Dimensionless Representation Research Articles

Integrating of LMIs with Buckingham Π theorem for control of uncertain oscillating systems

This paper introduces a novel framework for robust controller synthesis in oscillating systems by synergistically combining generalized linear matrix inequalities (GLMIs) with the Buckingham Π theorem. The primary goal is to enhance the design of robust controllers for systems with uncertain parameters through the exploitation of dimensionless groups derived from the Buckingham Π theorem. By establishing a dimensionless state-space representation, the proposed approach demonstrates adaptability to a broad spectrum of similar systems. The LMI-based formulation facilitates the systematic design of controllers capable of effectively mitigating the impact of parametric uncertainties. Simulation results for an uncertain inverted pendulum and a vehicle active suspension system validate the superior performance of the proposed method compared to conventional control techniques, such as MPC, LQG, SMC, PID, and LQR. For the uncertain inverted pendulum system, the proposed robust control scheme achieves a cart position stabilization in 5.35 s and pendulum stabilization in 6.3 s, which is faster than standard control algorithms. In the context of the vehicle active suspension system, the performance indices for sprung mass acceleration, suspension deflection, and tire deflection are 0.19, 0.47, and 0.07, respectively. These values indicate significant reductions when compared to conventional passive suspension systems and standard robust control methodologies.

Effects of sinusoidal wall temperature on thermal dynamics and irreversibility around an inclined plate embedded in a square cavity

Abstract Effective thermal and flow control within complex geometries is essential for engineering applications. In this study, an in-depth examination of flow dynamics, entropy, and thermal regulation is undertaken within a square cavity featuring sinusoidal wall temperature. To introduce complexity, an inclined plate obstacle is strategically positioned within the cavity with an inclination angle of 45°, and the investigation spans three distinct scenarios: adiabatic, cold, and hot conditions. The initial physical model is developed by formulating a system of partial differential equations, which are then transformed into a dimensionless representation using relevant variables. Subsequently, the Galerkin method is employed for approximated analysis of the simplified fluid flow model, and the computational code is verified in tabular format. The embedded physical parameters are constrained to specific numerical values to ensure the convergence of the physical model in each scenario. The physical characteristics of isotherms, streamlines, Nusselt numbers, entropy, and Bejan numbers are investigated. Notably, the results demonstrate that the introduction of a cold inclined plate leads to peak values in generating the entropy and average heat transfer rates. When comparing the cold inclined plate to the heated inclined plate, an increase of approximately 20% in the average heat transfer rate and a 15% rise in the entropy generation rate was found for the cold inclined plate. Furthermore, the Bejan number showed a 10% decrease for the cold inclined plate compared to the heated inclined plate. Additionally, increasing the amplitude and wavenumber led to a rise in average heat transfer and entropy generation rates, with 25% and 30% increases, respectively.

Numerical heat transfer enhancement in MHD boundary layer flow with Darcy-Forchheimer Bioconvection Nanofluid

Scientists have harnessed the diverse capabilities of nanofluids to solve a variety of engineering and scientific problems due to high-temperature predictions. The contribution of nanoparticles is often discussed in thermal devices, chemical reactions, automobile engines, fusion processes, energy results, and many industrial systems based on unique heat transfer results. Examining bioconvection in non-Newtonian nanofluids reveals diverse applications in advanced fields such as biotechnology, biomechanics, microbiology, computational biology, and medicine. This study investigates the enhancement of heat transfer with the impact of magnetic forces on a linearly stretched surface, examining the two-dimensional Darcy-Forchheimer flow of nanofluids based on blood. The research explores the influence of velocity, temperature, concentration, and microorganism profile on fluid flow assumptions. This investigation utilizes blood as the primary fluid for nanofluids, introducing nanoparticles like zinc oxide and titanium dioxide (. The study aims to explore their interactions and potential applications in the field of biomedicine. In order to streamline the complex scheme of partial differential equations (PDEs), boundary layer assumptions are employed. Through appropriate transformations, the governing partial differential equations (PDEs) and their associated boundary conditions are transformed into a dimensionless representation. By employing a local non-similarity technique with a second-degree truncation and utilizing MATLAB’s built-in finite difference code (bvp4c), the modified model’s outcomes are obtained. Once the calculated results and published results are satisfactorily aligned, graphical representations are used to illustrate and analyze how changing variables affect the fluid flow characteristics problems under consideration. In order to visualize the numerical variations of the drag coefficient and the Nusselt number, tables have been specially designed. Velocity profile of -blood and -blood decreases for increasing values of and , while temperature profile increases for increasing values of and . Concentration profile decreases for increasing values of , and microorganism profile increases for increasing values of . For rising values of and the drag coefficient increases and the Nusselt number decreases for rising values of and The model introduces a novel approach by conducting a non-similar analysis of the Darchy-Forchheimer bioconvection flow of a two-dimensional blood-based nanofluid in the presence of a magnetic field.Scientists have harnessed the diverse capabilities of nanofluids to solve a variety of engineering and scientific problems due to high-temperature predictions. The contribution of nanoparticles is often discussed in thermal devices, chemical reactions, automobile engines, fusion processes, energy results, and many industrial systems based on unique heat transfer results. Examining bioconvection in non-Newtonian nanofluids reveals diverse applications in advanced fields such as biotechnology, biomechanics, microbiology, computational biology, and medicine. This study investigates the enhancement of heat transfer with the impact of magnetic forces on a linearly stretched surface, examining the two-dimensional Darcy-Forchheimer flow of nanofluids based on blood. The research explores the influence of velocity, temperature, concentration, and microorganism profile on fluid flow assumptions. This investigation utilizes blood as the primary fluid for nanofluids, introducing nanoparticles like zinc oxide and titanium dioxide (. The study aims to explore their interactions and potential applications in the field of biomedicine. In order to streamline the complex scheme of partial differential equations (PDEs), boundary layer assumptions are employed. Through appropriate transformations, the governing partial differential equations (PDEs) and their associated boundary conditions are transformed into a dimensionless representation. By employing a local non-similarity technique with a second-degree truncation and utilizing MATLAB’s built-in finite difference code (bvp4c), the modified model’s outcomes are obtained. Once the calculated results and published results are satisfactorily aligned, graphical representations are used to illustrate and analyze how changing variables affect the fluid flow characteristics problems under consideration. In order to visualize the numerical variations of the drag coefficient and the Nusselt number, tables have been specially designed. Velocity profile of -blood and -blood decreases for increasing values of and , while temperature profile increases for increasing values of and . Concentration profile decreases for increasing values of , and microorganism profile increases for increasing values of . For rising values of and the drag coefficient increases and the Nusselt number decreases for rising values of and The model introduces a novel approach by conducting a non-similar analysis of the Darchy-Forchheimer bioconvection flow of a two-dimensional blood-based nanofluid in the presence of a magnetic field.

Advanced Deep Learning for microseismic events prediction for hydraulic fracture treatment via Continuous Wavelet Transform

Understanding hydraulic fracture propagation events would enable operators to estimate the fracture geometry, understand formation/fracture interactions, and estimate the total microseismic events cloud. This paper introduces a new method for understanding the dynamic fracture propagation events using a signal processing technique. Detection of the dynamic fracture event using continuous wavelet transform (CWT) is used to train a deep learning model with microseismic events to predict this cloud for every hydraulic fracture job. The deep learning model is used for the same formation. The CWT for treatment pressure is a convolution process that involves the application of a wavelet signal to the acquired pressure signal in a continuous manner. The wavelet is stretched, or compressed, and is moved along the acquired pressure signal, acting as a generic microscope to highlight small changes in the treating pressure signal. Using CWT as a mathematical microscope to discern diverse signals has been adopted by numerous engineering and medical applications since the 1990s.A normalized CWT scalogram for fracture-treating pressure is thus created as a unique representation of each fracture propagation mode in the hydraulic fracturing job. The new technique is calibrated with several fracture simulation runs and real field data using the previous techniques like moving reference point (MRP). That previous technique which has been previously validated through fracture simulation, is used as a calibration for the new normalized CWT scalogram technique. The technique was finally calibrated by comparing it with micro-seismic events recorded by the Marcellus Shale Energy and Environment Laboratory (MSEEL).The results of this comparison were exceptionally accurate. It can be used to train a deep learning model that can be used to estimate the cloud of microseismic events for hydraulic fracture jobs in Marcellus shale. The new deep learning framework uses CWT to convert the treating pressure during hydraulic fracture propagation to dimensionless representation (normalized CWT scalogram) which acts as a mathematical microscope for the fracture treating pressure on different wavelet stretch or compressions, enabling the detection of the major changes in the treating pressure then train the deep learning model to estimate microseismic events cloud.

PGD in thermal transient problems with a moving heat source: A sensitivity study on factors affecting accuracy and efficiency

AbstractThermal transient problems, essential for modeling applications like welding and additive metal manufacturing, are characterized by a dynamic evolution of temperature. Accurately simulating these phenomena is often computationally expensive, thus limiting their applications, for example for model parameter estimation or online process control. Model order reduction, a solution to preserve the accuracy while reducing the computation time, is explored. This article addresses challenges in developing reduced order models using the proper generalized decomposition (PGD) for transient thermal problems with a specific treatment of the moving heat source within the reduced model. Factors affecting accuracy, convergence, and computational cost, such as discretization methods (finite element and finite difference), a dimensionless formulation, the size of the heat source, and the inclusion of material parameters as additional PGD variables are examined across progressively complex examples. The results demonstrate the influence of these factors on the PGD model's performance and emphasize the importance of their consideration when implementing such models. For thermal example, it is demonstrated that a PGD model with a finite difference discretization in time, a dimensionless representation, a mapping for a moving heat source, and a spatial domain non‐separation yields the best approximation to the full order model.

Energetic properties of the (fast) charging and driving of an electric vehicle - a Ragone analysis

The energy efficiency of EVs is analysed for the charging and for the driving process where real parameters of a product of the automotive industry are considered. The efficiency in the charging mode is analysed and represented in function of the charging time. The maximum charging power allowed by the manufacturer is defining the lowest efficiency. After the calculation in a situation with an ideal charging station the influence of the resistance of the charging cable is taken into consideration. For the driving mode, the efficiency is estimated with the help of a special tool called ?The Theory of Ragone plots?. The driving efficiency is calculated for the maximum possible propulsion power of the car, and represented in a dimensionless Ragone representation. The rated power of the car is represented in reference to the maximum possible power that can deliver the car battery.

Non-similar analysis of MHD bioconvective nanofluid flow on a stretching surface with temperature-dependent viscosity

In this research, we explore the potential of magnetohydrodynamic (MHD) bioconvective nanofluids with varying viscosity through non-similarity analysis, aiming to enhance the thermal performance of biological and industrial systems. Recent years have witnessed significant advancements in energy applications, motivating our investigation. To enhance heat transfer, we employ propylene glycol as the base liquid, incorporating silicon dioxide and molybdenum disulfide nanomaterials. This unique configuration enables efficient heat dissipation and accommodates inner heat sources or sinks. Our model relies on partial differentials, and we derive a non-similar dimensionless representation of the governing system using appropriate transformations. We utilize ordinary differential equations (ODEs), approximating local non-similarity (LNS), to estimate transformed non-similar partial differential equations (PDEs). Numerical simulations are performed using the bvp4c algorithm. Throughout our analysis, we present various physical parameters, demonstrating their importance in fluid flow and thermal transport through graphical and tabular representations. Our findings show that alterations in the magnetic parameter lead to changes in fluid velocity and temperature profiles. Similarly, adjustments in the viscosity parameter affect fluid velocity, and variations in the temperature-dependent viscosity parameter influence velocity profiles, with temperature profiles responding to changes in the Brinkman number and heat source parameter. Additionally, we observe concentration profile adjustments with shifts in the Schmidt number and enhanced migration of particles or components within the nanofluid with rising Soret numbers, impacting the concentration profile. Furthermore, an increased Peclet number positively influences microorganism profiles, while the Lewis number exhibits contrasting behavior. To further validate our approach, we present comparative analyses of skin friction coefficients and Nusselt numbers in tabular form. Our primary objective in this study is to formulate non-similar transformations tailored to the specific problem under consideration. These transformations aim to produce accurate and efficient results, providing valuable insights for future research endeavors in the field of nanofluid flows.

Non-similar approach on the MHD Carreau nanofluid flow with quadratic radiation and Soret-Dufour effects

The present study aims to investigate the influence of magnetohydrodynamic (MHD) Carreau nanofluid flow past a stretching cylinder with quadratic Rosseland heat radiation. This paper examines the consequences of the Soret-Dufour effects when considering the influence of thermophoresis and Brownian effects. The convective and diffusive boundary conditions have been implemented. The modeled mathematical system of non-linear partial differential equations (PDEs) is transformed into a dimensionless representation using a non-similar approach. The ensuing set of dimensionless equations are solved numerically with local non-similarity method (LNM) aided by the finite difference algorithm. The findings of the study unveil that the presence of the Dufour and Soret effect declines the heat transfer and mass transfer rates, respectively. It is also noted that flow profiles are more profound in the case of stretching cylinder configuration. Per unit increase in the hydrodynamic slip parameter augments the drag coefficient by 35.87% and 33.40% for cylinder and sheet configurations, respectively. The present study has potential applications in biomedicine, such as targeted drug delivery, hyperthermia, theranostics and cardiovascular treatments.

Application of a fluid model in the local energy approximation to numerical simulation of the ionization wave front of negative polarity in He

The fluid equation model in the local energy approximation is applied to computer simulation of the negative ionization wave front in He stimulated by the applied electrostatic field. Numerical calculations are carried out based on 1D dimensionless representation of the equation system, in the context of streamer propagation in this gas. Pooling the known experimental and theoretical data on the ionization-transport coefficients of electrons in He enabled their approximations by the analytical functions within the range of the reduced electric field 10−3–104 Td and integration into the calculation code. The front propagation velocity and spatial thickness along the direction of its propagation, defined by the level 0.1–0.9 of the maximum electric field ahead of the front, and the electron density close on the front tail are calculated depending on the applied electric field strength and presented in the work. The obtained results allowed estimating the ratios of the electron momentum and mean energy relaxation rates to the rate of the changes induced in the gas by the front propagation. The local equilibrium condition of the fluid model validity requires the ratios to exceed the unity repeatedly. Their values are shown to decrease with an increase in the electric field, thus restricting its range from above the approved model application. For example, the admission of their excess over 10 to be sufficient for the electron relaxation within the front leads to the restriction of the application range by about 600 Td (the mean electron energy about 46 eV).

Steady-state thermodynamics: Description equivalence and violation of reservoir independence.

For stochastic lattice models in spatially uniform nonequilibrium steady states, an effective thermodynamic temperature T and chemical potential μ can be defined via coexistence with heat and particle reservoirs. We verify that the probability distribution P_{N} for the number of particles in the driven lattice gas with nearest-neighbor exclusion in contact with a particle reservoir with dimensionless chemical potential µ^{*} possesses a large-deviation form in the thermodynamic limit. This implies that the thermodynamic properties determined in isolation (fixed particle number representation) and in contact with a particle reservoir (fixed dimensionless chemical potential representation) are equal. We refer to this as description equivalence. This finding motivates investigation of whether the effective intensive parameters so obtained depend on the nature of the exchange between system and reservoir. For example, a stochastic particle reservoir is usually taken to insert or remove a single particle in each exchange, but one may also consider a reservoir that inserts or removes a pair of particles in each event. In equilibrium, equivalence of pair and single-particle reservoirs is guaranteed by the canonical form of the probability distribution on configuration space. Remarkably, this equivalence is violated in nonequilibrium steady states, limiting the generality of steady-state thermodynamics based on intensive variables.

Entropy analysis in single phase nanofluid in square enclosure under effectiveness of inclined magnetic field by executing finite element simulations

One of the important phenomena concerning with dynamical and thermal attributes of heat transferring liquids is the measure of randomness generated at molecular level. This randomness in the system is generated due to presence of multiple factors which includes extensive heat transfer, strong magnetic field and viscous diffusion. To control and minimize disorder ness the concept of entropy is taken into account. Minimization in entropy is valuable in optimization of design objectivity in engineering structures. In addition, it measures and controls exergy loss to generate highly efficient systems likes heat exchangers, heat pumps, power plants, nuclear reactors, air conditioners and so many. So, the prime objective of this work is to analyze entropy in square enclosure filled with water and containing Copper (Cu) particles. Convection in the considered physical domain is generated by providing uniform temperature at upper wall while keeping rest of boundaries cold. In view of velocity field distribution is concerned all the extremities of cavity are at no slip condition. Inclined magnetic field is also employed to measure change in entropy due to magnetization. Formulation of problem expressing thermophysical relation of inducted nanoparticles in manifested in the form dimensionless representation. Patel and Brinkman models for effective thermal conductivity and viscosity are opted to visualize their effectiveness in entropy change. Finite element computations are performed to simulate results showing the impact of flow controlling parameters on associated distributions. Three different types of entropy namely, magnetic, thermal and viscous are measured against different parameters. Quantity of interest like average heat flux coefficient is also measured. It is deduced from the analysis that by increasing nanoparticle volume fraction thermal entropy increases whereas viscous and magnetic entropy uplifts. In addition, it is noticed that by increasing Hartmann number entropy and velocity of fluid decrements. Uplift in temperature magnitude is observed against elevating values of Rayleigh number. It is concluded that employment of magnetic field will assist in controlling flow, thermal and irreversibility phenomenon.

Mixed convective thermal transport in a lid-driven square enclosure with square obstacle

The prime motive of this disquisition is to scrutinize simultaneous aspects of external forcing mechanism and internal volumetric forces on non-Newtonian liquid filled in square enclosure. Inertially driven upper lid is assumed by providing constant magnitude of slip velocity whereas thermal equilibrium is disturbed by assuming uniform temperature at lower boundary and by keeping rest of walls as cold. To enhance thermal diffusion transport with in the flow domain cold as well as adiabatic temperature situation is provided. In view of velocity constraints all the extremities at no-slip except the upper wall which is moving with ULid. Formulation is attained in dimensional form initially and afterwards variables are used to convert constructed differential system into dimensionless representation. A numerical solution of leading formulation is sought through Galerkin finite element discretization. Momentum and temperature equations are interpolated by quadratic polynomials whereas pressure distribution is approximated by linear interpolating function. Domain discretized version is evaluated in view of triangular and rectangular elements. Newton’s scheme is employed to resolve the non-linearly discretized system and a matrix factorization based non-linear solver renowned as PARADISO is used. Validation of results is ascertained by forming agreement with existing studies. In addition, grid independence test is also performed to show credibility of performed computations. Stream lines and isothermal contours patterns are portrayed to evaluate variation in flow distributions. Kinetic energy and local heat flux for uniform and non-uniform heating situations are also divulged in graphical and tabular formats. Increase in Reynold number produces decrease in kinetic energy of fluid. Enhancement in Grashof number causes enrichment of thermal buoyancy forces due to which Nusselt number uplifts. Clock wise rotations increase against upsurge in magnitude of Reynold number which is evidenced form stream lines. Squeezing of secondary vortex against Prandtl number arises due to dominance of viscous forces.

Multi-Dimensional Regression Models for Predicting the Wall Thickness Distribution of Corrugated Pipes.

Corrugated pipes offer both higher stiffness and higher flexibility while simultaneously requiring less material than rigid pipes. Production rates of corrugated pipes have therefore increased significantly in recent years. Due to rising commodity prices, pipe manufacturers have been driven to produce corrugated pipes of high quality with reduced material input. To the best of our knowledge, corrugated pipe geometry and wall thickness distribution significantly influence pipe properties. Essential factors in optimizing wall thickness distribution include adaptation of the mold block geometry and structure optimization. To achieve these goals, a conventional approach would typically require numerous iterations over various pipe geometries, several mold block geometries, and then fabrication of pipes to be tested experimentally—an approach which is very time-consuming and costly. To address this issue, we developed multi-dimensional mathematical models that predict the wall thickness distribution in corrugated pipes as functions of the mold geometry by using symbolic regression based on genetic programming (GP). First, the blow molding problem was transformed into a dimensionless representation. Then, a screening study was performed to identify the most significant influencing parameters, which were subsequently varied within wide ranges as a basis for a comprehensive, numerically driven parametric design study. The data set obtained was used as input for data-driven modeling to derive novel regression models for predicting wall thickness distribution. Finally, model accuracy was confirmed by means of an error analysis that evaluated various statistical metrics. With our models, wall thickness distribution can now be predicted and subsequently used for structural analysis, thus enabling digital mold block design and optimizing the wall thickness distribution.

Unique Relationship Between Rate and Cumulative Flow: A Property of Infiltration and Evaporation in Soils

AbstractInfiltration and evaporation are key components of the Earth hydrological cycle that depend on soil properties and climatic conditions. Here we show that, for both infiltration and evaporation, the water flow rate is a unique function of the cumulative flow in the soil. Hence, for a given soil, infiltration and evaporation curves corresponding to different wetting and drying rates are represented by one curve characterizing the capacity of the system for the relevant process. This insight reveals a natural and powerful property that shapes water interactions between soil and atmosphere. A quantitative expression of the evaporation capacity curve is proposed. A dimensionless representation of this model offers a simple tool to predict evaporation under natural soil and climatic conditions that vary in space and time. The infiltration and evaporation capacity models can be easily embedded in Earth System Models to estimate the hydrological response at various spatial and temporal scales.

Self-similarity of spanwise rotational motions’ population trends in decelerating open-channel flow

Decelerating open-channel flow is a type of flow that gradually moves forward with decreasing velocity and increasing water depth. Although all flow parameters change along the streamwise direction, previous studies have revealed that these parameters' vertical distributions at different sections can be universally described with a single profile when being nondimensionalised by appropriate scales. This study focuses on the population trends of spanwise rotational motions at various sections along the main flow direction by particle imaging velocimetry (PIV) measurement. The wall-normal population distributions of density, radius, swirling strength, and convection velocity of the prograde and retrograde motions show similar trends in uniform open-channel flows. The dimensionless representation is invariant along the main flow direction. This study's results indicate the self-similar characteristic of population trends of spanwise rotational motions prevails in decelerating open-channel flow.

Investigation of сomputational meshes for modeling the air dynamics in a vortex tube channel by OpenFOAM software

A vortex tube is a simple device with no moving parts that separates a swirling gas stream into two vortexes that differ in temperature, usually above and below the temperature of the inlet gas. This paper presents a mathematical model of a vortex tube which is based on gas dynamics laws and is supplemented by a k-ω turbulence model. A description of the technique for constructing a finite volume mesh with definition of the near-wall region based on the blockMesh utility is given when the conditions for the uniformity of the mesh elements are met while maintaining their orthogonalization. The numerical solution is carried out on a computational cluster using the sonicFoam solver of the OpenFOAM free software. Three series of numerical simulation experiments were carried out to determine the temperature distribution in the channel of a cold air diaphragm depending on the diaphragm diameter. One of the three computational mesh scales considered in this work is used. It is shown that mesh size reduction leads to convergence of simulation results. It is also demonstrated the qualitatively correct results can be obtained by generating a mesh in which the average linear size of a finite volume does not exceed 0.4 mm (0.025 in dimensionless representation). To improve the accuracy of quantitative data, an even greater computational mesh size reduction is required; in particular, a fine mesh with an average linear size of the finite volume less than 0.02 is considered in this work. The results obtained on a fine mesh are in a qualitative agreement with the results determined using a coarser mesh. However, the numerical values can differ significantly, which is shown by the calculations for the cold air diaphragm of large diameter. Thus, the computational time increases with decreasing mesh size, which implies that the construction of a computational mesh for vortex tube modeling requires finding a balance between the quality of results and the simulation time.

Temperature-baric dependence of the effective thermal conductivity of amorphous and polycrystalline rocks

The paper presents the results of experimental studies of the temperature-baric effective thermal conductivity of a number of sandstones and granites. For the presentation we have chosen four sandstone samples from Dagestan and Tyumen deposits, two of which have a prevailing crystalline ordering, and two – a structure close to amorphous, and two samples of granite from Dagestan and Kola deposits. The experiment was provided by the absolute stationary compensation method of flat plates in the temperature range of 273–523 K in the range of hydrostatic pressures from atmospheric to 400 MPa. The results confirmed the proposed low-parameter model. The measured values of the thermal conductivity of the samples at 300 K were in the range from 0.7 to 3.5 W/m K. The temperature dependence in the considered range in all cases is well described by the power-law dependence. In addition, we have found a fairly significant correlation between the baric dependence of the effective thermal conductivity itself in the normalized dimensionless representation and the baric dependence of the exponent in the temperature dependence. This correlation can be traced for all studied samples of granites and sandstones and it makes possible to reduce the number of independent parameters. We have also shown that for sandstones with an amorphous structure, a simultaneous increase in temperature and pressure can lead to a rather significant total contribution. If taking into account the temperature-baric dependence of the effective thermal conductivity for rocks with a more common predominantly crystalline order, as noted by a number of authors, is not necessary due to the compensation of the pressure and temperature contributions, then for significantly amorphous rocks these contributions are summed up, and the total contribution may turn out to be significant.

Breakthrough Investigation of Advective and Diffusive Transport in a Porous Matrix with a Crack

Fluid flow and transport processes in fractured porous media are of particular interest for geologists and in the material sciences. Here a systematic investigation is presented, dealing with a generic geometric set-up of a porous matrix with a crack. In such a combined porous medium/free fluid system flow patterns have been examined frequently, while the resulting transport patterns have attracted less attention. Using numerical modeling with finite elements the problem is approached using a dimensionless formulation. With a reduced number of dimensionless parameter combinations (Darcy-, Peclet- and Reynolds-numbers) solution dependencies are examined in parametric sweeps. Breakthrough curves are fitted in comparison to those of 1D model approaches, yielding effective diffusivities and velocities. The computations reveal highest sensitivity concerning the angle between crack axis and flow direction, followed by the Peclet number and the crack axes ratio. As a dimensionless representation is used the results are scale independent. Thus, they deliver estimations concerning effective heat and solute transport parameters that can be relevant in all application fields.

Predicting the co-extrusion flow of non-Newtonian fluids through rectangular ducts – A hybrid modeling approach

Co-extrusion has become the state-of-the-art process technology in nearly all application areas of polymer processing. By combining different types of polymeric materials within multilayer structures, products with a broad range of property profiles can be obtained for advanced applications. Design of co-extrusion dies and feedblock systems requires extensive knowledge of process and material behavior. To accurately describe the shear-thinning behavior of polymer melts in co-extrusion processes and to predict characteristic process quantities, numerical methods are essential. We present a hybrid approach to modeling stratified co-extrusion flows of two power-law fluids through rectangular ducts. By applying the theory of similarity and transforming the problem into dimensionless representation, we identified four independent influencing parameters that fully describe the flow situation: (i) the power-law index of the first fluid, (ii) the power-law index of the second fluid, (iii) the dimensionless position of the interface, and (iv) the ratio of dimensionless pressure gradients. We varied these input parameters within ranges that cover almost all combinations of industrial relevance, creating in the process a set of more than 44,000 design points. By means of the shooting method, numerical solutions were obtained for (i) pressure-throughput behavior, (ii) interfacial shear stress, (iii) interfacial velocity, and (iv) individual volume flow rates. Finally, we used symbolic regression based on genetic programming to model these target quantities as functions of their influencing parameters and obtain algebraic relationships between them. Our mathematical models thus enable accurate prediction of several characteristic process quantities in two-layer co-extrusion flows of shear-thinning fluids through rectangular ducts. The models are not restricted to the field of polymer processing, but can be used in all industrial applications that involve such co-extrusion flows.

En route towards a comprehensive dimensionless representation of precipitation processes

Precipitation of (nano-) particles is a unit operation for the preparation of suspensions. Despite its widespread use, no general understanding is established of how different operating conditions, such as mixing rates or reactant concentrations, affect the precipitation outcome (e.g. the particle size distribution). We obtain overarching relations between the operating conditions and the precipitation outcome by deriving dimensionless numbers governing the precipitation process. In particular, we consider the interdiffusion of two chemical compounds reacting to a sparingly soluble salt by coupling the reaction–diffusion equations for the solute concentrations, to a population balance equation for the evolution of the dispersed phase including nucleation and growth. We vary the relevant process parameters for different chemical systems and uncover three dimensionless numbers, which fully determine the precipitation outcome under the assumption of fast chemical reactions. Two of these dimensionless numbers are Damköhler numbers, which put the relevant mixing kinetics in relation to the relevant time scales for the nucleation and the growth kinetics, respectively. The third dimensionless number corresponds to a dimensionless solid concentration. Simple functional expressions for the Damköhler numbers valid for any chemical system allow estimating whether the precipitation product is controlled by mixing, or solely by the kinetics of solid formation. In the mixing-controlled regime, scaling laws relate the mean particle sizes and the number of particles to the Damköhler number.