Effect Of Different Equations Research Articles

Predictive modeling of flow characteristics in supersonic separators using machine learning

In the pursuit of cleaner energy sources, pre-processing fuel streams is crucial before distribution. Challenges arise during this process, leading to operational issues and diminished transmission efficiency. Among different technologies, supersonic separators are the ones that separate undesired components from the main gas stream more effectively. Precise forecasting of nozzle flow rate and shockwave location at a low cost can markedly enhance the efficiency of manufacturing and rating. In this research, the one-dimensional method has been developed to solve flow equations simultaneously by implementing equations of state. CFD has been used for the verification of the developed model, and the effect of different equations of state is investigated. Results show that the one-dimensional model significantly reduces the calculation time. Different EOSs result in up to 2.0 % and 3.5 % variation in the prediction of shock location and the mass flow rate, respectively.A machine learning methodology is employed to predict the location of shockwaves and the choked flow rate at an even lower cost. A dataset of 160 entries, generated using Peng Robinson's EOS, serves as the basis for this analysis. Prediction tasks are executed using Random Forest, k-nearest Neighbors, and Multilayer Perceptron models. While all three models demonstrate proficiency in data interpolation with R2 scores up to 0.9962 and 0.9951 for the shockwave location and mass flow rate, respectively, discerning their performance in extrapolation appears contingent on the specific case. In the case of extrapolation, Multilayer Perceptron and k-Nearest Neighbors show better match to one-dimensional results.

Hybrid Scour Depth Prediction Equations for Reliable Design of Bridge Piers

Numerous models have been proposed in the past to predict the maximum scour depth around bridge piers. These studies have all focused on the different parameters that could affect the maximum scour depth and the model accuracy. One of the main parameters individuated is the critical velocity of the approaching flow. The present study aimed at investigating the effect of different equations to determine the critical flow velocity on the accuracy of models for estimating the maximum scour depth around bridge piers. Here, 10 scour depth estimation equations, which include the critical flow velocity as one of the influencing parameters, and 8 critical velocity estimation equations were examined, for a total combination of 80 hybrid models. In addition, a sensitivity analysis of the selected scour depth equations to the critical velocity was investigated. The results of the selected models were compared with experimental data, and the best hybrid models were identified using statistical indicators. The accuracy of the best models, including YJAF-VRAD, YJAF-VARN, and YJAI-VRAD models, was also evaluated using field data available in the literature. Finally, correction factors were implied to the selected models to increase their accuracy in predicting the maximum scour depth.

Study of different models of prediction of the simple gas hydrates formation induction time and effect of different equations of state on them

Gas hydrates are crystals, similar to ice. In these crystals, no chemical bond is created between the water molecules (host) and the trapped gas molecules (guest). Gas hydrates are generally encountered in gas transportation pipelines and the industries related to natural gas. Gas hydrates block the path of transmission pipelines and process equipment, which in turn result in partial damage or destruction of the pipeline. For preventing these events, it is necessary and vital to predict the hydrate induction time. To tackle this important issue, this research aims at predicting different models of induction time for hydrate formation of simple gases. Moreover in the current study, these models are evaluated and compared based on the available experimental data in the literature. Additionally, the influence of different equations of state on the aforementioned models are investigated. The models of Natarajan et al., modified Natarajan, Kashchiev and Firoozabadi and Rasoulzadeh and Javanmardi were utilized to predict the induction time of hydrate formation of simple gases including methane and ethane. The results revealed that the models by Rasoulzadeh and Javanmardi, and modified Natarajan yielded the most accurate results. Furthermore, the results showed that various equations of states resulted in similar results, therefore, specified equation of state does not have a great influence on predicting the induction time of hydrate formation.

Jupiter internal structure: the effect of different equations of state (Corrigendum)

After publication of Miguel et al. (2016), we found an error in the calculation of Jupiter internal structure when using REOS3b-H and REOS3sc-H equations of state (EOSs). The lowest pressure in those tables (see appendix in Miguel et al. 2016) was P = 31.623 bars, while our calculations of Jupiter's internal structure started at P = 1 bar. This difference lead to an extrapo-lation of the EOS of hydrogen, which caused an overestimation of Jupiter's interior calculations. We fixed this problem by using the SCvH-H EOS (Saumon et al. 1995) for pressures lower than 6 kbar and merged it with REOS3b-H and REOS3sc-H (correspondingly) for higher pressures. There was also a small offset of ∼2% in the specific entropy at low pressures (P < 1 kbar) between the REOS3b and REOS3sc tables with respect to the SCvH table, caused by a small difference in the s 0 parameter chosen to calculate the specific entropy. In Miguel et al. (2016), this parameter was determined calculating s − s 0 from equation 14 at T = 29 500 K and ρ = 0.036 g cc −1 and then using the value of s in SCvH EOS at the same conditions. This temperature was much higher than the border condition in our interior models (at 165 K) and the intrinsic differences between the tables at those conditions lead to the offset in the specific entropy. In order to fix this issue, we performed new calculations at T = 150 K and ρ = 0.3 g cc −1 , which corrected the offset in S between the EOSs. We also improved our method for calculating the gravity harmonics. Following Nettelmann (2017) and using results calculated with the more accurate CMS method (Hubbard 2013) as a comparison, we corrected the coefficients of the theory of figures of fourth order and improved the numerical handling of density discontinuities. With these improvements, the results agree with Nettelmann et al. (2012) and Hubbard & Militzer (2016). The differences from previous calculations are of the Full appendix tables are only available at CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/618/C2 order of 6 × 10 −7 in J 2 , 1.4 × 10 −8 in J 4 , 2 × 10 −6 in J 6 and 6 × 10 −8 in J 8. We thus ran our simulations again and show the corrected figures below. We also include the corrected EOS tables (see Appendix A). For comparison purposes, the MH13+SCvH table for pure hydrogen was also recalculated by accounting for the entropy of mixing. Along a fixed adiabat, Jupiter's internal temperature is found to be 10% smaller with the new REOS3b table compared to the previous calculation. Nevertheless, the trend remains the same, with REOS3b models being the warmest and MH13 ones the coldest. The core masses found with REOS3b are now 5 < M core < 16 M Earth , i.e., the lower limit is about 2 M Earth smaller than previous calculations. The mass of heavy elements found with REOS3b is significantly lower than previously, being now 13 < M Z < 27 M Earth instead of 20 − 40 M Earth previously. The space of solutions of M core and M Z found with MH13 is almost the same as before with 1 < M Z < 8 M Earth and 10 < M core < 17 M Earth compared with our previous estimations 1-7 M Earth and 11-17 M Earth , correspondingly. Due to the changes in the calculation of gravity harmonics, the results using SCvH also changed. The core masses remain unchanged but M Z changed from 18-44 M Earth to 23-36 M Earth. The new results still show that the internal structure of Jupiter strongly depends on the accuracy of the EOSs. The differences between the MH13 and REOS3 solutions remain significant, in particular in terms of the total mass of heavy elements in the envelope. The location at which helium rain occurs still controls to a large extent the inferred core mass. The main conclusions of the paper therefore remain unchanged. We wish to apologise for this oversight. We thank Burkhard Militzer for noticing the EOS issue. We also thank William B. Hubbard and Nadine Nettelmann who shared codes and algorithms that allowed an accurate comparison of gravitational moments. Article published by EDP Sciences C2, page 1 of 6

Effects of equation of state on hydrodynamic expansion, spectra, flow harmonics and two-pion interferometry

We perform an extensive study of the role played by the equation of state (EoS) in the hydrodynamic evolution of the matter produced in relativistic heavy ion collisions. By using the same initial conditions and freeze-out scenario, the effects of different equations of state are compared by calculating their respective hydrodynamical evolution, particle spectra, harmonic flow coefficients [Formula: see text], [Formula: see text] and [Formula: see text] and two-pion interferometry radius parameters. The equations of state investigated contain distinct features, such as the nature of the phase transition, as well as strangeness and baryon density contents, which are expected to lead to different hydrodynamic responses. The results of our calculations are compared to the data recorded at two RHIC energies, 130[Formula: see text]GeV and 200[Formula: see text]GeV. The three equations of state used in the calculations are found to describe the data reasonably well. Differences can be observed among the studied observables, but they are quite small. In particular, the collective flow parameters are found not to be sensitive to the choice of the EOS, whose implications are discussed.

Effects of Different Equations of State on the Oblique Shock Wave Reflection in Solids

The equations of state of solids under high pressure are more complicated than that of gases in a variety of forms. While the existing studies on the oblique shock wave reflection usually take just one of the equations of state, lacking of the comparisons among them. This paper aims at the investigation of oblique shock wave reflection in solids through shock polar methodology. Four different forms of equations of state are considered, principal shock taking with vN particle velocity relationship and second shock taking with Grüneisen equation of state(1Du2Grüneisen), principal and second shock both taking with vN particle velocity relationship (1Du2Du), principal shock taking with vN particle velocity relationship and second shock taking with stiffened gas equation of state (1Du2Gamma), and principal and second shock both taking with stiffened gas equation of state (1Gamma2Gamma). The effects of different equations of state on the pressure behind the reflected shock show: different combination of EOS may lead to diverse results. In our opinion, the 1Du2Grüneisen and 1Du2Du shows almost the same trends in most conditions and is suitable for the theoretical analysis of oblique reflection, and 1Du2Gamma and 1Gamma2Gamma should be carefully employed in studies to avoid the incorrect result.

Jupiter internal structure: the effect of different equations of state

Heavy elements, even though its smaller constituent, are crucial to understand Jupiter formation history. Interior models are used to determine the amount of heavy elements in Jupiter interior, nevertheless this range is still subject to degeneracies due to uncertainties in the equations of state. Prior to Juno mission data arrival, we present Jupiter optimized calculations exploring the effect of different model parameters in the determination of Jupiter's core and heavy element's mass. We perform comparisons between equations of state published recently. The interior model of Jupiter is calculated from the equations of hydrostatic equilibrium, mass and energy conservation, and energy transport. The mass of the core and heavy elements is adjusted to match Jupiter's observational constrains radius and gravitational moments. We show that the determination of Jupiter interior structure is tied to the estimation of its gravitational moments and the accuracy of equations of state of hydrogen, helium and heavy elements. The location of the region where Helium rain occurs as well as its timescale are important to determine the distribution of heavy elements and helium in the interior of Jupiter. We show that differences find when modeling Jupiter's interior with recent EOS are more likely due to differences in the internal energy and entropy calculation. The consequent changes in the thermal profile lead to different estimations of the mass of the core and heavy elements, explaining differences in recently published Jupiter interior models. Our results help clarify differences find in Jupiter interior models and will help the interpretation of upcoming Juno data.

Binary neutron star mergers and short gamma-ray bursts: Effects of magnetic field orientation, equation of state, and mass ratio

We present fully GRMHD simulations of the merger of binary neutron star (BNS) systems. We consider BNSs producing a hypermassive neutron star (HMNS) that collapses to a spinning black hole (BH) surrounded by a magnetized accretion disk in a few tens of ms. We investigate whether such systems may launch relativistic jets and power short gamma-ray bursts. We study the effects of different equations of state (EOSs), different mass ratios, and different magnetic field orientations. For all cases, we present a detailed investigation of the matter dynamics and of the magnetic field evolution, with particular attention to its global structure and possible emission of relativistic jets. The main result of this work is that we found the formation of an organized magnetic field structure. This happens independently of EOS, mass ratio, and initial magnetic field orientation. We also show that those models that produce a longer-lived HMNS lead to a stronger magnetic field before collapse to BH. Such larger fields make it possible, for at least one of our models, to resolve the MRI and hence further amplify the magnetic field. However, by the end of our simulations, we do not observe a magnetically dominated funnel and hence neither a relativistic outflow. With respect to the recent simulations of Ruiz et al 2016, we evolve models with lower and more realistic initial magnetic field strengths and, because of computational reasons, we do not evolve the accretion disk for the long timescales that seem to be required in order to see a relativistic outflow. Since all our models produce a similar ordered magnetic field structure, we expect that the results found in Ruiz et al 2016, where they only considered an equal-mass system with an ideal fluid EOS, should be general and, at least from a qualitative point of view, independent from mass-ratio, magnetic field orientation, and EOS.

Using a bivariate generalized linear mixed model to analyze the effect of feeding pressure on pine weevil damage

The objective of the study is to derive a method by which one can analyze how the probability of damage made by pine weevils on seedlings treated with insecticides depends on the probability of damage on untreated control seedlings, called feeding pressure. Because the probabilities vary from stand to stand and from block to block, the analysis is done using a generalized linear mixed model. The dependency of probability of damage on the feeding pressure cannot be properly analyzed using observed relative frequency of damage of control seedlings as a covariate, but it can be analyzed using a bivariate model. One equation describes damage of control seedlings and another equation damage of treated seedlings. The random stand and block effects of different equations are correlated. For a given probability of stand level control seedling damage, the random stand effect for control seedlings can be computed using a link function, then random stand effects for treated seedlings can be predicted using the best linear predictor from the random effect for control seedlings. Using an inverse link the prediction can again be presented in the probability scale which is of interest to the user. Using these three steps the probability of damage of treated seedlings can be predicted from the control damage probability. The probability of damage of treated seedlings can also be predicted from the observed relative frequency of damaged control seedlings using simulation. The complementary log-log link was used for control seedlings and the log-log link for treated seedlings.

Role of model ingredients on the directed flow and its disappearance using isospin dependent quantum molecular dynamics model

We study the effect of different equations of state, momentum dependence of nuclear forces and in-medium nucleon-nucleon cross-sections on the directed flow and its disappearance. Our findings reveal that soft momentum-dependent equation of state along with reduced cross-section shows good agreement with the experimentally observed mass dependence of balance energy.

Relativistic equations of state in a Thomas-Fermi approach for neutron stars

In this work we investigate the effects of different equations of state (EOS) in explaining high density matter properties. We study not only \ensuremath{\beta} stable states, pure neutron, and symmetric matter, but also states with different proton fractions. We show that the influence of the parametrization is already felt at not so dense matter while the importance of the hyperon to meson coupling only appears at densities much larger than the nuclear matter saturation density. We have also checked the effects of considering a hyperon to meson coupling larger than the universal coupling. Neutron star properties are obtained with the EOS discussed in the present work.

Quasiequilibrium sequences of synchronously rotating binary neutron stars with constant rest masses in general relativity: Another approach without using the conformally flat condition

We compute quasiequilibrium sequences of synchronously rotating compact binary star systems with constant rest masses. This computation is carried out by using a numerical scheme which is different from the scheme based on the conformally flat assumption about the space. Stars are assumed to be polytropes with polytropic indices of $N=0.5,$ $N=1.0,$ and $N=1.5.$ Since we compute binary star sequences with a constant rest mass, they provide approximate evolutionary tracks of binary star systems. For relatively stiff equations of state $(N&lt;1.0),$ there appear turning points along the quasiequilibrium sequences plotted in the angular momentum---angular velocity plane. Consequently a secular instability against exciting internal motion sets in at those points. Qualitatively, these results agree with those of Baumgarte et al. who employed the conformally flat condition. We further discuss the effect of different equations of state and a different strength of gravity by introducing two kinds of dimensionless quantities which represent the angular momentum and the angular velocity. The strength of gravity is renormalized in these quantities so that the quantities are transformed to values around unity. Therefore we can clearly see relations among quasiequilibrium sequences for a wide variety of strength of gravity and for different compressibility.

Measurement Uncertainties Encountered During Gas Turbine Driven Compressor Field Testing

Field testing of gas turbine compressor packages requires the accurate determination of efficiency, capacity, head, power and fuel flow in sometimes less than ideal working environments. Nonetheless, field test results have significant implication for the compressor and gas turbine manufacturers and their customers. Economic considerations demand that the performance and efficiency of an installation are verified to assure a project?s return on investment. Thus, for the compressor and gas turbine manufacturers, as well as for the end-user, an accurate determination of the field performance is of vital interest. This paper describes an analytic method to predict the measurement uncertainty and, thus, the accuracy, of field test results for gas turbine driven compressors. Namely, a method is presented which can be employed to verify the validity of field test performance results. The equations governing the compressor and gas turbine performance uncertainties are rigorously derived and results are numerically compared to actual field test data. Typical field test measurement uncertainties are presented for different sets of instrumentation. Test parameters that correlate to the most significant influence on the performance uncertainties are identified and suggestions are provided on how to minimize their measurement errors. The effect of different equations of state on the calculated performance is also discussed. Results show that compressor efficiency uncertainties can be unacceptably high when some basic rules for accurate testing are violated. However, by following some simple measurement rules and maintaining commonality of the gas equations of state, the overall compressor package performance measurement uncertainty can be limited and meaningful results can be achieved.

OB stars and the structure of the interstellar medium - Cloud formation and effects of different equations of state

The effects of OB stars on the physical state of the interstellar medium have been investigated using a time-dependent numerical simulation which includes explicit two-dimensional hydrodynamics and implicit, coupled radiative transfer and thermodynamics. Using the observed birthrates, OB stars are placed randomly in space and time on an 180 pc square numerical grid where they ionize and push ambient gas for the duration of their main sequence lifetimes. Though they contribute a minuscule amount of ionization, the B stars are efficient excavators of ambient matter because their initial Stroemgren radii are much smaller than the distance that the shock front around the H II region can travel in the stellar lifetime.