THE INVARIANT REGION FOR THE EQUATIONS OF NONISENTROPIC GAS DYNAMICS

2017 ◽  
Vol 58 (3-4) ◽  
pp. 428-435 ◽  
Author(s):  
WEI-FENG JIANG ◽  
ZHEN WANG
Keyword(s):  
Riemann Problem ◽  
Gas Dynamics ◽  
Ideal Gas ◽  
Lagrangian Multiplier ◽  
Intensive Study ◽  
Invariant Region ◽  
One Dimensional ◽  
The Mean ◽  
Lagrangian Multiplier Method ◽  
The One

We study the existence of the invariant region for the equations of nonisentropic gas dynamics. We obtain the mean-integral of the conserved quantity after making an intensive study of the Riemann problem. Using the extremum principle and the Lagrangian multiplier method, we prove that the one-dimensional equations of nonisentropic gas dynamics for an ideal gas possess a unique invariant region. However, the invariant region is not bounded.

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.

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.

scholarly journals Tomographic retrievals of ozone with the OMPS Limb Profiler: algorithm description and preliminary results

2018 ◽  
Vol 11 (4) ◽  
pp. 2375-2393 ◽  
Author(s):  
Daniel J. Zawada ◽  
Landon A. Rieger ◽  
Adam E. Bourassa ◽  
Douglas A. Degenstein
Keyword(s):  
Polar Vortex ◽  
Retrieval Algorithm ◽  
Vertical Profiles ◽  
Two Dimensional ◽  
One Dimensional ◽  
Preliminary Results ◽  
Horizontal Gradients ◽  
The Mean ◽  
The One

Abstract. Measurements of limb-scattered sunlight from the Ozone Mapping and Profiler Suite Limb Profiler (OMPS-LP) can be used to obtain vertical profiles of ozone in the stratosphere. In this paper we describe a two-dimensional, or tomographic, retrieval algorithm for OMPS-LP where variations are retrieved simultaneously in altitude and the along-orbital-track dimension. The algorithm has been applied to measurements from the center slit for the full OMPS-LP mission to create the publicly available University of Saskatchewan (USask) OMPS-LP 2D v1.0.2 dataset. Tropical ozone anomalies are compared with measurements from the Microwave Limb Sounder (MLS), where differences are less than 5 % of the mean ozone value for the majority of the stratosphere. Examples of near-coincident measurements with MLS are also shown, and agreement at the 5 % level is observed for the majority of the stratosphere. Both simulated retrievals and coincident comparisons with MLS are shown at the edge of the polar vortex, comparing the results to a traditional one-dimensional retrieval. The one-dimensional retrieval is shown to consistently overestimate the amount of ozone in areas of large horizontal gradients relative to both MLS and the two-dimensional retrieval.

scholarly journals Existence and nonexistence of entire solutions to the logistic differential equation

2003 ◽  
Vol 2003 (17) ◽  
pp. 995-1003 ◽  
Author(s):  
Marius Ghergu ◽  
Vicentiu Radulescu
Keyword(s):  
Blow Up ◽  
Entire Solutions ◽  
One Dimensional ◽  
Nonexistence Result ◽  
Nonnegative Solutions ◽  
Existence And Nonexistence ◽  
Logistic Problem ◽  
Whole Space ◽  
The Mean ◽  
The One

We consider the one-dimensional logistic problem(rαA(|u′|)u′)′=rαp(r)f(u)on(0,∞),u(0)>0,u′(0)=0, whereαis a positive constant andAis a continuous function such that the mappingtA(|t|)is increasing on(0,∞). The framework includes the case wherefandpare continuous and positive on(0,∞),f(0)=0, andfis nondecreasing. Our first purpose is to establish a general nonexistence result for this problem. Then we consider the case of solutions that blow up at infinity and we prove several existence and nonexistence results depending on the growth ofpandA. As a consequence, we deduce that the mean curvature inequality problem on the whole space does not have nonnegative solutions, excepting the trivial one.

Analysis of Uncertainty in the Calculation of Ideal-Gas Thermodynamic Properties Using the One-Dimensional Hindered Rotor (1-DHR) Model

2016 ◽  
Vol 62 (1) ◽  
pp. 445-455 ◽  
Author(s):  
Ctirad Červinka ◽  
Michal Fulem ◽  
Vojtěch Štejfa ◽  
Květoslav Růžička
Keyword(s):  
Thermodynamic Properties ◽  
Ideal Gas ◽  
One Dimensional ◽  
The One
Sign in / Sign up

Export Citation Format

Share Document