Momentum Source Terms Research Articles

Application of the fast 3D simplified simulation method for the large CAP1400 nuclear island evaporator based on the coupled source term method

As for the evaporator of the large CAP1400 nuclear power plant, it has a large volume with numerous tubes along with the complex flow heat transfer phenomenon. The traditional direct simulation method usually takes a lot of time and computing resources to obtain the flow heat transfer data. To solve the problem, a fast simulation method established on the porous medium source term was herein proposed. In this simplified simulation method, the complex evaporator model is replaced with the porous medium model, where the derived heat and momentum source terms are added into the governing equation to control the heat flows. Five kinds of simplified evaporator models with different numbers of pipes were set to be the research objects, the internal flows inside the evaporator were studied with the traditional direct simulation method and the newly proposed simplified simulation method. Via comparative analysis, it can be found that: 1) The newly proposed simplified simulation method accurately captures the distribution characteristics of pressure, temperature, and entropy production in the evaporator, serving as a viable alternative to traditional direct simulation methods. Specifically, the average simulation errors for inlet-outlet pressure difference and temperature difference are both less than 5 % and 7 %, respectively. 2) The newly proposed simplified simulation method can capture the mutual interference effects between the evaporator and the nuclear main pump. When the evaporator is connected in series with the main nuclear pump, the average head of the main pump increases by 0.34 m, while the efficiency decreases by an average of 0.34 %. The average simulation errors of the simplified simulation method are 0.06 m and 0.13 %, respectively. 3) The application of the simplified simulation method leads to a significant 85 % decrease in the average computational cost for evaporator calculations and a notable 36 % decrease for combined calculations of the evaporator and main pump. The study here is expected to provide technique support for the simulation and evaluation of the large nuclear island.

A data–driven sensibility tool for flow control based on resolvent analysis

This study presents a novel application of data-driven resolvent analysis algorithm for flow control. The objective is to identify key coherent structures connected to regions of the flow that are highly sensitive to structural changes. Modifying such regions, i.e., including momentum source terms, flow stabilizers, or changing the shape of the body under study, we can control the appearance of flow instabilities. The method is tested in two different applications: the laminar flow behind a two-dimensional circular cylinder and a turbulent channel flow including heat transfer to the endwall. In the first test case, the flow unsteadiness is controlled by including two stabilizers (formed by two small cylinders) in the areas suggested by resolvent analysis. This is a benchmark problem in fluid dynamics that serves to validate the idea of using this tool for flow control. In the second test case, data-driven resolvent analysis is applied as a mean to control, enhance or reduce, convective heat transfer. Modifications in the geometry, in the form of cavities and ribs included in the areas pointed by resolvent analysis, show the possibility of enhancing heat transfer while reducing drag. The findings highlight the importance of resolvent analysis in understanding flow dynamics and designing effective flow control strategies.

Effect of Surface Roughness on Aerodynamic Loads of Bluff Body in Vicinity of Smoothed Moving Wall

This paper contributes to a new Lagrangian vortex method for the statistical control of turbulence in two-dimensional flow configurations around a rough circular cylinder in ground effect when considering higher subcritical Reynolds numbers, namely 3 × 104 ≤ Re ≤ 2 × 105. A smoothed moving wall (active control technique) is used to include the blockage effect in association with the variation in cylinder surface roughness (passive control technique), characterizing a hybrid approach. In contrast with the previous approaches of our research group, the rough cylinder surface is here geometrically constructed, and a new momentum source term is introduced and calculated for the investigated problem. The methodology is structured by coupling the random Discrete Vortex Method, the Lagrangian Dynamic Roughness Model, and the Large Eddy Simulation with turbulence closure using the truncated Second-Order Velocity Structure Function model. This methodological option has the advantage of dispensing with the use of both a refined near-wall mesh and wall functions. The disadvantage of costly processing is readily solved with Open Multi-Processing. The results reveal that intermediate and high roughness values are most efficient for Reynolds numbers on the orders of 105 and 104, respectively. In employing a moving wall, the transition from the large-gap to the intermediate-gap regime is satisfactorily characterized. For the conditions studied with the hybrid technique, it was concluded that the effect of roughness is preponderant and acts to anticipate the characteristics of a lower gap-to-diameter ratio regime, especially with regard to intermittency.

An improved semi-resolved computational fluid dynamics-discrete element method for simulating liquid–solid systems with wide particle size distributions

Vertical hydraulic transport of particles with wide particle size distributions is a crucial process for coal physical fluidized mining. In the present study, an improved semi-resolved computational fluid dynamics (CFD)-discrete element method was developed to simulate particle flows with wide particle size distributions. In this model, the CFD cells allocated to the particle volume and the momentum source term were defined as the dependent domain and the influential domain, respectively. On this basis, the two-way domain expansion method and the one-way domain expansion method were adopted for the liquid–solid simulation of coarse and fine particles, respectively. The dependent domain expansion coefficient and the influential domain expansion coefficient were proposed to determine the spatial range of the dependent domain and influential domain for the coarse particles, and the optimal modeling strategy for the dependent domain and influential domain expansion coefficient for the coarse particles was determined. Furthermore, a volume expansion method and a momentum source expansion method were proposed for calculating the solid volume fraction of the dependent domain and the source term of the influential domain for the coarse particles. Furthermore, the sample point method was adopted to obtain the solid volume fraction in the dependent domain for the fine particles, and the momentum source term was only updated to the particle-located cell. Subsequently, single-particle settling and binary-particle fluidizing numerical experiments were used to verify the calculation accuracy of the model. The investigation can provide a new method for numerical simulation of liquid–solid flow with wide particle size distributions.

Numerical simulations of fluid flows and heat transfer in melt pools of Directed Energy Deposition of SS316L

This paper presents the numerical model developed to simulate fluid flow and heat transfer in melt pools formed in Directed Energy Deposition of stainless steel SS316L. The model incorporated important heat and momentum source terms. The energy source terms included laser energy, latent heat of phase change, convective heat loss, radiative heat loss, evaporative heat loss, and energy addition due to molten particle deposition into the melt pool. The momentum source terms were due to surface tension effect, thermocapillary (Marangoni) effect, thermal buoyancy, momentum damping due to phase change, molten particle momentum, and recoil effect due to evaporation. The simulations suggested that the predicted flow and heat transfer in the melt pool affected the resulting shape and size. With the process parameters currently employed, the melt pool was elongated, wide and shallow, with depressed free surface and outward convective flow. The outward flow was caused by the dominant region of high temperature in the centre of the melt pool, such that the temperature gradient of surface tension is negative.

Study on the effects of manifold structure on the gas flow distribution uniformity of anode of PEMFC stack with 140-cell

The gas maldistribution of the large proton exchange membrane fuel cell (PEMFC) stack leads to the deterioration of power performance. This numerical investigation studies the gas flow rate distribution in anode of two U-type stacks (a 15-cell stack and a 140-cell stack) which are composed of the same type of unit fuel cells. The anode gas channels of the two stacks are regarded as porous medium whose characteristic parameters are determined from pressure drop test data. To consider the nitrogen permeation from cathode to anode gas channel during the purging process, an expression of an additional momentum source term is proposed which helps to better fit the simulation results with pressure drop test data. Results show that the anode of the 140-cell stack has a quite good flow distribution uniformity. However, its asymmetric feed header of the manifold structure still has some negative effect. The same 140-cell stack installed with a rotational symmetric feed header is investigated and the simulation result shows that it can reduce the original maximum non-uniformity by about 50%.

On the use of deep learning and computational fluid dynamics for the estimation of uniform momentum source components of propellers

This article proposes a novel method based on Deep Learning for the resolution of uniform momentum source terms in the Reynolds-Averaged Navier-Stokes equations. These source terms can represent several industrial devices (propellers, wind turbines, and so forth) in Computational Fluid Dynamics simulations. Current simulation methods require huge computational power, rely on strong assumptions or need additional information about the device that is being simulated. In this first approach to the new method, a Deep Learning system is trained with hundreds of Computational Fluid Dynamics simulations with uniform momemtum sources so that it can compute the one representing a given propeller from a reduced set of flow velocity measurements near it. Results show an overall relative error below the for momentum sources for uniform sources and a moderate error when describing real propellers. This work will allow to simulate more accurately industrial devices with less computational cost.

Mathematical-Based CFD Modelling and Simulation of Mushroom Drying in Tray Dryer

In this study, CFD simulations that incorporate the inherent coupling between the moisture content of the mushroom and hot air flow in the tray dryer were performed. Conservation principles were applied to the fundamental quantities of mass, momentum, and heat. The source terms due to the moisture evaporation, the viscous and inertial resistance, and continuous evaporative cooling were determined through experimental results. Experiments were conducted to study and select the drying kinetics model at the optimum drying conditions and moisture sorption isotherm model at 30, 40, and 50°C temperatures. The best model describing the drying kinetics of mushrooms and moisture sorption isotherm model was chosen based on the lowest RMSE values and the highest R 2 value. Midilli et al.’s drying kinetics model and the modified Henderson sorption isotherm model were adopted in CFD modelling. The CFD software ANSYS Fluent was used for the 3D modelling of mushroom drying in a tray dryer. The mass and energy source term equations were added to the ANSYS Fluent software using a user-defined function (UDF). The parameter permeability of medium ( α ) and pressure-jump coefficient ( C 2 ) appearing in the momentum source term were directly introduced in the Fluent setup as cell zone conditions. The simulation results of the moisture removal and drying temperatures were validated against experimental data. Both results are in good agreement with the experimental data, with R 2 values of 0.9906 for moisture contents and 0.926 for drying temperature. Thus, simulation can be an option to study the drying mechanisms and alleviate some drawbacks of doing experiments.

Groupiness effect on irregular wave train propagation and impact on cylinder

A wave flume based on solving the Reynolds-averaged Navier-Stokes equation is modelled to simulate the irregular wave group interacting with a cylinder. The irregular wave groups are generated based on the wave envelope spectrum and the improved JONSWAP spectrum. The wave-making boundary and the momentum source term for wave-making and wave dissipation are developed based on the irregular wave theory. To suppress excessive growth of turbulent viscosity, a modified formula for turbulent viscosity is implemented in the shear stress transport turbulence model. Several sets of irregular waves with different groupiness factors are simulated. The effects of groupiness on the wave parameters, wave run-up height and wave force on the cylinder are investigated. The results show that the wave parameters increase as the groupiness increase. The group height factor has a larger influence on the significant wave height than the group length factor. The group length factor mainly influences the average wave period and average wavelength. When the average wavelength is larger than the diameter of the cylinder, the increase in wave group length results in a decrease in wave run-up height and wave force on the cylinder.

Research on shell-side heat and mass transfer with multi-component in LNG spiral-wound heat exchanger under sloshing conditions

The spiral-wound heat exchanger (SWHE) is the primary low-temperature heat exchanger for large-scale LNG plants due to its high-pressure resistance, compact structure, and high heat exchange efficiency. This paper studied the shell-side heat and mass transfer characteristics of vapor-liquid two-phase mixed refrigerants in an SWHE by combining a multi-component model in FLUENT software with a customized multicomponent mass transfer model. Besides, the mathematical model under the sloshing condition was obtained through mathematical derivation, and the corresponding UDF code was loaded into FLUENT as the momentum source term. The results under the sloshing conditions were compared with the relevant parameters under the steady-state condition. The shell-side heat and mass transfer characteristics of the SWHE were investigated by adjusting the component ratio and other working conditions. It was found that the sloshing conditions enhance the heat transfer performance and sometimes have insignificant effects. The sloshing condition is beneficial to reduce the flow resistance. The comprehensive performance of multi-component refrigerants has been improved and the improvement is more significant under sloshing conditions, considering both the heat transfer and pressure drop. These results will provide theoretical support for the research and design of multi-component heat and mass transfer enhancement of LNG SWHE under ocean sloshing conditions.

Analysis of Sharp Eagle Oscillating Surge Wave Energy Converter Based on a Two-Dimensional Numerical Wave Flume Model

To investigate the overtopping and slamming phenomena that occur in the interactions between waves and oscillating surge wave energy converters (OSWECs), a two-dimensional numerical wave flume was established using computational fluid dynamics (CFD) software Fluent by adding the momentum source terms into the original Navier–Stokes equation. Numerical convergence studies of the mesh sizes and time steps were firstly performed to ensure the sufficient accuracy of the numerical model. The variations in the wave heights along the wave propagation direction in the wave-generating area, working area, and wave-absorbing area were analyzed. The dynamics of the flap-type OSWEC were simulated using the overset mesh function embedded in Fluent. In addition, the numerical results were compared with the experimental data, and good agreements were achieved. External torque was applied to the hinge joint of the OSWEC to simulate the forces due to the power take-off (PTO) system, and the identified optimal PTO damping was compared with the numerical results based on the potential flow theory, which verified the correctness of the numerical PTO system. On this basis, nonlinear wave slamming by the sharp-eagle OSWEC was analyzed. The results show that under certain incident wave conditions, the sharp-eagle OSWEC can effectively reduce the maximum rotation angle and angular velocity compared with those of the flap-type OSWEC, and there is no overtopping that occurring for the sharp-eagle OSWEC. Furthermore, the sharp-eagle OSWEC performs better than the flap-type OSWEC.

Experimentally based testing of the enthalpy-porosity method for the numerical simulation of phase change of paraffin-type PCMs

The enthalpy-porosity method is generally applied as an economical resort for the numerical simulation of phase change materials (PCMs). However, having been developed strictly for metals, its suitability for the task is unclear, nor is the rationale for assigning its internal parameters, e.g., latent enthalpy and the constant of the momentum source term representing the “mushy” region. We first experimentally and exhaustively characterize a paraffin-type PCM, including differential scanning calorimetry (DSC) at several heating rates, T-history, and fusion visualization. Then, we develop a numerical model and systematically run simulations under different internal parameters and thermophysical properties of the PCM. Simulation results exhibit significant disagreement with experiments that cannot be reduced by any strategy for combining different material properties and model parameters. Among other effects, the constant of the momentum source term, which has to be assigned somewhat arbitrarily, has more relevance in the accuracy than any set of properties obtained by DSC and other experimental techniques. Thus, a rather negative, although interesting, conclusion is suggested: the enthalpy-porosity method may fail to model the phase change of paraffin-type PCMs. This is, of course, of paramount importance for the studies of their utilization in practical systems since it puts a fundamental point of uncertainty in any numerical study or lumped-type model derived thereof. The paper concludes with a tentative discussion of the possible causes of this failure and perspectives for developing more proper models.

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.

Experimental and computational investigation into hydrodynamic and heat transfer characteristics of subcooled flow boiling on the International Space Station

This study is part of a long-term initiative to investigate flow boiling of n-perfluorohexane (n-PFH) under microgravity on the International Space Station (ISS). Investigated are data received from the ISS during 2022 using the Flow Boiling and Condensation Experiment (FBCE) (actual name of experimental payload). FBCE is designed to accommodate one of two test modules, one for flow boiling and another for condensation. Data for the present study are acquired using FBCE's Flow Boiling Module (FBM), which features a rectangular channel of 5.0-mm height, 2.5-mm width, and 114.6-mm heated length. Examined are results for three different mass velocities of 199.9, 799.9, and 2399.9 kg/m2.s, and heat fluxes corresponding to approximately 20, 40, and 60% of critical heat flux (CHF). Detailed development of the interfacial behavior is captured by high-speed video through the channel's transparent sidewalls. In the Computational Fluid Dynamics (CFD) model, numerical solver is constructed in ANSYS-Fluent wherein the multiphase model is combined with appropriate models for turbulence, surface tension, and interfacial phase change. Also incorporated are momentum source terms governing bubble shear-lift, bubble drag, and bubble dispersion. Accuracy of the CFD predictions is assessed by comparison against both the heat transfer data and video-captured interfacial behavior. Very good agreement is achieved against measured axial profile of heated wall temperatures and further validated by accurately capturing such interfacial features as bubble formation, detachment, coalescence, and downstream wavy vapor layer development. Additionally, the CFD simulations enable prediction of other transport parameters vitally important to understanding evolution of the boiling flow but not possible from experiment, such as cross-sectional profiles of void fraction, fluid velocity, and mixture temperature.

Simulation study on noise reduction effect of porous material on electronic expansion valve

To reduce the flow-induced noise caused by the refrigerant in the refrigeration system and improve the comfort of air conditioning, porous materials are used to rectify the refrigerant in the refrigeration system. To simulate the flow field characteristics and flow-induced noise level in the electronic expansion valve before and after adding porous material at the outlet of the electronic expansion valve orifice for rectifying, the commercial simulation software Fluent is applied, which adopts the mixture multiphase model and cavitation model, and compile UDF to set the momentum source term in the porous medium region. The results show that adding porous material can rectify the refrigerant in the electronic expansion valve without changing the cooling capacity of the refrigeration system. The flow-induced noise generated in the porous material rectified electronic expansion valve is reduced in many directions. After rectification, the gas phase distribution in the electronic expansion valve is more uniform. The turbulent kinetic energy intensity at the outlet can be reduced to 25% of the originally designed electronic expansion valve; the bubble bursting phenomenon can be effectively inhibited. The noise reduction effect of porous material is suitable for the electronic expansion valve under a small opening and is more evident in the high-frequency noise.

Investigations of Vertical-Axis Wind-Turbine Group Synergy Using an Actuator Line Model

The presence of power augmentation effects, or synergy, in vertical-axis wind turbines (VAWTs) offers unique opportunities for enhancing wind-farm performance. This paper uses an open-source actuator-line-method (ALM) code library for OpenFOAM (turbinesFoam) to conduct an investigation into the synergy patterns within two- and three-turbine VAWT arrays. The application of ALM greatly reduces the computational cost of simulating VAWTs by modelling turbines as momentum source terms in the Navier–Stokes equations. In conjunction with an unsteady Reynolds-Averaged Navier–Stokes (URANS) approach using the k-ω shear stress transport (SST) turbulence model, the ALM has proven capable of predicting VAWT synergy. The synergy of multi-turbine cases is characterized using the power ratio which is defined as the power coefficient of the turbine cluster normalized by that for turbines in isolated operation. The variation of the power ratio is characterized with respect to the array layout parameters, and connections are drawn with previous investigations, showing good agreement. The results from 108 two-turbine and 40 three-turbine configurations obtained using ALM are visualized and analyzed to augment the understanding of the VAWT synergy landscape, demonstrating the effectiveness of various layouts. A novel synergy superposition scheme is proposed for approximating three-turbine synergy using pairwise interactions, and it is shown to be remarkably accurate.

Prediction of droplet size distributions from a pre-orifice nozzle using the Maximum Entropy Principle

The atomized droplet size distribution (DSD) produced by a nozzle is a fundamental information to define the performance of application systems. In this paper a new model to represent the atomization of a pre-orifice nozzle is presented. It is based on the Maximum Entropy Principle (MEP), the Linearized Instability Sheet Atomization (LISA) model and Computational Fluid Dynamics (CFD) simulations. Different atomization liquids with varied physical properties were sprayed at different pressures and their droplet size distributions were measured for model calibration and validation. The LISA model correctly predicts the effect of the pressure and physical properties of the mixtures on the most probable droplet diameter. The CFD studies allow to predict the influence of the flowrate on the energy source term of the MEP energy balance, which is not negligible. On the other hand, based on the LISA model, the calculated momentum source term does not impact on the DSD prediction significantly. The developed model, which just includes two adjustable parameters, is able to well represent experimental DSDs from a pre-orifice nozzle operating at different pressures.

Prediction of thermohydraulics in shell side of CAP1400 steam generator by two-fluid porous media model

Three-dimensional thermohydraulics in the shell side of the u-tube steam generator are essential for the thermal design and tube flow-induced vibration analysis, which are crucial for the equipment economy and integrity. In this work, the Eulerian two-fluid framework along with porous media model was employed to predict the thermal-hydraulic parameters in the shell side of the CAP1400 steam generator. The two-phase flow in the shell side was treated as flow in porous media with additional momentum and energy source terms for each phase to consider the effects of structure resistance and primary-to-shell heat transfer. The primary side was simplified by the multi-channel model with 16 equivalent tubes. The distributions of thermal-hydraulic parameters for each phase and the mixture phase were obtained. High non-uniformity can be observed for the flow and heat transfer parameters. The ratio between heat released in the hot side and cold side was as large as 2.7. The crossflow energy related to the flow-induced vibration was also derived to find the possible location of tube damage. The most probable location for a potential tube rupture locates at approximate 0.4 rad in the hot side.

The Structure of Multiphase Galactic Winds

Abstract We present a novel analytic framework to model the steady-state structure of multiphase galactic winds comprised of a hot, volume-filling component and a cold, clumpy component. We first derive general expressions for the structure of the hot phase for arbitrary mass, momentum, and energy source terms. Next, informed by recent simulations, we parameterize the cloud–wind mass transfer rates, which are set by the competition between turbulent mixing and radiative cooling. This enables us to cast the cloud–wind interaction as a source term for the hot phase and thereby simultaneously solve for the evolution of both phases, fully accounting for their bidirectional influence. With this model, we explore the nature of galactic winds over a broad range of conditions. We find that (i) with realistic parameter choices, we naturally produce a hot, low-density wind that transports energy while entraining a significant flux of cold clouds, (ii) mixing dominates the cold cloud acceleration and decelerates the hot wind, (iii) during mixing thermalization of relative kinetic energy provides significant heating, (iv) systems with low hot phase mass loading factors and/or star formation rates can sustain higher initial cold phase mass loading factors, but the clouds are quickly shredded, and (v) systems with large hot phase mass loading factors and/or high star formation rates cannot sustain large initial cold phase mass loading factors, but the clouds tend to grow with distance from the galaxy. Our results highlight the necessity of accounting for the multiphase structure of galactic winds, both physically and observationally, and have important implications for feedback in galactic systems.

Method of reconstructing two-dimensional velocity fields on the basis of temperature field values measured with a thermal imaging camera

This paper describes a novel numerical reconstruction procedure (NRP) of the velocity field during natural convective heat transfer from a two-sided, isothermal, heated vertical plate based only on the known temperature field obtained, e.g. with a thermal imaging camera. It has been demonstrated that with a knowledge of temperature distributions, the NRP enables the reconstruction of velocity fields by solving the Navier-Stokes equation with an additional momentum source term that replaces the Fourier-Kirchhoff equation. This is because its role is played by the known temperature field, which is the equivalent of its solution.Experimental tests were performed in the air on a symmetrically heated, double-sided, isothermal vertical plate with dimensions of 150×75×2.1 mm. In this test we used a thermal imaging camera with a temperature field detector in the form of a mesh parallel to the gravity acceleration vector, perpendicular to the heating surface and adjacent to the plate in the middle of its width. It was demonstrated that with a temperature field in the form of a results matrix, such reconstruction was possible and that the results obtained were consistent with other experimental results reported elsewhere and with SNC.Along with recreating the velocity field using a standard numerical calculation (SNC), the temperature distributions and velocity fields of the plate under consideration were carried out in parallel and then compared with thermal imaging camera temperature measurements (CTM) and a reconstructed velocity field (NRP).