Effect of friction and heat losses on the mean structure of one-dimensional detonations

2013 ◽  
Author(s):  
A. Sow ◽  
A. Chinnayya ◽  
A. Hadjadj
Keyword(s):  
Heat Losses ◽  
One Dimensional ◽  
Mean Structure ◽  
The Mean

Mean structure of one-dimensional unstable detonations with friction

2014 ◽  
Vol 743 ◽  
pp. 503-533 ◽  
Author(s):  
Aliou Sow ◽  
Ashwin Chinnayya ◽  
Abdellah Hadjadj
Keyword(s):  
Reaction Zone ◽  
Friction Forces ◽  
One Dimensional ◽  
Post Shock ◽  
Reactive Euler Equations ◽  
Frictional Forces ◽  
Mean Structure ◽  
The Mean ◽  
Energy Balances ◽  
Fifth Order

AbstractThis investigation deals with the study of the mean structure of a mildly unstable non-ideal detonation wave. The analysis is based on the integration of one-dimensional reactive Euler equations with friction forces using a third-order Runge–Kutta scheme and a fifth-order weighted essentially non-oscillatory (WENO5) spatial discretization. A one-step Arrhenius reaction mechanism is used for modelling the chemical reaction. When the frictional forces are active, the limit cycle based on the post-shock pressure reveals an enhanced pulsating behaviour of the downstream subsonic reaction zone compared to the ideal case. The results show that the detonation-velocity deficit increases as the mean reaction zone becomes thicker compared to the generalized ZND model. A new master equation, based on the Favre-averaged quantities, is derived and analysed along with new sonicity and thermicity conditions. The analysis of the species, momentum and energy balances reveals that the presence of mechanical fluctuations within the reaction zone constitutes another source of energy withdrawal, meaning that the detonation deviates from its laminar structure. Furthermore, the compressibility of the flow is analysed and the relationships between the fluctuations of temperature, velocity and reactive scalar are discussed in terms of strong Reynolds analogies.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Mathematical Analysis for Off-Design Performance of Cryogenic Turboexpander

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Subrata K. Ghosh ◽  
R. K. Sahoo ◽  
Sunil K. Sarangi
Keyword(s):  
Pressure Ratio ◽  
Expansion Ratio ◽  
Flow Conditions ◽  
Flow Properties ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Design Performance ◽  
Fluid Properties ◽  
The Mean ◽  
Inlet Conditions

A study has been conducted to determine the off-design performance of cryogenic turboexpander. A theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed. The model uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. In this analysis, the changes of fluid and flow properties between different components of turboexpander have been considered. Overall, turbine geometry, pressure ratio, and mass flow rate are input information. The output includes performance and velocity diagram parameters for any number of given speeds over a range of turbine pressure ratio. The procedure allows any arbitrary combination of fluid species, inlet conditions, and expansion ratio since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example.

scholarly journals Estimation of peak discharges of historical floods

2014 ◽  
Vol 11 (5) ◽  
pp. 5463-5485 ◽  
Author(s):  
J. Herget ◽  
T. Roggenkamp ◽  
M. Krell
Keyword(s):  
Flood Frequency ◽  
River Channels ◽  
Sources Of Information ◽  
Mean Flow ◽  
General Outline ◽  
One Dimensional ◽  
Flood Level ◽  
Alternative Approaches ◽  
The Mean ◽  
Generalized Statement

Abstract. There is no doubt, that the hazard assessment of future floods especially under consideration of the recent environmental change can be significantly improved by the consideration of historic flood events. While flood frequency inventories on local, regional and even European scale are already developed and published, the estimation of their magnitudes indicated by discharges is still challenging. Such data are required due to significant human impact on river channels and floodplains though historic flood levels cannot be related to recent ones or recent discharges. Based on own experiences from single local key studies the general outline of an approach to estimate the discharge of the previous flood based on handed down flood level and topographic data is presented. The model for one-dimensional steady flow is based on the empirical Manning equation for the mean flow velocity. Background and potential sources of information, acceptable simplifications and data transformation for each element of the model-equation are explained and discussed. Preliminary experiences on the accuracy of ±10% are documented and potential approaches for the validation of individual estimations given. A brief discussion on benefits and limitations including a generalized statement on alternative approaches closes the review presentation of the approach.

scholarly journals Assessment of CFD turbulence models for free surface flow simulation and 1-D modelling for water level calculations over a broad-crested weir floodway

Water SA ◽  
2019 ◽  
Vol 45 (3 July) ◽  
Author(s):  
Ahmed M Helmi
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Water Level ◽  
Dimensional Analysis ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Cfd Simulations ◽  
One Dimensional ◽  
The Mean ◽  
The One

Floodways, where a road embankment is permitted to be overtopped by flood water, are usually designed as broad-crested weirs. Determination of the water level above the floodway is crucial and related to road safety. Hydraulic performance of floodways can be assessed numerically using 1-D modelling or 3-D simulation using computational fluid dynamics (CFD) packages. Turbulence modelling is one of the key elements in CFD simulations. A wide variety of turbulence models are utilized in CFD packages; in order to identify the most relevant turbulence model for the case in question, 96 3-D CFD simulations were conducted using Flow-3D package, for 24 broad-crested weir configurations selected based on experimental data from a previous study. Four turbulence models (one-equation, k-ε, RNG k-ε, and k-ω) ere examined for each configuration. The volume of fluid (VOF) algorithm was adopted for free water surface determination. In addition, 24 1-D simulations using HEC-RAS-1-D were conducted for comparison with CFD results and experimental data. Validation of the simulated water free surface profiles versus the experimental measurements was carried out by the evaluation of the mean absolute error, the mean relative error percentage, and the root mean square error. It was concluded that the minimum error in simulating the full upstream to downstream free surface profile is achieved by using one-equation turbulence model with mixing length equal to 7% of the smallest domain dimension. Nevertheless, for the broad-crested weir upstream section, no significant difference in accuracy was found between all turbulence models and the one-dimensional analysis results, due to the low turbulence intensity at this part. For engineering design purposes, in which the water level is the main concern at the location of the flood way, the one-dimensional analysis has sufficient accuracy to determine the water level.

Ground state of one-dimension repulsing particles on disordered lattice

2014 ◽  
Vol 25 (08) ◽  
pp. 1450028 ◽  
Author(s):  
L. A. Pastur ◽  
V. V. Slavin ◽  
A. A. Krivchikov
Keyword(s):  
Ground State ◽  
Domain Walls ◽  
Host Lattice ◽  
One Dimension ◽  
Weak Disorder ◽  
Interacting Particles ◽  
One Dimensional ◽  
Lattice Disorder ◽  
Disordered Lattice ◽  
The Mean

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.

Microscale temperature and velocity spectra in the atmospheric boundary layer

1977 ◽  
Vol 83 (3) ◽  
pp. 547-567 ◽  
Author(s):  
R. M. Williams ◽  
C. A. Paulson
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Temperature Fluctuations ◽  
Inertial Subrange ◽  
Velocity Fluctuations ◽  
One Dimensional ◽  
Temperature Spectra ◽  
The Mean ◽  
Velocity Spectra ◽  
The One

High-frequency fluctuations in temperature and velocity were measured at a height of 2 m above a harvested, nearly level field of rye grass. Conditions were both stably and unstably stratified. Reynolds numbers ranged from 370000 to 740000. Measurements of velocity were made with a hot-wire anemometer and measurements of temperature with a platinum resistance element which had a diameter of 0[sdot ]5 μm and a length of 1 mm. Thirteen runs ranging in length from 78 to 238 s were analysed.Spectra of velocity fluctuations are consistent with previously reported universal forms. Spectra of temperature, however, exhibit an increase in slope with increasing wavenumber as the maximum in the one-dimensional dissipation spectrum is approached. The peak of the one-dimensional dissipation spectrum for temperature fluctuations occurs at a higher wavenumber than that of simultaneous spectra of the dissipation of velocity fluctuations. It is suggested that the change in slope of the temperature spectra and the dissimilarity between temperature and velocity spectra may be due to spatial dissimilarity in the dissipation of temperature and velocity fluctuations. The temperature spectra are compared with a theoretical prediction for fluids with large Prandtl number, due to Batchelor (1959). Even though air has a Prandtl number of 0[sdot ]7, the observations are in qualitative agreement with predictions of the theory. The non-dimensional wavenumber at which the increase in slope occurs is about 0[sdot ]02, in good agreement with observations in the ocean reported by Grantet al. (1968).For the two runs for which the stratification was stable, the normalized spectra of the temperature derivative fall on average slightly below the mean of the spectra of the remaining runs in the range in which the slope is approximately one-third. Hence the Reynolds number may not have always been sufficiently high to satisfy completely the conditions for an inertial subrange.Universal inertial-subrange constants were directly evaluated from one-dimensional dissipation spectra and found to be 0[sdot ]54 and 1[sdot ]00 for velocity and temperature, respectively. The constant for velocity is consistent with previously reported values, while the value for temperature differs from some of the previous direct estimates but is only 20% greater than the mean of the indirect estimates. This discrepancy may be explained by the neglect in the indirect estimates of the divergence terms in the conservation equation for the variance of temperature fluctuations. There is weak evidence that the one-dimensional constant, and hence the temperature spectra, may depend upon the turbulence Reynolds number, which varied from 1200 to 4300 in the observations reported.

Uniqueness and Symmetry for the Mean Field Equation on Arbitrary Flat Tori

2020 ◽  
Author(s):  
Guangze Gu ◽  
Changfeng Gui ◽  
Yeyao Hu ◽  
Qinfeng Li
Keyword(s):  
Field Equation ◽  
Level Sets ◽  
Mean Field ◽  
Flat Torus ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
Flat Tori ◽  
The Mean ◽  
Symmetry Result ◽  
Mean Field Equation

Abstract We study the following mean field equation on a flat torus $T:=\mathbb{C}/(\mathbb{Z}+\mathbb{Z}\tau )$: $$\begin{equation*} \varDelta u + \rho \left(\frac{e^{u}}{\int_{T}e^u}-\frac{1}{|T|}\right)=0, \end{equation*}$$where $ \tau \in \mathbb{C}, \mbox{Im}\ \tau>0$, and $|T|$ denotes the total area of the torus. We first prove that the solutions are evenly symmetric about any critical point of $u$ provided that $\rho \leq 8\pi $. Based on this crucial symmetry result, we are able to establish further the uniqueness of the solution if $\rho \leq \min{\{8\pi ,\lambda _1(T)|T|\}}$. Furthermore, we also classify all one-dimensional solutions by showing that the level sets must be closed geodesics.

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