Transient Boundary Conditions Research Articles

Prediction of Cleaning by Means of Computational Fluid Dynamics: Implication of the Pre‐wetting of a Swellable Soil

The cleaning behavior of a pre-wetted soil is studied experimentally and modeled numerically for the prototypical case of plane channel flow. One of the channel walls is soiled with a food-based model soil containing luminescent tracer particles to perform space- and time-resolved investigations of the cleaning process. Pre-wetting is applied for a few minutes before the soil removal is started with flow of Reynolds number up to 20,000. Physical model and simulation are based on a transient boundary condition to represent the behavior of the soil. Pre-wetting is taken into account by an initial removal of a certain amount of soil due to cohesive separation and the subsequent cleaning modeled as being limited by a diffusive process. Compared to a conventional multiphase simulation, the computation time is lowered by about three orders of magnitude. The results obtained with this elementary approach match the experiments astonishingly well.

Simulation of a NOx Sensor for Model-Based Control of Exhaust Aftertreatment Systems

Optimal control of the exhaust aftertreatment components is an important aspect for minimizing pollutants. Nitrogen oxides are therefore monitored using amperometric gas sensors. However, they show marked cross-sensitivities to ammonia, which can be disadvantageous, e.g., if they are applied in NH3 selective catalytic reduction systems. In this study, a model that simulates the operation of a NOx sensor is developed. The three oxygen pumping cells and the upstream diffusion barriers were implemented in a 1D geometry, with the relevant electrode reactions taking place over its length. The diffusion barriers were calculated quasi-stationary. The dynamics of incoming gas components as a function of the exhaust mass flow were integrated with a first order linear time invariant system. The problem was calculated using the convection–diffusion equation. The reaction kinetics were determined based on stationary measurements in laboratory atmosphere, whereby initially only the reaction with respect to NO and NO2 was considered. Then, the cross-sensitivities to oxygen, water and ammonia were examined. The developed data set could then be used for transient boundary conditions. The simulated and the measured sensor signals in the case of engine test bench conditions with real driving cycles agree very well.

Simulation of jet cleaning: Diffusion model for swellable soils

A physical-numerical simulation model for the cleaning of swellable soils by diffusive dissolution or cohesive separation of small soil particles, which was developed targeting a low computational effort, is presented and validated. The flow calculation, based on the Reynolds averaged Navier Stokes equations (RANS), and the calculation of the soil transport, modelled following the unsteady RANS concept, are performed successively. The behaviour of the soil is modelled as a transient Dirichlet boundary condition, its parameters being determined in laboratory experiments using plane channel flow. A validation is performed for a coherent water jet impinging vertically on a substrate, which is covered by a starch-based model soil, at a distance of 100mm to the nozzle. Using a nozzle diameter of 1.69mm and pressures in the nozzle ranging from 1.5 to 5bar, corresponding to Reynolds numbers between 17700 and 55600, the wall shear stress in this configuration exceeds the values given in the laboratory tests by two orders of magnitude. Despite this difference, the simplicity of the model and the complexity of the test case, the simulated cleaning times correspond very well to the measured values. Thus, the targeted scalability and transferability of the model to other flow configurations are ensured.

Electrical response of thermoelectric generator to geometry variation under transient thermal boundary condition

A three-dimensional numerical model is applied in this study to illustrate the electrical response of a thermoelectric generator (TEG) during transient heat flux at the hot side. In this work, various types of thermal boundary conditions are considered to evaluate the performance of the TEG. Thus, a TEG under pulsed heat flux is studied numerically, and the numerical model is verified by experimental results. With the consideration of a defined reference geometry, different heat flux frequencies are applied in order to evaluate the corresponding electrical output by the TEG. In addition, variation of the module performance for various TEG leg lengths and its cross-sectional area are studied over a wide range of heat fluxes. The results indicate that the open circuit voltage in the experiment is in a good agreement with the open circuit voltage in the simulation results. The results show that the range of power oscillation reduces at higher frequency of the applied heat flux. Furthermore, the variability of the output power increases as the thermoelectric element length increases and the area of the element reduces.

A novel non-iterative method for estimating boundary conditions and geometry of furnace inner wall made of FGMs

A non-iterative inverse method based on the precise integration finite element method (PIFEM) is established for estimating the transient boundary conditions and the geometry of furnace inner wall made of functional gradient materials. For estimating boundary conditions, a two-step scheme is presented. First of all, after obtaining the temperatures at measurement points, a matrix system of equations of transient heat conduction problem is formed by a series of matrix operations based on the PIFEM. After that, the transient temperature or heat flux at inner boundary nodes can be obtained by the least-square method, in which basis functions approximation and Tikhonov regularization method are used to reduce the ill-posed level of inverse problem. For identification of geometry of inner boundary, a three-step scheme based on the PIFEM is proposed. After obtaining the temperature at measurement points, a virtual boundary is introduced to form the new computing domain. Estimation the temperature of the virtual boundary is a primary task in this step. Finally, the geometry of the furnace inner wall is identified by searching the isotherm in the new domain. Numerical results show that the present method can obtain the great performance on both the accuracy and the efficiency.

Prediction of Cooling Curves for Controlled Unidirectional Solidification Under the Influence of Shrinkage: A Semi-analytical Approach

Quality of casting products can be significantly improved by controlling the crystal growth rate. Both dendritic and equiaxed grain structures depend strongly on crystal growth rate along the crystallographic direction. Uncontrolled solidification processes may lead to the formation of porous and columnar material with an extremely non-homogeneous composition distribution. These undesirable micro-structures can be avoided by adopting an optimal cooling rate (K/s) during the crystal growth. The present work focuses on determining suitable cooling curves to obtain desired unidirectional crystal growth rates, by implementing a semi-analytical model. Here, we defined cooling curve as the time history of temperature evolution at the cold boundary. The proposed semi-analytical heat transfer model is diffusion driven and accounts for shrinkage effect during solidification. The proposed model is found capable of predicting cooling curves for prescribed interface velocities. The model is self-sufficient in validating itself by means of solving inverse and forward problems. The cooling curve prediction by the model is validated by using it as the transient boundary condition for an existing enthalpy updating scheme-based numerical model. The proposed model is also applied to empirical data reported in literature, to validate the model against experimental results. All the validations showcased excellent fit. The proposed model will facilitate controlled unidirectional crystal growth rate by providing cooling rate (K/s) as an input for the experiments involving directional solidification.

Estimating the transient thermal boundary conditions with an improved space marching technique

This paper presents an improved space marching technique for estimating the transient thermal boundary conditions including heat flux and temperature, based on the measured interior temperature history. The algorithm employs a fully implicit difference scheme thus is unconditionally stable for various space and time steps. In each space marching step, the number of used future temperatures can be randomly designated. The proposed method was tested with numerical and experimental data to verify its performances for both linear and nonlinear problems. Comparisons between the proposed method and the method of Raynaud and Bransier (1986) were also conducted using both the numerical and experimental data. In the testing with numerical data, the present method is better than the method of Raynaud and Bransier (1986) for small time steps where the estimating accuracy was dominated by the random error. In the testing with cryogenic quenching experimental data, it was found that the present method is applicable for processing temperature data involving local fluctuations and abrupt changes. By incorporating more future temperatures in each space marching step, the present method demonstrated a better performance in processing the experimental data.

Identification of transient boundary conditions with improved cuckoo search algorithm and polynomial approximation

The cuckoo search (CS) algorithm combined with Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm (CS-BFGS) is proposed to identify time-dependent boundary conditions for 2-D transient heat conduction problems in functionally gradient materials. Firstly the dual reciprocity boundary element method (DRBEM) is used to solve the direct problem. Then taking the unknown boundary conditions as a polynomial function of coordinates with time-dependent coefficients, the CS-BFGS is applied to obtain the unknown coefficients of the polynomial. As a result, the transient boundary conditions are evaluated. The convergence speed of the CS-BFGS algorithm is faster than the CS algorithm. What's more, the effect of the polynomial degree is discussed. As the polynomial degree increases, the inverse results are more accurate but the iterative number and computation time also increase. Finally, the influences of the position and number of measurement points, and random errors on the inverse results are investigated. With the measurement points closer to the boundary, with the increase of measurement point number and with the decrease of measurement errors, the results are more accurate.

Towards Full-Stack Scale Simulation of PEFC System Transient Control

Overview We will show results of computer simulations on full-stack scale behavior of the PEFC stack system, which also take into account models of auxiliary systems including hydrogen injectors, recirculation pumps, exhaust valves and radiators of coolant. Our simulations focus on transient internal states of the PEFC stack system under driving conditions of FCVs. In particular, we assumed transient loading profiles in similar to automotive uses, and various controlling ways of the stack system (control of injector and/or exhaust valves, recirculation pump and coolant flowrate, for example). Results of simulations show detailed distribution of gas species concentration, temperature, liquid water and electrochemical reaction current. We can discuss possibilities of hydrogen or oxygen local starvation and effect of temperature difference between stacked cells. We also try to investigate the behavior of condensed liquid water. Finally it is discussed how we utilize these results for developments of control systems of PEFC stacks. Numerical Modeling and Results Simulations are performed by our own simulation software for PEFCs, which can deal with full-stack PEFC systems for automotive uses (up to 100s cells) under transient operating conditions. The most important feature of the software is the employed macroscopic model comprehensively dealing with all the relevant transport phenomena coupled with electrochemical reactions. In anode and cathode channels and porous structures in GDL and MPL, mass transport of gas and liquid phase are solved by considering the two-phase fluid dynamics with taking into account the effects of phase changing. Here mass transport is coupled with heat and chemical species transport equations. Those all transport phenomena are coupled with electrochemical reactions in the MEA. Transport of chemical species and water through the MEA are also considered. In the software, compared with ordinary fully-resolved CFD-based models, the computational cost is greatly reduced by use of macroscopic engineering models. For example, two-phase fluid flow is solved by Darcy’s law on the coarse-grained mesh instead of solving Navier-Stokes equation. In order to recover appropriate flow and pressure distribution in channels, the distribution of the equivalent hydraulic parameter in flow channels is estimated by detailed CFD in advance, and mapped to the coarse mesh. Many engineering models are employed in order to consider various transport phenomena, like water up-take into electrolytes and effective transport of oxygen from gas phase to reaction cites in catalyst layers, etc. Electrochemical reactions are modeled by Butler-Volmer equation, in the manner of lumped parameter models. The detail of computational models of a cell stack system (300 cm2 reaction area in each cell) are followings. The numerical model for anode system includes transient boundary conditions for an injector and an exhaust system with an ejector valve. An interconnection between inflow and outflow manifolds by recirculation pump is also taken into account by adding interconnecting computational elements representing volume of pipes and recirculation pump with forced flow conditions. Recirculation of coolant is also considered in the same way, in addition with modeled effects of the radiator. The transient behavior of the stack system is calculated under transient loading profiles in similar to automotive driving conditions, where the following elements of stack system conditions are taken into account; controlled hydrogen and air feeding, purging of gas and liquid water, recirculation pumps and coolant flow. Simulation results show behaviors of transient internal states of the PEFC stack system under driving conditions. Possibilities of starvation of hydrogen and oxygen at high loading current are ones of interesting results. Temperature distribution between stacked cells and dependency on coolant flow control are also discussed. We also try to work on accumulation and purging of liquid water and effects on cell performance. These discussions can provide useful information for developments of efficient control system for PEFC stack, aiming to avoid possible drawbacks on durability and cost issues.

Effects of Convection and Fracture Boundary Conditions on Heat Transfer Shape Factor in Fractured Geothermal Reservoirs

Advection–conduction equation (ACE) used to explain the combined conduction and convection mechanisms of heat transfer thorough porous media has received considerable attention with a wide range of applications in various disciplines. The present study concentrates on developing a generalized analytical solution to ACE through incorporation of Fourier series and a new dependent variable for the problem of heat transfer through porous media in one-dimensional finite spatial region assuming transient boundary conditions. Then, assuming that a fracture acts as the time-dependent boundary condition, an analytical solution is obtained for a typical fractured porous medium. Based on the analytical solution, heat transfer shape factor is also obtained, on which the effects of governing parameters of matrix block such as Peclet number are investigated throughout transient and pseudo-steady-state (PSS) periods for the first time. Moreover, a correlation is generated to estimate the PSS heat transfer shape factor in terms of dimensionless time and Peclet number for constant concentration and linearly ascending temperature boundary conditions. Additionally, the numerical finite difference and finite element methods were utilized to validate the analytical solution results. The results demonstrated that the obtained generalized analytical solution can be regarded as a reliably excellent and accurate mathematical lever to describe the heat transfer phenomenon through porous media subject to determine transient boundary conditions and also to verify numerical results.

Experimental and numerical investigation of the transient characteristics and volute casing wall pressure fluctuations of a single-blade pump

In contrast to conventional multiblade centrifugal pumps, single-blade pumps are characterized by a significant fluctuation of head and highly transient and circumferentially nonuniform flow field even in the best-efficiency point. For a contribution to a better understanding of the flow field and an improvement of numerical methods, a combined experimental and numerical study is performed with special emphasis on the analysis of the transient pressure field. In an open test rig, piezoresistive pressure sensors are utilized for the measurement of transient in- and outflow conditions and the volute casing wall pressure fluctuations. The quality of the numerical simulations is ensured by a careful adoption of the real geometry details in the simulation model, a grid study and a time step study. While the power curve is well reproduced by the numerical simulations, the time-averaged head is systematically overpredicted, probably due to underestimation of losses. Transient pressure boundary conditions for the numerical simulation show a better prediction of the measured pressure amplitude than constant boundary conditions, whereas the time-averaged head prediction is not improved. For a more accurate prediction of the transient flow field and the time-averaged characteristics, the utilization of scale-resolving turbulence models is assumed to be indispensable.

A Hydrodynamic Study of a Propeller Turbine During a Transient Runaway Event Initiated at the Best Efficiency Point

This paper presents a hydrodynamic study of a propeller turbine runaway based on flow simulations and measurements results. Runaways are considered one of the most structurally damaging conditions a hydraulic turbine may encounter. This study focuses specifically on the flow dynamics in the runner and draft tube of a model propeller turbine installed on the test stand of the Hydraulic Machines Laboratory of Laval University, Quebec, Canada. The controlled runaway event reproduced on the test stand was part of a larger study into transient flow conditions. Besides global performance parameters, the measurements also featured 31 pressure transducers mounted on two runner blades. Using those measurements' results, both as boundary conditions and for validation purposes, unsteady Reynolds-averaged Navier-Stokes simulations of the entire turbine were performed. Those simulations featured transient boundary conditions to reproduce discharge and runner speed variations. Using wavelet transforms analysis, the evolution of the dominant pressure fluctuations is tracked in both, the measurements and the simulations. The wavelet analysis revealed the presence of pressure fluctuations with frequencies at a fraction of the runner rotation speed. Numerical results revealed that a vortex structure in the draft tube, similar to a part-load vortex rope, is the cause of those high-pressure fluctuations in the runner. A slight flow separation is observable on the pressure side of the blades but does not alter the flow in the inter-blade channels. Comparisons between experimental and numerical data also outline the limits of the methodology related, among others, with the imposition of strict boundary conditions.

Investigation on Steady-State and Transient Boundary Condition Scenarios for Optimizing the Creation of Multiport Surrogate Thermal Models

Board-level simulation has to consider, at the earliest stage of the conception, the impact of the vicinity of numerous high- and medium-powered devices. In 1996, the European consortium DELPHI defined the concept of a surrogate, or compact thermal model (CTM), to minimize the computation times from days to minutes. A DELPHI-style CTM resumes an electronic component as a simple cuboid form and a network of resistors that links a single temperature-sensitive node to the major surfaces of heat extraction. That steady-state network is derived from a detailed numerical model, which is subjected to a set of boundary conditions (BCs) applied on its external surfaces. At first, this paper investigates the combinations of various sets of scenarios to generate and to test a multiport surrogate model. The objective is to define the lowest number of numerical simulations required while keeping the highest accuracy level of the derived BC-independent (BCI) thermal network. Then, this paper demonstrates the need of a smart selection of the isothermal surfaces to create a most relevant surrogate model. Finally, using that calibrated steady-state model, an extension of the DELPHI method to create multiport dynamic surrogate model is proposed as well as a set of BCs dedicated to transient network fitting.

Numerical Analysis of the VAD Outflow Cannula Positioning on the Blood Flow in the Patient–Specific Brain Supplying Arteries

Abstract The primary objective of this research can be divided into two separate aspects. The first one was to verify whether own software can be treated as a viable source of data for the Computer Aided Design (CAD) modelling and Computational Fluid Dynamics CFD analysis. The second aspect was to analyze the influence of the Ventricle Assist Device (VAD) outflow cannula positioning on the blood flow distribution in the brain-supplying arteries. Patient-specific model was reconstructed basing on the DICOM image sets obtained with the angiographic Computed Tomography. The reconstruction process was performed in the custom-created software, whereas the outflow cannulas were added in the SolidWorks software. Volumetric meshes were generated in the Ansys Mesher module. The transient boundary conditions enabled simulating several full cardiac cycles. Performed investigations focused mainly on volume flow rate, shear stress and velocity distribution. It was proven that custom-created software enhances the processes of the anatomical objects reconstruction. Developed geometrical files are compatible with CAD and CFD software – they can be easily manipulated and modified. Concerning the numerical simulations, several cases with varied positioning of the VAD outflow cannula were analyzed. Obtained results revealed that the location of the VAD outflow cannula has a slight impact on the blood flow distribution among the brain supplying arteries.

Transient boundary condition approach for simulating mechanical mixing in large wine tanks

Since wine is not continuously stirred during or after fermentation, it is common to use movable mixers on a variety of tank sizes or to install small, fast-rotating propeller mixers in large tanks. Many practically relevant optimization problems relate to processes occurring directly after the start of the propeller (flow field initialization period), which require 3D instationary models if CFD simulations are used. Based on traditional instationary models, these simulations are very time-consuming even on fast computers and limit the part of the flow field initialization period that can be computed. In this work, a new method was developed to speed up the transient simulation of mechanical mixing in large wine tanks. The method uses the traditional CFD techniques of moving reference frame (MRF) and several ensuing propeller rotations using sliding mesh (SM), to calculate a steady-state flow field and to compute the flow behavior in the propeller region. Subsequently, the flow’s key figures are extracted for the propeller region at multiple time-points during one rotation and continuously mapped to a new simulation starting from a flow field with zero velocity. This new approach using a transient boundary condition (BC), was validated with tank mixing experiments and literature data. In contrast to the MRF method, it allows e.g. for an estimation of minimum mixing times similar to the SM method, while computation times are reduced by a factor of up to 20 for tank-mixer scenarios evaluated in this work. For a mixing simulation in a wine tank, the new method takes only 3 days compared to more than 60 days using the traditional SM approach.

Evaluating drywells for stormwater management and enhanced aquifer recharge.

Drywells are increasingly used for stormwater management and enhanced aquifer recharge, but only limited research has quantitatively determined the performance of drywells. Numerical and field scale experiments were, therefore, conducted to improve our understanding and ability to characterize the drywell behavior. In particular, HYDRUS (2D/3D) was modified to simulate transient head boundary conditions for the complex geometry of the Maxwell Type IV drywell; i.e., a sediment chamber, an overflow pipe, and the variable geometry and storage of the drywell system with depth. Falling-head infiltration experiments were conducted on drywells located at the National Training Center in Fort Irwin, California (CA) and a commercial complex in Torrance, CA to determine in situ soil hydraulic properties (the saturated hydraulic conductivity, Ks , and the retention curve shape parameter, α) for an equivalent uniform soil profile by inverse parameter optimization. A good agreement between the observed and simulated water heights in wells was obtained for both sites as indicated by the coefficient of determination 0.95-0.99-%, unique parameter fits, and small standard errors. Fort Irwin and Torrance drywells had very distinctive soil hydraulic characteristics. The fitted value of Ks =1.01 × 10-3 m min-1 at the Torrance drywell was consistent with the sandy soil texture at this site and the default value for sand in the HYDRUS soil catalog. The drywell with this Ks = 1.01 × 10-3 m min-1 could easily infiltrate predicted surface runoff from a design rain event (∼51.3 m3) within 5760 min (4 d). In contrast, the fitted value of Ks=2.25 × 10-6 m min-1 at Fort Irwin was very low compared to the Torrance drywell and more than an order of magnitude smaller than the default value reported in the HYDRUS soil catalog for sandy clay loam at this site, likely due to clogging. These experiments and simulations provide useful information to characterize effective soil hydraulic properties in situ, and to improve the design of drywells for enhanced recharge.

Numerical and experimental investigation of post-oxidation of a four-stroke SI engine under fuel-rich conditions

The calibration of high-performance engines is a delicate task. During this procedure certain load points occur when the engine is running on fuel rich mixture. Temperature measurements have shown, that under these conditions the exhaust gas temperature right behind the exhaust valves is lower than in the junction where the separated exhaust pipes merge. This phenomenon is hardly investigated in the state-of-the-art literature and is the purpose of this work. Measurements of the exhaust gas composition at various positions are conducted for further analysis. It can be shown that the amount of hydrocarbon emissions (HC) is reduced significantly with increasing residence time in the exhaust pipes. It can be concluded post-combustion occurs which leads to an additional heat input and a temperature increase of approximately 120 K in the exhaust duct.Numerical methods are used in this work to investigate this effect. Principle studies which focus on premixed combustion models are carried out. For this reason, the experimental results obtained by the Sandia D flame model are used for validation. Finally, the transient flow conditions within the exhaust manifold are investigated. The transient boundary conditions are gained from a 1D GT-Power Simulation and are simplified for the 3D Computational Fluid Dynamics (CFD) Simulation. A very time efficient method is shown to compute the heat release within the exhaust pipes in dependence on the exhaust gas composition.The results point out, that post-combustion occurs at the junction and is strongly influenced by the grade of turbulence. The measured reduction of HC, O2 and CO, as well as the increase of CO2 can be reproduced in the simulation. Moreover, the temperature increase in the numerical simulation is similar as indicated by the measurements.

Validated dynamic model of an organic Rankine cycle (ORC) for waste heat recovery in a diesel truck

Recovering waste heat from the exhaust gas of diesel trucks using an organic Rankine cycle (ORC) is considered a promising option to reduce emissions and fuel consumption. As the system operates under highly transient boundary conditions, the development of a predictive model accounting for its dynamic behavior is of high relevance. In this contribution, such a model is presented. Evaporator and condenser are modeled using a dynamic moving boundary model, while pump and turbine are represented with pseudo-steady state models, as dynamics are assumed to be negligible here. A fundamental thermodynamic equation of state based on the free Helmholtz energy is implemented for the working fluid ethanol. As unknown parameters, e.g., in heat transfer, occur, a parameter estimation is conducted with the use of measurement data. The model is then validated using different experimental data. It is able to capture the system dynamics well both qualitatively and quantitatively, e.g., the mean relative temperature deviations are all smaller than 4%.

Estimation of boundary condition on the furnace inner wall based on precise integration BEM without iteration

This study develops a non-iterative method for estimating the boundary condition of transient heat conduction problems on the furnace inner wall based on the precise integration boundary element method (PIBEM). Generally, the problem of inversing boundary condition needs the iteration direct process about many times. The computational cost is high especially for inversing the transient boundary condition. However, the present method can directly inverse the temperature and heat flux boundary conditions by the least-square error method without iteration. In addition, using the precise integration method and BEM can fully play the superiority of solving the time-domain problem and reducing the dimension of problem, respectively. Meanwhile, an expanding coefficient method is introduced to approximate the unknown boundary condition. Numerical results show that the steady and accurate results can be obtained by the approximation of quadratic polynomials. A number of examples validate that the present method has very high efficiency and precision by investigating the effect of many factors such as the measurement error, the position and number of measurement points.

Control-oriented modeling of geothermal borefield thermal dynamics through Hammerstein-Wiener models

Abstract Geothermal energy is considered a clean and sustainable form of renewable energy, that can be exploited directly or indirectly by means of specific devices. Ground-coupled heat pumps are widely used systems to obtain this energy. Control of ground-coupled heat pump systems, where thermal energy is extracted or injected from and to a geothermal borefield, is important for optimal geothermal energy use in the building sector and smart grids. Model-based control of such systems is potentially an optimal solution but this requires control-oriented models for the borefield thermal dynamics, which is quite complicated due to thermal interactions between the boreholes, large-scale nonlinear system dynamics, transient surface boundary conditions, etc. In this paper, we propose and demonstrate the successful identification of these complex dynamics through simple and well-structured nonlinear Hammerstein-Wiener models, which can be used in some advanced convex model-based control algorithms. The results are validated for different borefield configurations and parameters with reference to a detailed finite-element borefield thermal model. Finally, a set of advanced convex model-based control methods are shortly described where Hammerstein-Wiener models can be used as control models.