Water Tank Simulation Research Articles

Robust identification for input non‐uniformly sampled Wiener model by the expectation‐maximisation algorithm

The problems of inconsistent data sampling frequency, outliers, and coloured noise often exist in system identification, resulting in unsatisfactory identification results. In this study, a novel identification method of input non-uniform sampling Wiener model with a coloured heavy-tailed noise is proposed. The lifted Wiener model with coloured noise and outlier value disturbed is constructed. Under the expectation-maximisation (EM) algorithm framework, the student's t-distribution is introduced to model the contaminated output data. The variance scale is regarded as a unique latent variable, and the iterative parameter estimation formula of the non-uniform sampling Wiener model is derived. The idea of the auxiliary model is applied to acquire the unmeasured middle variable and handle the coloured noise variable in the non-uniformly sampled Wiener model. The Differential Evolution algorithm is used to calculate the intractable part of the Q-function. The convergence analysis of the proposed algorithm is given. Two numerical examples and one water tank simulation are employed to indicate the effectiveness of the proposed method.

Development of a Hot Water Tank Simulation Program with Improved Prediction of Thermal Stratification in the Tank

A simulation programSpiralSolwas developed in previous investigations to calculate thermal performance of a solar domestic hot water (SDHW) system with a hot water tank with a built-in heat exchanger spiral[1]. The simulation program is improved in the paper in term of prediction of thermal stratification in the tank. The transient fluid flow and heat transfer in the hot water tank during cooling caused by standby heat loss are investigated by validated computational fluid dynamics (CFD) calculations. Detailed CFD investigations are carried out to determine the influence of thickness and material property of the tank wall on thermal stratification in the tank. It is elucidated how thermal stratification in the tank is influenced by the natural convection and how the heat loss from the tank sides will be distributed at different levels of the tank at different thermal conditions. The existing equation of the heat loss removal factor used in SpiralSol is evaluated by means of the detailed CFD calculations. A generalized new equation for the heat loss removal factor is obtained by regression. The new equation calculates the heat loss removal factor for a given temperature gradient in the tank,taking into account the influences of tank volume, height to diameter ratio, tank insulation, thickness and material property of the tankand initial thermal conditions of the tank. The equation is validated for a tank volume between 150 l and 500 l, a tank height to tank diameter ratio of 1-5,a tank wall thickness of 1.5 mm to 3 mm for a stainless steel tank and a tank wall thickness of between 3 mm to 5 mm for a normal steel tank. Accuracy and reliability of the SpiralSol program with the improved prediction of heat loss removal factor will be examined in future investigations.

Dose response of selected solid state detectors in applied homogeneous transverse and longitudinal magnetic fields.

MR-Linac devices under development worldwide will require standard calibration, commissioning, and quality assurance. Solid state radiation detectors are often used for dose profiles and percent depth dose measurements. The dose response of selected solid state detectors is therefore evaluated in varying transverse and longitudinal magnetic fields for this purpose. The Monte Carlo code PENELOPE was used to model irradiation of a PTW 60003 diamond detector and IBA PFD diode detector in the presence of a magnetic field. The field itself was varied in strength, and oriented both transversely and longitudinally with respect to the incident photon beam. The long axis of the detectors was oriented either parallel or perpendicular to the photon beam. The dose to the active volume of each detector in air was scored, and its ratio to dose with zero magnetic field strength was determined as the "dose response" in magnetic field. Measurements at low fields for both detectors in transverse magnetic fields were taken to evaluate the accuracy of the simulations. Additional simulations were performed in a water phantom to obtain few representative points for beam profile and percent depth dose measurements. Simulations show significant dose response as a function of magnetic field in transverse field geometries. This response can be near 20% at 1.5 T, and it is highly dependent on the detectors' relative orientation to the magnetic field, the energy of the photon beam, and detector composition. Measurements at low transverse magnetic fields verify the simulations for both detectors in their relative orientations to radiation beam. Longitudinal magnetic fields, in contrast, show little dose response, rising slowly with magnetic field, and reaching 0.5%-1% at 1.5 T regardless of detector orientation. Water tank and in air simulation results were the same within simulation uncertainty where lateral electronic equilibrium is present and expectedly differed at the beam edge in transverse field orientations only. Due to the difference in design, the two detectors behaved differently. When transverse magnetic fields are present, great care must be taken when using diamond or diode detectors. Dose response varies with relative detector orientation, magnetic field strength, and between detectors. This response can be considerable (∼20% for both detectors). Both detectors in longitudinal fields exhibit little to no dose response as a function of magnetic field. Water tank simulations seem to suggest that the diode detector is better suited to general beam commissioning, and each detector must be investigated separately.

SU‐E‐J‐51: Dose Response of Common Solid State Detectors in Homogeneous Transverse and Longitudinal Magnetic Fields

Purpose:Solid state radiation detectors are often used for dose profiles and percent depth dose measurements. The dose response of selected solid state detectors is evaluated in varying transverse and longitudinal magnetic fields for eventual use in MR‐Linac devices.Methods:A PTW 60003 and IBA PFD detector were modeled in the Monte Carlo code PENELOPE, incorporating a magnetic field which was varied in strength and oriented both transversely and longitudinally with respect to the incident photon beam. The detectors' long axis was in turn oriented either parallel or perpendicular to the photon beam. Dose to the active volume of each detector was scored, and its ratio to dose with zero magnetic field strength (dose response) was determined. Accuracy of the simulations was evaluated by measurements using both chambers taken at low field with a small electromagnet. Simulations were also performed in a water phantom to compare to the in air results.Results:Significant dose response was found in transverse field geometries, nearing 20% at 1.5T. The response is highly dependent on relative orientations to the magnetic field and photon beam, and on detector composition. Low field measurements confirm these results. In the presence of longitudinal magnetic fields, the detectors exhibit little dose response, reaching 0.5–1% at 1.5T regardless of detector orientation. Water tank simulations compared well to the in air simulations when not at the beam periphery, where in transverse magnetic fields only, the water tank simulations differed from the in air results.Conclusion:Transverse magnetic fields can cause large deviations in dose response, and are highly position orientation dependent. Comparatively, longitudinal magnetic fields exhibit little to no dose response in each detector as a function of magnetic field strength. Water tank simulations show longitudinal fields are generally easier to work with, but each detector must be evaluated separately.

A review of water tank modeling of the convective atmospheric boundary layer

Several studies have been selected to review water tank modeling of the atmospheric boundary layer (ABL) and demonstrate that water tank simulations have been a key factor in developing scientific knowledge and promoting further research of the ABL. The areas discussed include similarity analysis of modeling, basic dispersion processes, characteristics of the convective boundary layer (CBL), parameterizations of the entrainment zone (EZ), the characteristics of turbulence in the CBL, and the influence of plain-valley terrain and other inhomogeneities on atmospheric boundary layer structure. Technical values of some parameters are noted and potential improvements in water tank modeling based on continuing advances in new technology are also discussed. The limitations of water tank models for characteristics of the CBL and possible solutions to their limitations are briefly discussed.

Poster — Wed Eve—39: Using DOSRZnrc to Study the SFD Si‐Diode for Small Field Relative Dosimetry

Purpose: The goal of this work was to study the SFD Si‐diode (IBA Dosimetry, previously Scanditronix/Wellhofer) for small field dosimetry. Methods and Materials: The EGSnrc user code DOSRZnrc was used to construct a geometrically accurate model of the detector. The active volume was modelled as pure silicon () and 6HSiC (). For field sizes between 0.5 and 5.0 cm, water tank simulations were run and validated experimentally for isocentric detector placement at depths of 1.5, 5.0 and 10.0 cm. Detector response was investigated and correction factors calculated according to Capote et al (Med. Phys. 31 2416–22) and Alfonso et al (Med. Phys. 35 5179–86). Results: The SFDSi simulated ROFs were generally higher than the experimental values yet still within the statistical uncertainty of 1.3 to 1.5%. However, for the two smallest field sizes the data was high by as much as 3.0%. The simulated ROFs revealed no such disagreement with experiment and were statistically equivalent to the measured data. Conclusion: The active volume of the SFD detector is most likely a substrate very similar to 6HSiC and should not be modelled as pure silicon, modelling the detector as a “chip in water” may be considered a reasonable approximation but does hinge on the correct choice of material for the active volume and it appears no correction factor is required for small field relative output factors measured with the SFD Si‐diode detector, however a reduction in the statistical uncertainty would be desirable.

Numerical study of dispersion in the convective boundary layer

A simple one-dimensional turbulence model developed by Sun and Chang (1986a, J. clim. appl. Met. 25,1445–1453) is modified by including γ c (a reference potential temperature gradient) in the diffusion term of the heat equation to study the moist convective boundary layer. The results show that the stratification becomes neutral to slightly unstable in the middle and lower mixed layer but slightly stable in the upper mixed layer as observed, while the wind, moisture and eddy fluxes are very similar to those discussed by Sun and Chang. The results from the one-dimensional model are then applied to a two-dimensional dispersion model. The new concentrations are better than the previous results (Sun, 1986, Atmospheric Environment 20, 1877–1886). The ground level concentration, the mean height of concentration, and vertical speed simulated from this higher order closure model are also in good agreement with field experiments, water tank simulations and results obtained from the statistical models.

Sensitivity analysis of a Monte Carlo atmospheric diffusion model

A Monte Carlo model simulating atmospheric transport and diffusion in the PBL is presented. In a previous study, it was shown that it works well in homogeneous turbulence and fits well the Willis and Deardorff water tank simulations in convective nonhomogeneous conditions. In the present paper a sensitivity analysis aimed at estimating the importance and effectiveness of the model parameters is performed and discussed. Our model makes use of Hanna's scheme for the vertical structure of the turbulent parameters, and of an empirical parametrization of updrafts and downdrafts in convective unstable conditions. Emitting the particles either from a point source or uniformly distributed along the vertical we found that the model avoids the particle accumulation at the top and bottom of the PBL and recovers the Eulerian turbulent statistics. This demonstrates that our numerical scheme is consistent with the physical constraints,i.e. mass and energy are preserved and an initial uniform distribution remains so. Finally it is shown that considering the contribution of the cross-correlation term\(\overline {u'w'} \) does not improve significantly the model performances.