Calculation Of Velocity Field Research Articles

CME Velocity Field Calculation Model Based on an Unsupervised Transformer Optical Flow Network

The optical flow algorithm (OF) is one the main methods for calculating image velocity field and has many applications in space weather. Most OF calculations are applied to the motion of labeled rigid objects and are not suitable for velocity detection of high-energy particles, such as in a coronal mass ejection (CME). Fluctuations in exposure time and the influence of space weather will lead to inconsistent brightness of the same feature point at different times. To address this problem, we propose an unsupervised multiscale optical flow network based on Vision Transformer, named UTFlowNet. The network comprises a multiscale feature extraction module and a coarse-to-fine global optical flow calculation module. The movement of high-energy particles emitted during a CME eruption follows certain physical rules. Therefore, we apply fluid motion–based loss functions to analyze the motion of high-energy particles more effectively, addressing the problem of CME motion field extraction. Our method can be applied to the real-time automatic extraction of a CME’s velocity field and performs well with inconsistent brightness, large-scale motion, and strong CME noise. Additionally, we can estimate subpixel level fine-grained velocity. Our model may be affected by overfitting during cross–data set inference, so we encourage performing a small amount of transfer learning on new data sets to mitigate this issue. In order to verify the accuracy of our method, we conducted experiments and verification on the Solar and Heliospheric Observatory LASCO C2 data and the High Altitude Observatory MLSO data. We constructed a large-scale displacement simulation data set based on LASCO C2 data and tested on it, achieving the best results.

A Bayesian Approach To Locally Varying Regularization In Optical Flow Velocimetry

A recent method for determining accurate, dense velocity fields from a pair of particle images is to solve the optical flow problem, but the ill-posed inverse problem of optical flow velocimetry (OFV) generally entails minimizing a weighted sum of two terms--fidelity and regularization--and the weights in the sum are parameters that require manual tuning based on the flow properties and particle images. This tuning of the weighting parameters makes the experimental applicability of the method much more challenging as the calculated velocity field has demonstrated sensitivity to the value of the weights. This work proposes a hierarchical model for the weighting parameters in the framework of maximum a posteriori (MAP)-based Bayesian optimization approaches. The resulting method is tested on three different synthetic datasets and on experimental particle images. The method is found to be capable of self-adjusting the local weights of the optimization process in real-time while simultaneously determining the velocity field, leading to a more accurate estimate of the velocity field without requiring any dataset-specific manual tuning of parameters.

Computational fluid dynamics model-based design of continuous forced convection freezing processes for human induced pluripotent stem cells considering supercooling of extracellular solutions

This work presents a computational fluid dynamics (CFD) model-based process design of forced convection continuous freezing for human induced pluripotent stem (hiPS) cells considering supercooling of extracellular solutions. The overall model consists of a CFD model for velocity field and heat transfer calculations including the effect of the supercooling, and a cell layer model for cell survival rate calculations. Experimental temperature profiles were obtained using a forced convection-based batch freezer, and the validation of the heat transfer and solidification models was performed. The experiments were carried out by applying a 1.0 K min–1 cooling rate with an inlet velocity of 2.0 m s–1. The model was applied to three different freezer sizes with shelves containing 10, 20 and 30 rows. The applied coolant inlet velocities ranged from 0.50 m s–1 to 4.0 m s–1. It was found that the application of an inlet velocity of 3.0 m s−1 yielded an average cell survival rate of 0.934 with low survival rate heterogeneity in the freezers. This way, the freezing process for hiPS cells could be scaled to up to 170-fold compared to currently used equipment for hiPS cell freezing.

Investigation on algorithms for simulating large deformation and impact loads

It is a challenge to simulate the hydrodynamic problems covering the large deformation of the free surface arising in severe circumstances with intense flow. This paper investigates algorithms based on the moving particle semi-implicit method for simulating large deformation and impact loads. The algorithm discretizes the fluid domain into a series of particles, each representing a part of the fluid. The pressure field calculation is implicit, and the velocity field calculation is explicit. Three models, including the gradient model, source term, and free-surface detection, have been improved and compared to determine which improvement is the best to enhance the accuracy and stability. The enhanced pressure gradient guarantees that momentum conservation can be satisfied. Particle density and velocity divergence are incompressible conditions combined in the mixed source term approach. The arc approach is used in the free-surface judging process. The results show that the combination of three models is the most effective in exploring the problems of hydrodynamic pressure and dam break. The issue of liquid sloshing including roll and sway investigates the effect of the initial distance and time step. It is found that the simulation accuracy of impact pressure can be increased as the initial distance and the time step decrease. Finally, the free surface breaking and liquid splashing phenomena are easily observed, and the method can accurately simulate the massive deformation of the free surface. These findings are helpful for hazard assessments of the various fluid mechanics-related problems.

Пульсации течения жидкого металла, генерируемые переменным магнитным полем

This paper studies numerically a vortex flow of liquid metal driven by an electromagnetic force, which is generated by the interaction of the alternating magnetic field of a short solenoid with the induced electrical current. A short solenoid is placed coaxially to a cylindrical cell at half of its height. The mathematical model used to describe the process is based on the equations of magnetic hydrodynamics in the induction-free approximation. Calculations, which are carried out by the control volume method using the ANSYS Fluent package, show that the average flow has the form of two toroidal vortices. The calculated velocity fields are indicative of the oscillatory behavior of vortices, accompanied by a change in their sizes. In the examined range of the force parameter, the predominant flow pattern is the single-mode oscillatory flow. The dependences of characteristic frequency and Reynolds number on the force parameter, are obtained using spectral analysis. It has been found that the oscillation period is close to the period of rotation of a large-scale vortex. It has been established that the oscillations are of quasi-periodic character, and a distinct oscillation frequency is observed only in the flow region near the solenoid. The effect of velocity fluctuations is strong and can be detected in laboratory conditions when using gallium eutectic. Such experiment is planned for the near future. The flow rate of gallium eutectic will be measured by an ultrasonic Doppler anemometer. The results of numerical modeling and their verifications can be useful in determining the ways of reducing the intensity of vortex flows during the electromagnetic separation of impurities, which is based on the induction mechanism responsible for the generation of electromagnetic force that displaces particles. The data on the oscillation frequency of the unsteady flow can be used in the development of a non-contact technique for estimating the average electrical conductivity of a two-phase medium, such as a liquid metal with undesirable impurities.

A Novel Method for Analyzing the Spatiotemporal Characteristics of GNSS Time Series: A Case Study in Sichuan Province, China

The motion of a continuously operating reference station is usually dominated by the long-term crustal motions of the tectonic block on which the station is located. Monitoring changes in the coordinates of reference stations located at tectonic plate boundaries allows for the calculation of velocity fields that reflect the spatial and temporal characteristics of the region. This study analyzes the spatiotemporal relationships of regional reference frame points with GNSS data from 25 reference stations in Sichuan, China, from 2015 to 2021. The common mode errors are extracted and eliminated by principal component analysis. A time series function model is developed for the reference stations and their constituent baselines for calculating the velocity field. Subsequently, the spatiotemporal characteristics of the regional reference frame in Sichuan is analyzed by a stochastic model. The results show that the influences of the common mode error on the horizontal and vertical directions of the reference stations is 2.5 mm and 4.3 mm, respectively. Generally, the horizontal motion of the reference stations in the Sichuan region tends to be in the southeast direction and the vertical motion trend is mainly uplifting. The east–west and vertical components of the baseline tend to be shortened, and the random influence among the reference stations is larger in the north–south and east–west directions—0.39 mm and 0.54 mm, respectively. Polynomial functions are more appropriate for constructing the fitted random influence covariance model.

Study of the blood flow structure in personalized models of graft branch from the femoral artery

The paper presents the methodology and results of calculating the pulsating flow of blood-mimicking fluid in three personalized models of proximal anastomosis of the femo-ral artery after femoral popliteal bypass surgery performed using synthetic grafts. Per-sonalized models were built based on computed tomography data and ultrasound meas-urements of blood flow velocity in the common femoral artery and in the graft. The char-acteristics of the pulsating flow of blood-mimicking fluid were calculated by numerically solving the three-dimensional unsteady Navier-Stokes equations. Comparison of the calculated velocity field obtained for one of the personalized models with clinical meas-urement data using ultrasonic high-speed vector imaging (applying the V Flow technol-ogy implemented in the Mindray scanner) showed satisfactory agreement of the results. A comparative analysis of the flow structure in two personalized models built for the sec-ond patient one and seven months after surgery is given. It was established that the nar-rowing of the flow sections of the vascular bed, detected after seven months, due to the growth of neointima in the common femoral artery (immediately before the anastomosis) and in the initial section of the graft, led to a significant increase in gradients of the ve-locity field and the time-averaged wall shear stress (TAWSS) in the area of the anastomo-sis; at the same time, the value of the oscillatory shear index (OSI) on the wall throughout the entire anastomosis area decreased. It was also revealed that at a distance of several calibers from the anastomosis, a single-vortex, weakly swirling flow is formed in the graft, the direction of swirl in which is determined by the individual geometry of the anastomo-sis area.

Research into CUP-VISAR velocity reconstruction based on weighted DRUNet and total variation joint optimization.

This Letter proposes a CUP-VISAR data reconstruction algorithm for laser-driven inertial confinement fusion (ICF) research. The algorithm combines weighted deep residual U-Net (DRUNet) and joint optimization with total variation (TV) to improve shockwave velocity fringe image reconstruction. The simulation results demonstrate that the proposed algorithm outperforms the ADMM-TV and enhanced 3D total variation (E-3DTV) algorithms, enhancing the quality of the reconstructed images and thereby improving the accuracy of velocity field calculations. Furthermore, it addresses the challenges of the high compression ratio caused by the diagnostic requirements of the larger number of sampling frames in the CUP-VISAR system and the issues of aliasing within a large encoding aperture. The proposed algorithm demonstrates good robustness to noise, ensuring reliable reconstruction even under Gaussian noise with a relative intensity of 0.05. This algorithm contributes to ICF diagnostics in complex environmental conditions and has theoretical significance and practical application value for achieving controlled thermonuclear fusion.

Lagrangian Chaotic Mixing in a Nonlinear Model of Resistive Drift-wave Turbulence in Tokamak Plasmas

In fusion plasma, numerical simulations are commonly employed to investigate the confinement properties of plasma in the bulk region of tokamaks. The modified Hasegawa-Wakatani (MHW) equations are used to model the behavior of the plasma, which enables us to understand the radial transport in two-dimensional numerical simulations of electrostatic resistive drift-wave turbulence. By utilizing the MHW equations, we have gained insights into the low-to-high confinement (L-H) transitions that occur spontaneously in the plasma when it moves from a low confinement stage, characterized by turbulent flow, to a turbulence-suppressed regime known as zonal flow. To investigate these transitions, we vary the value of a control parameter \(\alpha\), which is related to adiabaticity, in numerical simulations, and observe the transition between the two regimes. This simplified model of L-H transitions can provide valuable information for tokamaks. To identify the Lagrangian coherent structures (LCS) and to better characterize the chaotic mixing during the L-H transition, we computed the finite-time Lyapunov exponent (FTLE) of the calculated velocity field derived from the electrostatic potential. We further compared the statistics of the chaotic mixing of the two regimes. The results of our study offer insights into the turbulent transport processes in magnetic confinement fusion plasmas.

Mathematical Model of the Flow in a Nanofiber/Microfiber Mixed Aerosol Filter

A new mathematical model of an aerosol fibrous filter, composed of a variety of nano- and microfibers, is developed. The combination of nano- and microfibers in a mixed-type filter provides a higher overall quality factor compared with filters with monodisperse fibers. In this paper, we propose a mathematical model of the flow of an incompressible fluid in a porous region consisting of a set of cylinders of various diameters in the range of nano- and micrometers to describe a mixed-type aerosol filter. The flow domain is a rectangular periodic cell with one microfiber and many nanofibers. The motion of the carrier medium is described by the boundary value problem in Stokes flow approximation with the no-slip boundary condition for microfibers and the slip condition for nanofibers. The boundary element method taking into account the slip and non-slip conditions is developed. The calculated velocity field, streamlines, vorticity distribution, and drag of separate fibers and the entire periodic cell are presented. Numerical results for the drag force of the porous medium of a mixed-type filter for the various ratios of mass proportion of nano- and microfibers, porosity, and filtration velocity are presented. The obtained results are compared with the analytical formulas based on the approximate theory of filtration of bimodal filters and with known experimental data. It is shown that with an increase in the mass fraction of nanofibers, the total drag force of the cell increases, while the relative contribution of nanofibers to the total drag force tends toward the value that is less than unity. An approximate analytical formula for the drag coefficient of a mixed aerosol filter is derived. The developed flow model and analytical formulas allow for estimating the aerodynamic drag of a mixed filter composed by nano- and microfibers.

A MATLAB toolbox for computation of velocity and strain rate field from GNSS coordinate time series

We propose a MATLAB toolbox for the computation of the strain rate field from the coordinate time series of some continuous GNSS stations. It consists of several functions, also compatible with GNU Octave, implementing the following steps: (i) time series download from a data repository (e.g., the Nevada Geodetic Laboratory database); (ii) calculation of velocities of the selected stations by means of the Maximum Likelihood Estimation (MLE) method implemented in the external package Hector, including modeling of offsets, outliers, noise and periodic components; (iii) (optional) filtering of Common Mode Errors; (iv) calculation of the strain rate field with the modified least squares method, in which a scale factor can be introduced to define the locality of the deformation analysis and, besides uncertainty estimation, a geometric evaluation of the significance of the results is provided; (v) visualization of the results for immediate use and easy interpretation for scientific purposes. The toolbox is divided into two components: the first one, named StaVel, performs the steps (i)-(iii) and the second component, GridStrain, performs the steps (iv) and (v). The potential of the toolbox is demonstrated on a real dataset. Time series from several continuous GNSS stations in South-Eastern Sicily (Southern Italy) are processed by means of StaVel and GridStrain in order to provide the strain rate field.

Tightly coupled hyperbolic treatment of buoyant two-phase flow and transport in porous media

Buoyant incompressible multiphase flow and transport in porous media typically is simulated by coupling an elliptic flow equation with a hyperbolic transport description. The tight coupling between flow and transport either requires a fully implicit solution algorithm or very small time steps, if solved sequentially. In any case, however, a large linear system has to be solved each time step.Here a new solution approach is devised, which relies on solving a coupled hyperbolic system of conservation laws with an explicit finite volume method. Consequently, only local operations have to be performed, which is a great advantage in case of massive parallel simulations and if GPUs are employed.The devised method is based on the isothermal Euler equations with momentum source terms accounting for resistance due to the porous medium and buoyancy. In this system the pressure is proportional to the density and in case of very small Mach numbers and relative density variation, the computed velocity field is divergence free and converges towards the mean total volumetric flow in the porous domain. To account for saturation transport, the system was augmented by an additional hyperbolic equation. In order to obtain the numerical fluxes, a characteristic based approximative Riemann solver was developed and 2nd order accuracy in space and time is achieved by piecewise linear reconstruction.Two-phase flow test cases with buoyant plumes and a lock exchange problem demonstrate that the devised hyperbolic approach recovers the correct incompressible solutions. Numerical experiments also demonstrate that the method is accurate and efficient.Thus the devised method is very promising, and conceptually it also can be applied for flow and transport in heterogeneous media; but it remains to be investigated how well it performs for such cases.

Online measurement of granular velocity of rotary drums by a fast PIV deep network FPN-FlowNet

The measurement of velocity field of granules with respect to time in one rotary drum is of great significance in the study of mixing process. However, the existing measurement methods are not suitable to be used in online processing in real applications for the following reasons: limited spatial resolution, brightness sensitivity and long time-consumption. In this work, a hybrid framework containing an unsupervised deep network FPN-FlowNet and one particle-center detection model is proposed. FPN-FlowNet is built by introducing the FPN model for 4-level environment-robust feature extraction and weighted fusion for dense velocity field calculation; Particle center detection model is designed based on graph-cut and another well-trained deep model VGG16-LUnet to accurately obtain the particle positions. Extensive experiments including the actual granular flows in rotary drum along with the corresponding software simulation results demonstrate that our approach achieves competitive performance over the state-of-the-art method and satisfactory speed for online processing.

EVALUATION OF THE EFFICIENCY OF A MULTI-CHANNEL DUST COLLECTOR USING NUMERICAL SIMULATION

Multi-channel dust collectors are based on previously known designs of vortex dryers for bulk products. However, their use for air dust removal is promising. In earlier studies of these devices using numerical simulations, the dust capture coefficient was not evaluated, although it is the most important indicator of their efficiency. In this article, the numerical simulation of MCDC is carried out. The first stage of modeling is the calculation of the gas flow velocity and pressure fields in the device under study. At the second stage, a large number of trajectories of dust particles of different diameters were calculated with subsequent statistical processing. Dust capture coefficients and hydraulic loss coefficients were calculated. It is shown that for the reliability of the results of the numerical experiment, the number of dust particles should be at least 2000. To determine the effect of the outer half-shells on the efficiency of the device, these half-shells were discarded, as a result of which the multi-channel dust collector turned into a cyclone. The comparison of characteristics showed that, other things being equal, the devices being investigated have some advantages over cyclones in capturing of small fractions of dust. The hypothesis that the capture of particles in curved channels occurs mainly due to particle collisions with the front edges of metal half-shells was put forward and refuted. The results of numerical modeling do not support the hypothesis that some dust particles rotate along closed trajectories and form a filter for other particles. The formulas of other authors, which do not take into account the parameters of dust particles, are recognized as unworkable. The speculations of some authors about the influence of the Ranque-Hilsch vortex effect on the process of dust capture cannot be taken into account due to the low subsonic air velocities under the operating conditions of the apparatus.

Quantifying Equiaxed vs Epitaxial Solidification in Laser Melting of CMSX-4 Single Crystal Superalloy

The competition between epitaxial vs. equiaxed solidification has been investigated in CMSX-4 single crystal superalloy during laser melting as practiced in additive manufacturing. Single-track laser scans were performed on a powder-free surface of directionally solidified CMSX-4 alloy with several combinations of laser power and scanning velocity. Electron backscattered diffraction (EBSD) mapping facilitated identification of new orientations, i.e., “stray grains” that nucleated within the fusion zone along with their area fraction and spatial distribution. Using high-fidelity computational fluid dynamics simulations, both the temperature and fluid velocity fields within the melt pool were estimated. This information was combined with a nucleation model to determine locations where nucleation has the highest probability to occur in melt pools. In conformance with general experience in metals additive manufacturing, the as-solidified microstructure of the laser-melted tracks is dominated by epitaxial grain growth; nevertheless, stray grains were evident in elongated melt pools. It was found that, though a higher laser scanning velocity and lower power are generally helpful in the reduction of stray grains, the combination of a stable keyhole and minimal fluid velocity further mitigates stray grains in laser single tracks.

Commercial toilets emit energetic and rapidly spreading aerosol plumes.

Aerosols can transmit infectious diseases including SARS-CoV-2, influenza and norovirus. Flushed toilets emit aerosols that spread pathogens contained in feces, but little is known about the spatiotemporal evolution of these plumes or the velocity fields that transport them. Using laser light to illuminate ejected aerosols we quantify the kinematics of plumes emanating from a commercial flushometer-type toilet, and use the motion of aerosol particles to compute velocity fields of the associated flow. The toilet flush produces a strong chaotic jet with velocities exceeding 2 m/s; this jet transports aerosols to heights reaching 1.5 m within 8 seconds of initiating a flush. Quantifying toilet plumes and associated flow velocities provides a foundation for future design strategies to mitigate plume formation or to disinfect pathogens within it.

The Experimental and Simulation Results of LIVE-J2 Test—Investigation on Heat Transfer in a Solid–Liquid Mixture Pool

Since the reactor pressure vessel (RPV) lower head failure determines the subsequent ex-vessel accident progression, it is a key issue to understanding the accident progression of the Fukushima Daiichi Nuclear Power Station (1F). The RPV failure is largely affected by thermal loads on the vessel wall, and thus, it is inevitable that the thermal behavior of the molten metallic pool with the co-existence of solid oxide fuel debris must be understood. In past decades, numerous experiments have been conducted to investigate homogeneous molten pool behavior. Few experiments, however, address the melting and heat transfer process of the debris bed consisting of materials with different melting temperatures. The LIVE-J2 experiment aims to provide experimental data on a solid-liquid mixture pool in a simulated RPV lower head under various conditions. The experiment was performed in the LIVE-3D facility at the Karlsruhe Institute of Technology. The LIVE-J2 experiment started from the end state of the previous LIVE-J1 experiment where a eutectic binary mixture of KNO3-NaNO3 (nitrate) was solidified and filled the gap of the ceramic beads inside the LIVE-vessel. The information obtained in the LIVE-J2 experiment includes transient and steady-state melting temperature and vessel wall temperature distributions. The extensive measurements of the melting temperature indicate the heat transfer regimes in a solid-liquid mixture pool. The test results showed that the conductive heat transfer is dominant during steady state along the vessel wall boundary and that convective heat transfer takes place inside the mixture pool. After the addition of liquid nitrate on top of the mixture pool, different behavior was observed in each layer. In the upper pure-liquid nitrate layer, convective heat transfer was well developed, resulting in a homogeneous temperature, while within the lower solid/liquid debris mixture zone a large temperature gradient was observed, suggesting that conductive heat transfer was dominant. Besides the experimental performance, the test case was numerically simulated using Ansys Fluent. The simulation results generally agree with the measured experimental data. The flow regime and transient melt evolution were able to be estimated by the calculated velocity field and the crust thickness, respectively.

Particle Image Velocimetry to Evaluate Pulse Wave Velocity in Aorta Phantom with the lnD-U Method.

Pulse wave velocity (PWV) is an indicator of arterial stiffness used in the prediction of cardiovascular disease such as atherosclerosis. Non-invasive methods performed with ultrasound probes allow one to compute PWV and aortic stiffness through the measurement of the aortic diameter (D) and blood flow velocity (U) with the lnD-U method. This technique based on in vivo acquisitions lacks validation since the aortic elasticity modulus cannot be verified with mechanical strength tests. In the present study, an alternative validation is carried out on an aorta phantom hosted in an aortic flow simulator which mimics pulsatile inflow conditions. This in vitro setup included a Particle Image Velocimetry device to visualize flow in a 2D longitudinal section of the phantom, compute velocity fields (U), and track wall displacements in the aorta phantom to measure the apparent diameter (AD) variations throughout cycles. The lnD-U method was then applied to evaluate PWV (5.79 ± 0.33m/s) and calculate the Young's modulus of the aorta phantom (0.56 ± 0.12MPa). This last value was compared to the elasticity modulus (0.53 ± 0.07MPa) evaluated with tensile strength tests on samples cut from the silicone phantom. The PIV technique PWV measurement showed good agreement with the direct tensile test method with a 5.6% difference in Young's modulus. Considering the uncertainties from the two methods, the measured elasticities are consistent and close to a 50-60years old male aortic behavior. The choice of silicone for the phantom material is a relevant and promising option to mimic the human aorta on in vitro systems.

Application of phase field model coupled with convective effects in binary alloy directional solidification and roll casting processes

Based on the Kim-Kim-Suzuki (KKS) phase field model coupled with the thermodynamic parameters, the transformation process from columnar dendrites to equiaxed crystals during directional solidification of aluminium alloy was simulated, and the effects of phase field parameters on the growth morphology and dendrite segregation were discussed. Furthermore, considering the effect of the microcosmic flow field, the convection influence gradient term is introduced into KKS formula near the solid-liquid interface, and the phase field model considering flow field was applied to the inherent convective environment of the actual roll casting process, also the multiple dendrites growth behavior of magnesium alloy under the action of microscopic convection was further explored. When coupling calculation of microscopic velocity field and pressure field, the staggered grid method was used to deal with the complex interface. The combined solution of Marker in Cell (MAC) algorithm and phase field discrete calculation was realized. In order to further describe the influence of convection on the solidification process, the roll casting experiments are used to verify the impact growth of multiple dendrites under convection. The results show that the dendrites undergo solute remelting and the dendrites melt into equiaxed crystals, showing the phenomenon of Columnar to Equiaxed Transition (CET).

A new camera model combining an analytical model and a discrete correction to overcome refractive index variation challenges

When performing Tomo-PIV experiments, the calculation of accurate camera models is a key point for successful measurements. In severe configurations, where optical interfaces are involved and refractive index variations occur along the line of sight, analytical models can fail to accurately represent the projection and back-projection functions. This inability can lead to significant inaccuracies in particle location and volume reconstruction, which has a considerable impact on the calculation of velocity fields. In order to overcome these limitations, an innovative camera model based on the combination of an analytical model, such as a pinhole model or a polynomial model, with discrete corrections is proposed. In this method, the analytical projection and back-projection are adjusted with a discrete correction stored in two adaptive grids that save both memory and computation time. These correction grids require calibration which is performed with triangulation procedures similar to those used in misalignment corrections. The calculation and operation of the model are described in this paper. The performance of the camera model is evaluated on simulated and experimental setups based on a large depth-of-field calibration performed in a glass water tank. The presence of multiple optical interfaces and fluids, resulting in large light deviations, makes it difficult to compute a high accuracy camera model. In this configuration, the proposed technique successfully reduces the triangulation error from 1 pixel to less than 0.01 pixel. The usefulness of the model is demonstrated in a Tomo-PIV experiment where the deflection of light through the water tunnel walls prevents classical analytical functions from accurately modelling the projection and back-projection functions. This corrected model can also solve discontinuity problems in the projection functions and can be used when there are interfaces in the measurement volume. It opens new perspectives in the study of fluid-structure interaction when transparent solids are involved.