Mean Total Kinetic Energy Research Articles

Investigation of the local apparent viscosity in a stirred tank with a shear-thinning fluid through particle image velocimetry

The local apparent viscosity in a cylindrical stirred tank was investigated using Particle Image Velocimetry in a shear-thinning fluid. Two impellers were studied, a Rushton turbine for validation and an axial impeller HTPG4, for three Reynolds numbers corresponding to the transition regime between laminar and turbulent flows. Mean and instantaneous velocity contours and profiles are analysed. Then, the different contributions to the mean total kinetic energy are investigated with the HTPG4 impeller. The sensitivity of the mean apparent viscosity to the method of determining the shear rate is discussed. This work shows that the mean apparent viscosity is highly sensitive to the method of determining the shear rate. Future work will focus on improving the measurement of the local shear rate.

Total kinetic, excitation energy and neutron multiplicity distribution of californium isotopes

The mean total kinetic energy as a function of fission fragments, <TKE>(A), is calculated for neutron-induced fission of 247,249,251,253,255Cf, as well as for spontaneous fission of 248,250,252,254Cf using the scission point model. A comparative analysis is performed between the calculated results and existing experimental data. Investigation into the behavior of <TKE>(A) is conducted, particularly focusing on intermediate and heavy actinides. While nuclear and Coulomb energy evaluations suffice for estimating <TKE> values in light actinides, this approximation proves inadequate for evaluating TKE values for intermediate and heavy actinides. Additionally, an evaluation is made of the total excitation energy as a function of fission fragments, <TXE>(A), concerning spontaneous fission in 247−254Cf. It is found that TXE values sharply increase near the symmetric region across all isotopes and exhibit a gradual increase in heavy fission fragments. Furthermore, an exploration of the total neutron multiplicity as a function of fission fragments, νT(A), is conducted for 252Cf fission using two methods. The νT(A) results obtained through these methods are compared with experimental data, and νT(A) is estimated for unmeasured californium isotopes. The average neutron emission per fission event, ν¯(Ai), is then calculated for spontaneous fission of 251Cf and 253Cf, yielding values of 3.46 and 3.59, respectively.

Measurement of mass-angle and mass-total kinetic energy distributions from the fission of 190Pt compound nucleus

We have measured the fission fragment mass-angle and mass-total kinetic energy (TKE) distributions for the neutron-deficient 190Pt compound nucleus (CN) populated via 12C + 178Hf reaction, at around and above barrier energies. No mass-angle correlation was observed in the fission of 190Pt signifying the absence of quasi-fission events in the studied reaction. The observed mass-TKE distributions have expected triangular shape and TKE distributions are well described with the single Gaussian fits, and mean TKE shows parabolic dependence on fragment mass as predicted based on liquid drop fission behaviour. The widths of measured TKE distributions agree well with the observed systematics for CN fission in this mass region. Though the CN is relatively neutron deficient, these observations suggest a clear picture of true CN fission behaviour for the chosen reaction in the studied energy domain.

The performance of different unsteady Reynolds-averaged Navier-Stokes models mined by Fuzzy C-means algorithm with Fourier coefficient-based distance on the constructed vortex structures around a single building

ABSTRACT The Fuzzy C-means (FCM) method with Fourier coefficient-based distance was firstly used to construct the vortex features and analyze the large-scale unsteady flow pattern around the building by the transient ensemble velocity magnitude and Q criterion value. The performance of the unsteady Reynolds-averaged Navier-Stokes (URANS) turbulence models, including Standardmodel, Realizable, Renormalization Group (RNG) theoryand Shear-Stress Transport (SST) models on the flow structures around a high-rise building, was examined and compared by data analysis. The transient data was analyzed to identify the root of the different flow structures. The vortex structure was used to distinguish the different turbulence simulation performance directly. The result indicated that the RNGmodel shown the best simulation results on the mean velocity and total turbulent kinetic energy fields. The RNG model could simulate the modest scales of vortices which approximates the experiment data around the building, while the SSTmodel could simulate the abundant scales of vortices which led larger turbulence viscosity coefficient. In addition, the nature pressure difference ventilation partition method was proposed and verified in simulating the nature pressure difference around a single building.

Modelling the flow within forests: the canopy-related terms in the Reynolds-averaged formulation

Abstract

Kinetic energy distribution for neutron-induced fission of neptunium isotopes

The mean total kinetic energy as a function of fission fragments, the <TKE> distribution, is presented for neutron-induced fission of Np using the scission point model. The calculated results of <TKE> for neutron-induced fission of Np are compared with the available experimental data to obtain the deformation parameters in the scission point model. The deformation parameters of fission fragments are discussed at the scission point. The calculated results are also compared with the results from other methods and with experimental data. The behavior of the <TKE> distribution is then studied for the neutron-induced fission of actinides. This indicates that the <TKE> values for neutron-induced fission of actinides with odd mass numbers are greater than for those with even mass numbers.

Sensitivity of neutron observables to the model input in simulations of 252Cf(sf)

Within the framework of $\mathtt{FREYA}$ event-by-event fission simulations, we study the sensitivity of various neutron observables to the input yield function $Y(A,Z,\mathrm{TKE})$ on which the fission event sampling is based. We first perform a statistical analysis of the available fission data in order to determine the distribution of possible yield functions $Y(A,Z,\mathrm{TKE})$ and we then construct a sample of 15 000 such yield functions. For each of these, $\mathtt{FREYA}$ is used to generate one million fission events, leading to a corresponding ensemble of fission observables, including the neutron multiplicity distribution and its factorial moments, the neutron energy spectrum, and the neutron-neutron angular correlation. This procedure allows us to study the sensitivity of those neutron observables to the uncertainty in the experimental data. Particular attention is given to the pronounced anticorrelation between the mean neutron multiplicity $\overline{\ensuremath{\nu}}$ and the mean total fragment kinetic energy $\overline{\mathrm{TKE}}$. Because the former observable is very well determined experimentally, it is possible to exploit that inherent anticorrelation to derive a significantly stricter tolerance on $\overline{\mathrm{TKE}}$. In addition, we study the sensitivity to the various $\mathtt{FREYA}$ parameters and we introduce a method for determining a $A$-dependent $x$ parameter, $x(A)$, based on the measured $A$-dependent neutron multiplicity, $\overline{\ensuremath{\nu}}(A)$.

Fully microscopic scission-point model to predict fission fragment observables

We present an upgraded version of the SPY model, called SPY2 for version 2 of the scission point yield, to estimate mainly the yields and the kinetic energy distributions of fission fragments: The theoretical framework is similar to our previous version, i.e., a statistical scission point model, but this version is based on fully microscopic nuclear ingredients describing the fragments properties at the scission point. These include the static properties of some 7000 nuclei at 120 axial quadrupole deformations, such as binding energies, proton densities, single-particle level schemes, and states densities, coherently calculated within the constrained Hartree-Fock-Bogoliubov model on the basis of the Skyrme BSk27 interaction. The use of microscopic ingredients has been extended to the proton density distribution and the nuclear states densities. Considering realistic proton densities of fragments allows us to improve the definition of the scission point as well as the prediction of the kinetic energy distribution and to link the kinetic energy to the diffuseness of the fragments' proton density. New microscopic nuclear states densities improve the general coherence of the model, in particular regarding the inclusion of the odd-even pairing effect. In this updated SPY2 version, the calculation of the fission yields and kinetic energy distributions is significantly improved and found to be in relatively good agreement with experiments, at least qualitatively. A detailed study is performed for three well known fissioning systems, namely, thermal neutron induced fission of $^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}$ and spontaneous fission of $^{252}\mathrm{Cf}$. A systematic analysis of the fission mode as well as mean fragments deformation and total kinetic energies has been performed for some 2000 fissioning nuclei with $78\ensuremath{\le}Z\ensuremath{\le}110$ lying between the proton and neutron drip lines.

Total Kinetic Energy Measurements for Spontaneous Fission of $^{255,\,256,\,258}$Rf

Spontaneous fission of 255Rf, 256Rf and 258Rf was studied at SHIP in GSI Darmstadt. The isotopes were produced in fusion–evaporation reactions 50Ti + 207,208Pb and 50Ti + 209Bi (compound nuclei 257Rf, 258Rf and 259Db, respectively) and implanted into the focal plane detector of the SHIP setup. The deficit in the measured fragments energies was evaluated as a function of implantation depth of evaporation residues in the silicon detector. This correction was applied to obtain the mean total kinetic energies of 255Rf, 256Rf and 258Rf.

Prompt neutron emission and energy balance in 235U(n,f)

Investigations of prompt fission neutron (PFN) emission are of importance in understanding the fission process in general and the sharing of excitation energy among the fission fragments in particular. Experimental activities at JRC-Geel on PFN emission in response to OECD/NEA nuclear data requests is presented in this contribution. The focus lies on on-going investigations of PFN emission from the reaction 235 U(n,f) in the region of the resolved resonances taking place at the GELINA facility. For this reaction strong fluctuations of fission fragment mass distributions and mean total kinetic energy have been observed as a function of incident neutron energy in the resonance region. In addition, fluctuations of prompt neutron multiplicities have also been observed. The goal of the present study is to verify the current knowledge of PFN multiplicity fluctuations and to study correlations with fission fragment properties. The experiment employs a scintillation detector array for neutron detection, while fission fragment properties are determined via the double kinetic energy technique using a position sensitive twin ionization chamber. Results on PFN multiplicity correlations with fission fragment properties from the present study show significant differences compared to earlier studies on this reaction, induced by thermal neutrons. Specifically, the total kinetic energy dependence of the neutron multiplicity per fission shows an inverse slope FX 1TKE/FX 2ν approximately 35% weaker than observed in earlier studies of thermal neutron induced fission on 235 U. The inverse slope is related to the energy carried away per emitted neutron and is, thereby, closely connected to the energy balance of the fission reaction. The present result should have strong impact on the modeling of both prompt neutron and prompt γ-ray emission in fission of the 236 U compound nucleus.

Asymmetry of fission fragment mass distribution for Po and Ir isotopes

Using the improved scission-point model, the mass distributions are calculated for induced fission of several Po and Ir isotopes. The calculated mass distributions and mean total kinetic energies of fission fragments are compared with the existing experimental data. The revealed coexistence of both symmetric and asymmetric modes in the $\ensuremath{\beta}$-delayed fission of $^{194,196}\mathrm{At}$ is in agreement with the experimental observations. The change of the shape of mass distribution with increasing $A$ of fissioning $^{A}\mathrm{Ir}$ nucleus from asymmetric for $^{185}\mathrm{Ir}$ to symmetric for $^{193}\mathrm{Ir}$ is found.

Investigating Prompt Fission Neutron Emission from235U(n,f) in the Resolved Resonance Region

Investigations of prompt emission in fission is of importance in understanding the fission process in general and the sharing of excitation energy among the fission fragments in particular. Experimental activities at IRMM on prompt neutron emission from fission in response to OECD/NEA nuclear data requests is presented in this contribution. Main focus lies on currently on-going investigations of prompt neutron emission from the reaction 235 U(n,f) in the region of the resolved resonances. For this reaction strong fluctuations of fission fragment mass distributions and mean total kinetic energy have been observed [Nucl. Phys. A 491, 56 (1989)] as a function of incident neutron energy in the resonance region. In addition fluctuations of prompt neutron multiplicities were also observed [Phys. Rev. C 13, 195 (1976)]. The goal of the present study is to verify the current knowledge of prompt neutron multiplicity fluctuations and to study correlations with fission fragment properties.

Cluster aspects of binary fission

With the improved scission-point model the mass distributions are calculated for induced fission of different Hg isotopes with even mass numbers A =180, 184, 188, 192, 196, 198. The calculated mass distribution and mean total kinetic energy of fission fragments are in a good agreement with the existing experimental data. The change in the shape of the mass distribution from asymmetric to more symmetric is revealed with increasing A of the fissioning AHg nucleus, and the reactions are proposed to verify this prediction experimentally.

Influence of shell effects on mass asymmetry in fission of different Hg isotopes

With the improved scission-point model mass distributions are calculated for induced fission of Hg isotopes with even mass numbers A = 174 – 198. The calculated mass distributions and mean total kinetic energy of fission fragments are in good agreement with the existing experimental data. The asymmetric mass distribution of fission fragments of 180 Hg observed in the recent experiment is explained. The change in the shape of the mass distribution with increasing A of the fissioning A Hg nucleus from symmetric for 174 Hg to asymmetric around 180 Hg, and to more symmetric for 192−198 Hg is revealed.

Mass distributions for induced fission of different Hg isotopes

With the improved scission-point model mass distributions are calculated for induced fission of different Hg isotopes with even mass numbers $A=180,$ 184, 188, 192, 196, and 198. The calculated mass distribution and mean total kinetic energy of fission fragments are in good agreement with the existing experimental data. The asymmetric mass distribution of fission fragments of ${}^{180}$Hg observed in the recent experiment is explained. The change in the shape of the mass distribution from asymmetric to more symmetric is revealed with increasing $A$ of the fissioning ${}^{A}$Hg nucleus, and reactions are proposed to verify this prediction experimentally.

Neutron induced fission of234U

The fission fragment properties of 234 U(n,f) were investigated as a function of incident neutron energy from 0.2 MeV up to 5 MeV. The fission fragment mass, angular distribution and kinetic energy were measured with a double Frisch-grid ionization chamber using both analogue and digital data acquisition techniques. The reaction 234 U(n,f) is relevant, since it involves the same compound nucleus as formed after neutron evaporation from highly excited 236 U*, the so-called second-chance fission of 235 U. Experimental data on fission fragment properties like fission fragment mass and total kinetic energy (TKE) as a function of incident neutron energy are rather scarce for this reaction. For the theoretical modelling of the reaction cross sections for Uranium isotopes this information is a crucial input parameter. In addition, 234 U is also an important isotope in the Thorium-based fuel cycle. The strong anisotropy of the angular distribution around the vibrational resonance at En = 0.77 MeV could be confirmed using the full angular range. Fluctuations in the fragment TKE have been observed in the threshold region around the strong vibrational resonance at En = 0.77 MeV. The present results are in contradiction with corresponding literature values. Changes in the mass yield around the vibrational resonance and at En = 5 MeV relative to En = 2 MeV show a different signature. The drop in mean TKE around 2.5 to 3 MeV points to pair breaking as also observed in 235,238 U(n,f). The measured two-dimensional mass yield and TKE distribution have been described in terms of fission modes. The yield of the standard 1 (S1) mode shows fluctuations in the threshold of the fission cross section due to the influence of the resonance and levels off at about 20% yield for higher incident neutron energies. The S2 mode shows the respective opposite behaviour. The mean TKE of both modes decreases with En . The decrease in mean TKE overrules the increase in S1 yield, so the mean TKE is dropping as a function of En above 2.5 MeV.

Total kinetic energy in four global eddying ocean circulation models and over 5000 current meter records

We compare the total kinetic energy (TKE) in four global eddying ocean circulation simulations with a global dataset of over 5000, quality controlled, moored current meter records. At individual mooring sites, there was considerable scatter between models and observations that was greater than estimated statistical uncertainty. Averaging over all current meter records in various depth ranges, all four models had mean TKE within a factor of two of observations above 3500 m, and within a factor of three below 3500 m. With the exception of observations between 20 and 100 m, the models tended to straddle the observations. However, individual models had clear biases. The free running (no data assimilation) model biases were largest below 2000 m. Idealized simulations revealed that the parameterized bottom boundary layer tidal currents were not likely the source of the problem, but that reducing quadratic bottom drag coefficient may improve the fit with deep observations. Data assimilation clearly improved the model-observation comparison, especially below 2000 m, despite assimilated data existing mostly above this depth and only south of 47 °N. Different diagnostics revealed different aspects of the comparison, though in general the models appeared to be in an eddying-regime with TKE that compared reasonably well with observations.

Properties of the reaction 238U [formula omitted] at the vibrational resonances

Recent fission cross-section calculations for the reaction 238U ( n , f ) , based on an extended statistical model, predict a significant change of fission fragment properties, such as the mean mass by Δ A = 1.5 and a notable increase in total kinetic energy in the region of the vibrational resonance at an incident neutron energy E n = 0.9 MeV . This model includes individual fission cross-sections by the asymmetric standard 1 (S1) and standard 2 (S2) as well as the symmetric super-long (SL) mode. In order to verify the model predictions, a dedicated experiment on 238U has been carried out to measure fission-fragment mass yield distributions for incident neutron energies from E n = 2.0 MeV down to 0.9 MeV, where the fission characteristics at the vibrational resonance at E n = 0.9 MeV were investigated for the first time. The previously reported distinct structure in the angular anisotropy around E n = 1.2 and 1.6 MeV was observed at E n = 0.9 MeV as well. The predicted large changes in fission fragment mass yield and total kinetic energy could not be confirmed. In the resonance the mean total kinetic energy is only about 0.5 MeV higher than at E n = 1.8 MeV . At the same time, a slight decrease of the mean heavy fragment mass was observed, probably indicating a slightly increased contribution of the S1 fission mode.

The Dependency on the Dissipation Tensor of Multi-modal Nuclear Fission

In the study of the fission of actinide nuclei at low excitation energies including the spontaneous fission, it was found that the fragment mass distribution and the total kinetic energy (TKE) distribution consist of more than one component, in contrast to the simple single peak structure that is found in the fission at high excitation energies. 1– 6 This phenomenon is attributed to the existence of more than one fission path and is called the multi-modal fission. The mass and TKE distributions depend sensitively on the excitation energy and the position of the peaks of the mass distribution suggests the influence of the closed shell structure of the fragments. Therefore, it is supposed that the microscopic energy plays an important role for the manifestation of this phenomenon. It is a great challenge for us to understand this phenomenon in terms of nuclear many-body dynamics. Several authors studied the potential energy surface (PES) including the microscopic energy in a multi-dimensional parameter space that describes various nuclear shapes; one can deduce the possible fission paths by studying the location of the saddle points and the fission valleys in multi-dimensional parameter space. 7 With this method, they could explain the general trend of the position of the peaks of the mass distribution. The dynamical point of view is necessary to progress the study of the fission mode. We have applied the Langevin approach to the study of the fission modes in uranium nuclei and in fermium nuclei. 8–10 We studied the mass and TKE distributions and demonstrated that we can decompose the fission events into several components by tracing the Langevin trajectories. We also studied the isotope dependence and the excitation energy dependence of the fission mode. 8–10 In the previous studies, we adopted the wall-and-window type one-body friction as the dissipation mechanism of the nuclear fission dynamics. The validity of this dissipation mechanism has been demonstrated by one of the authors (T.W.) who studied the dissipation tensor dependence of the pre-scission neutron multiplicity and the mean TKE. 11–14 From the comparison of the results of the dynamical calculation with experimental data, they excluded the possibility of the two-body type dissipation to be the dominant mechanism by showing that it cannot reproduce the pre-scission neutron data and the TKE data simultaneously. On the other hand, they showed that the wall-and-window type one-body friction can reproduce both data reasonably well and concluded that it is a reasonable model for the dissipation mechanism of nuclear fission. There are other models that are of one-body nature, e.g. surface-plus-window formula, modified wall-and-window formula and chaos weighted wall formula. 15–17 Though there were no free parameters in the original derivation of the one-body friction, 18, 19 the strength has been modified frequently in order to reproduce some experimental data. For example, in the study of the light particle evaporation and the mass distribution, Schmitt et al. used the strength as a free parameter. 17 The modification itself should be acceptable when we take account of the simplicity of the model; it is a macroscopic model without any microscopic effect and it has no dependence on the temperature. However, when one modifies the strength of the nuclear dissipation just to reproduce only one physical quantity, it might be inappropriate to conclude that the deduced strength has definite physical meanings. It may reflect the other effects completely different from the dissipation, like the insufficiency of the model space. It is very important to compare many (at least more than one) physical quantities at the same time. Among the physical quantities that are measured in nuclear fission, the TKE and mass distributions are well investigated experimentally in many cases. In this study, we use these quantities to discuss the dissipation dependence of the fission modes. It is shown that the TKE distribution is, as was expected, directly connected to the strength of the dissipation and we can put some constraints on the strength of the dissipation. Furthermore, it is shown that the mass distribution changes rather drastically when one uses different models for the dissipation mechanism. These results demonstrate the importance and the usefulness of the dynamical approach to the study of the fission mode. Section 2 gives a concise description of our framework. Results are shown in Sec. 3 concerning the fission of 264 Fm nucleus at Ex = 20 MeV. Summary is given in Sec. 4. 2. Methods

Fission of 239Pu with resonance neutrons

A measurement of fission fragment energy and mass distributions in the 239Pu(n, f) resolved resonance region has been performed applying the twin Frisch-gridded ionization chamber technique. An improved pile-up rejection system has been developed to cope with the strong α background.The results for the mass and mean total kinetic energy (TKE) distributions for resolved resonances do not show any strong ‘pattern’ of fluctuations, unlike it was the case for 235U(n, f) in the same neutron energy region. This can be explained in the frame of existing theoretical models, according to which the only possible low-energy spin states available (Jπ=0+, 1+) belong to two well separated (~1.25 MeV) transition state bands with given fission fragment properties. An anti-correlation between TKE and ⊽p was found to be not significant. The obtained small spin dependence of TKE of about 70 keV is in agreement with literature values. A slight correlation was found between TKE versus 1/Γf. But also this was considered not to be significant.