽  
Annette Miltenberger ◽  
Corinna Hoose ◽  
Michael Kunz
Keyword(s):  
Initial Conditions ◽  
Weather Prediction ◽  
Parametric Uncertainty ◽  
Radar Data ◽  
Cloud Microphysics ◽  
Initial Condition ◽  
Relative Contribution ◽  
Cloud Properties ◽  
Set Up ◽  
The Impact

<p>Forecasting high impact weather events is a major challenge for numerical weather prediction. Initial condition uncertainty plays a major role but so potentially do uncertainties arising from the representation of physical processes, e.g. cloud microphysics. In this project, we investigate the impact of these uncertainties for the forecast of cloud properties, precipitation and hail of a selected severe convective storm over South-Eastern Germany.<br>To investigate the joint impact of initial condition and parametric uncertainty a large ensemble including perturbed initial conditions and systematic variations in several cloud microphysical parameters is conducted with the ICON model (at 1 km grid-spacing). The comparison of the baseline, unperturbed simulation to satellite, radiosonde, and radar data shows that the model reproduces the key features of the storm and its evolution. In particular also substantial hail precipitation at the surface is predicted. Here, we will present first results including the simulation set-up, the evaluation of the baseline simulation, and the variability of hail forecasts from the ensemble simulation.<br>In a later stage of the project we aim to assess the relative contribution of the introduced model variations to changes in the microphysical evolution of the storm and to the fore- cast uncertainty in larger-scale meteorological conditions.</p>

scholarly journals Parametric Study of Tsunamis Generated by Earthquakes and Landslides

2019 ◽  
Vol 7 (5) ◽  
pp. 154 ◽  
Author(s):  
Natalia Perez del Postigo Prieto ◽  
Alison Raby ◽  
Colin Whittaker ◽  
Sarah J. Boulton
Keyword(s):  
Predictive Models ◽  
Initial Conditions ◽  
Quality Data ◽  
Tsunami Generation ◽  
Fault Rupture ◽  
Physical Experiments ◽  
Dual Source ◽  
Set Up ◽  
Displacement Scale ◽  
The University

Tsunami generation and propagation mechanisms need to be clearly understood in order to inform predictive models and improve coastal community preparedness. Physical experiments, supported by mathematical models, can potentially provide valuable input data for standard predictive models of tsunami generation and propagation. A unique experimental set-up has been developed to reproduce a coupled-source tsunami generation mechanism: a two-dimensional underwater fault rupture followed by a submarine landslide. The test rig was located in a 20 m flume in the COAST laboratory at the University of Plymouth. The aim of the experiments is to provide quality data for developing a parametrisation of the initial conditions for tsunami generation processes which are triggered by a dual-source. During the test programme, the water depth and the landslide density were varied. The position of the landslide model was tracked and the free surface elevation of the water body was measured. Hence the generated wave characteristics were determined. For a coupled-source scenario, the generated wave is crest led, followed by a trough of smaller amplitude decreasing steadily as it propagates along the flume. The crest amplitude was shown to be influenced by the fault rupture displacement scale, whereas the trough was influenced by the landslide’s relative density.

scholarly journals Dependence on the Initial Data for the Continuous Thermostatted Framework

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 602
Author(s):  
Bruno Carbonaro ◽  
Marco Menale
Keyword(s):  
Complex System ◽  
Initial Data ◽  
External Force ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Complete Information ◽  
Complete Picture ◽  
Order Moment ◽  
Lack Of Information ◽  
Activity Variable

The paper deals with the problem of continuous dependence on initial data of solutions to the equation describing the evolution of a complex system in the presence of an external force acting on the system and of a thermostat, simply identified with the condition that the second order moment of the activity variable (see Section 1) is a constant. We are able to prove that these solutions are stable with respect to the initial conditions in the Hadamard’s sense. In this connection, two remarks spontaneously arise and must be carefully considered: first, one could complain the lack of information about the “distance” between solutions at any time t ∈ [ 0 , + ∞ ) ; next, one cannot expect any more complete information without taking into account the possible distribution of the transition probabiliy densities and the interaction rates (see Section 1 again). This work must be viewed as a first step of a research which will require many more steps to give a sufficiently complete picture of the relations between solutions (see Section 5).

Experimentally Measured Boundary and Initial Conditions for Simulations

2014 ◽  
Vol 1041 ◽  
pp. 293-296 ◽  
Author(s):  
Dušan Katunský ◽  
Marek Zozulák ◽  
Marián Vertaľ ◽  
Jozef Šimiček
Keyword(s):  
Boundary Conditions ◽  
Indoor Environment ◽  
Initial Conditions ◽  
Weather Data ◽  
Initial Condition ◽  
Dynamic Boundary Conditions ◽  
Climate Monitoring ◽  
Set Up ◽  
Water Profile

Real dynamic boundary conditions and initial condition has to be taken into an account when simulations need to be done. The most helpful are in situ measurement facilities with climate monitoring. Indoor environment operation modes with different air temperature and relative humidity made indoor boundary conditions. Measured weather data are used to create complete boundary conditions for the research locality. Initial condition of masonry water profile is set up. The initial and boundary conditions are considered for an individual locality simulation proposes.

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