Analytical Flow Model Research Articles

Coupled model for liquid lithium plasma facing components

Numerical analysis provides the design choice and operating window of liquid metal Plasma Facing Components (PFC) concepts. Coupled analysis of boundary plasma together with the surrounding boundary structures is required. To achieve this goal, PPPL is developing a comprehensive multi-physics model for modeling of PFCs in fusion devices. The model includes the fluid-kinetic code SOLPS-ITER and the flow and heat transfer code CFX from ANSYS. SOLPS-ITER was augmented with a liquid metal boundary condition algorithm, allowing direct two-way coupling of the plasma analysis with the two-dimensional analytical slab flow model which includes heat convection in the liquid metal PFC. The target heat flux resulting from this coupled analysis is used as a boundary condition for detailed 3D Computational Fluid Dynamics (CFD) Magneto Hydro Dynamics (MHD) and heat transfer analysis. A new formulation of MHD equations is introduced in the numerical procedure ensuring current conservation of the discretized equations. Results of the 3D analysis are used for final validation of the coupled model. A PFC design where a porous wall is used to stabilize the liquid metal surface, while MHD drive is used to push the liquid metal flow inside the PFC, will be investigated in the regimes where vapor shielding is created for enhanced volumetric plasma heat dissipation.

Extended analytical model of Tesla turbine with advanced modelling of velocity profile in minichannel between corotating disks with consideration of surface roughness

Consideration of roughness effects in the flow in a minichannel has been a major scientific problem for many decades. Roughness can alter the momentum diffusion, heat transfer conditions or laminar-turbulent transition. These effects are even more pronounced in minichannel flows where the roughness can occupy a large part of the cross-section. Modelling methods applied so far usually fall short in internal flows with high relative roughness. The presented paper pertains to the analytical flow model in Tesla turbine components with consideration of roughness on the rotor walls. The model uses the equivalent sand grain approach to modify dynamic viscosity in the governing equations to achieve a desired downward shift of the dimensionless velocity profile. The model solves two-dimensional equations of continuity, momentum and energy. The semi-empirical function was derived to consider the change in the shape of the radial velocity. The applied model incorporates Euler's turbomachinery equation to determine the influence of roughness on the turbine performance under varied operating conditions. Roughness shortens the streamlines inside the rotor, but the overall turbine's performance is improved. The roughness equal to 10−5 m increased the power generated and isentropic efficiency by factors of 3 and 2.5, respectively, compared to the smooth rotor.

Compressible Flow Through Flat Valve Seals at Microscale Displacements

Abstract Existing analytical flow models for predicting flow rates at microscale seal displacements are limited to two separate domains. The first assumes a small channel length to height aspect ratio at relatively large seal displacements. The second assumes a large channel length to height aspect ratio at relatively small seal displacements. A piecewise analytical model for compressible flow is developed here to enable predicting flow rates in valves with fluid pathways of any aspect ratio. The new model is validated by numerical studies and experiment. The results are applicable to flat valve seals having a cylindrical seal boss feature with fluid passage length to height aspect ratios ranging from 3.3 to 800. The new model is particularly useful for the design of microvalves and macroscale valves with small actuator displacements.

Rock fines breakage by flow-induced stresses against drag: geo-energy applications

The paper presents a strength-failure mechanism for colloidal detachment by breakage and permeability decline in reservoir rocks. The current theory for permeability decline due to colloidal detachment, including microscale mobilisation mechanisms, mathematical and laboratory modelling, and upscaling to natural reservoirs, is developed only for detrital particles with detachment that occurs against electrostatic attraction. We establish a theory for detachment of widely spread authigenic particles due to breakage of the particle-rock bonds, by integrating beam theory of particle deformation, failure criteria, and creeping flow. Explicit expressions for stress maxima in the beam yield a graphical technique to determine the failure regime. The core-scale model for fines detachment by breakage has a form of maximum retention concentration of the fines, expressing rock capacity to produce breakable fines. This closes the governing system for authigenic fines transport in rocks. Matching of the lab coreflood data by the analytical model for 1D flow exhibits two-population particle behaviour, attributed to simultaneous detachment and migration of authigenic and detrital fines. High agreement between the laboratory and modelling data for 16 corefloods validates the theory. The work is concluded by geo-energy applications to (i) clay breakage in geological faults, (ii) typical reservoir conditions for kaolinite breakage, (iii) well productivity damage due to authigenic fines migration, and (iv) feasibility of fines breakage in various geo-energy extraction technologies.

An analytical model for saturated nonuniform laminar flow through rough fractures

Estimating the flow rate accurately through a single rough fracture poses a fundamental challenge. This study presents an analytical model for single-phase saturated nonuniform laminar flow through rough fractures. The flow analytical model of the fractures is constructed using homotopy thinning methods, average inertia approaches, and shortest path techniques, thereby simplifying the nonuniform flow problem to solving the integral of the incircle aperture function, from which the modified average Darcy velocity considering inertial effects is expressed. The flow equations in the global coordinates are then derived. The validity of the proposed model is verified by comparing it with flow simulations with the Navier–Stokes equations, perturbation solutions, previously corrected Reynolds equations, and experimental flow tests. The results obtained from the proposed model agree very well with those from simulations and experiments. The effective errors Di range within ±4.0% of the simulation results with an arithmetic mean of |Di| equal to 1.03%. As surface roughness increases, the proposed model can effectively capture the inertial behaviors arising from the nonuniform flow field. Compared to the previous corrected Reynolds equations and perturbation solutions, the proposed model demonstrates enhanced accuracy and applicability, introducing a new approach to address nonuniform flow problems in rough fractures with more complex geometries.

Analytical Dynamic Energy-Carbon Flow Model and Application in Cost Allocation for Integrated Energy Systems

Analytical Dynamic Energy-Carbon Flow Model and Application in Cost Allocation for Integrated Energy Systems

Analytical modeling of 2D groundwater flow in a semi-infinite heterogeneous domain with variable lateral sources

<abstract> <p>In nature, aquifers are usually composed of distinct kinds of media, i.e., heterogeneous domains rather than homogeneous domains. Groundwater level and flow changes in such domains are more complicated than those in homogeneous domains; thus, building a mathematical model for addressing groundwater flow in heterogeneous aquifers is the present research goal. In conventional research on similar topics, many one-dimensional (1D) analytical models have been presented, but it is challenging to simulate real-world scenarios. This study develops a two-dimensional (2D) analytical model for modeling groundwater flow in a conceptual sloping heterogeneous domain imposed by variable recharge. This model can consider distinct slope angles, medium heterogeneity, and any type of lateral recharge for a semi-infinite domain. The results indicate that groundwater level and flow discharge are greatly affected by the abovementioned factors. The recharge intensity significantly affects the peak of the groundwater level. For example, when the recharge rate increases by 30%, the peak water level increases by 50% as the groundwater flows from the sandy loam zone to the loam zone. The loops delineating the relationship between discharge and groundwater level for different bottom slopes cannot become close for heterogeneous aquifers. The presented 2D analytical model can simulate and better predict results of groundwater changes than previous 1D analytical models. Further, this model can simultaneously consider the effect of varying recharge over time and space on groundwater level change.</p> </abstract>

МОДЕЛЮВАННЯ ЕВАКУАЦІЇ ЛЮДЕЙ ПРИ ПОЖЕЖІ ЗА ДОПОМОГОЮ ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ PATHFINDER

This research analyses scientific publications that highlight the problems of evacuation of people during emergencies and the latest methods, techniques and strategies. It is determined that the PATHFINDER software complex gives a more accurate calculation compared to the simplified analytical model. The PATHFINDER software complex allows to simulate evacuation in various buildings and areas. Moreover it gives a wider range of possibilities, such as: simulation of evacuation of people with disabilities; ability to set and adjust the speed of agents in different sections of the escape route; the presence of a function that regulates the onset of movement of agents in a given behaviour. In this work the computer simulation of the actual time of evacuation of people from the integral property complex of industrial and household facilities was carried out. The duration of the evacuation of people from the rooms of buildings and structures bases on the model of the movement of people to the exit in one of the following ways: based on a simplified analytical model of human flow; based on a mathematical model of the individual-flowing movement of people from a building or structure; based on a simulation-stochastic model of human flows. These calculations were performed in accordance with the recommendations and instructions using the PATHFINDER software for the two most likely fire scenarios. According to the scenario, the fire occurred in the room with the highest fire-hazardous load or in the room with the smallest volume: scenario 1 - fire occurs in the hot shop; scenario 2 - a fire occurs in the administrative room. The software provides an opportunity to quickly calculate various ways of evacuating people from the rooms. The use of PATHFINDER software gives more accurate results than the calculation given in regulatory document, due to the greater detalization of the evacuation calculation, and also helps to avoid possible errors and reduce calculation errors.

Production performance analysis of a continental shale oil reservoir in Bohai Bay basin

Due to the extremely low permeability of shale formations, the combination of horizontal well and volume fracturing has been proposed as an effective technique to improve the production of Dagang continental shale oil reservoirs. Based on the flow material balance method (FMB) and straight-line analysis (SLA) method, the stimulated reservoir volume (SRV) and drainage volume are determined to identify the flow regimes of the seepage mechanism of shale oil reservoirs. To resolve the challenges of multi-scaled flow regimes and bottom hole pressure (BHP) variation before and after pumping in shale oil wells, a multi-linear analytical flow model was established to predict the future production and the final expected ultimate recoverable oil (EURo) after fitting the historical production dynamics. Based on the results, it can be concluded that the flow regime of a shale oil well in production can be divided into two stages consisting of linear flow within SRV and composite flow from the un-stimulated area to SRV. The effects of fracturing operation parameters, such as fracturing fluid volume and sand/liquid ratio, on shale oil productivity, are analyzed, and insightful suggestions are drawn for the future development of this pay zone.

Numerical and analytical flow models in ecological channels with interaction of vegetation and freshwater

Aquatic vegetation interferes with river hydrodynamics, thus affecting the mass transport and energy transfer in an ecosystem. The flow over submerged vegetation is characterized by a complex velocity profile and multiple turbulence structures, which have been usually simulated using cylinders or strips in previous studies. Because the simplified vegetation configuration may hide or amplify some physical processes found in natural conditions, we investigate the velocity distribution and turbulence structure in foliaged vegetation flows using both analytical and numerical approaches. The main innovations and findings can be summarized as follows: 1) numerical and analytical models adopted in this paper accurately simulate the flow velocity profile in vegetated channel; 2) the Karman constant is found to be unsuitable for complex vegetation morphologies, so we proposed adjusted coefficient; 3) an image processing method is adopted to quantify the vegetation morphology accurately; 4) the existing mixing-layer thickness formula is found to be unsuitable for vegetation with leaves, an improved formula is proposed showing high correlation coefficient (0.9562) between measured and predicted data; 5) to ensure applicability to larger-scale hydrodynamic simulations, an analytical expression of Manning’s coefficient is proposed based on an analytical multi-layer flow velocity model. These research findings can provide theoretical support for the design of vegetated river and ecological restoration.

Flow physics and loss mechanisms of tip leakage flow in variable-blade-pitch-angle ducted fans

This paper investigates a ducted fan, which is able to adjust the output characteristics to meet different requirements of VTOL (Vertical Take-Off and Landing) aircrafts at various states, e.g., take-off, landing and high-speed cruise. The variable-blade-pitch-angle method is employed for the ducted fan, so that the fan can present more various performance. The loss mechanisms of the ducted fan are analyzed at seven different blade pitch angles ranging from −15 degrees to 15 degrees, and the importance of the tip leakage flow on the aerodynamic performance of the fan is highlighted. Results show that there exists a critical value for the blade pitch angle, and below the critical value, the tip leakage vortex sweeps to the adjacent blade tip and simultaneously causes the double tip leakage, which results in the high relative-total-pressure loss and a severe deterioration of rotor efficiency. The flow physics and loss mechanisms are discussed in detail. In addition, an analytical model of the tip leakage flow is established, and the effects of blade solidity on the critical blade pitch angle are discussed. The results provide useful guidelines on the design and the control of the variable-blade-pitch-angle fans.

On the near-field interaction of vertically offset turbulent plumes

The flow in and around a pair of plumes from sources that are vertically and horizontally offset is investigated. An analytical potential flow model is developed using an adapted version of the Milne–Thomson circle theorem to represent the flow due to adjacent circular and point sinks. This approximates the horizontal section through offset plumes, which have differing radii at the same vertical position. The predictions of this model are compared against Reynolds-averaged Navier–Stokes (RANS) simulations of the same system. These yield time-averaged results and so are particularly suitable for investigating the relatively weak entrainment field. Single and double plume results from RANS are also presented to compare with known results. Good agreement is found between the features in the analytical model and in the numerical solutions including the location of the stagnation point between the two plumes.

Physics-informed neural networks for integrated traffic state and queue profile estimation: A differentiable programming approach on layered computational graphs

This paper presents an integrated framework for physics-informed joint traffic state and queue profile estimation (JSQE) on freeway corridors, utilizing heterogeneous data sources. The integrated modeling framework aims to maximize the benefits of information from physics-informed analytical traffic flow models and field observations while leveraging joint estimation spaces. Potential inconsistencies between different modeling components must be acknowledged and carefully managed to ensure model feasibility. To minimize such inconsistencies, a nonlinear programming model is formulated for the JSQE problem, taking into account traffic flow models and observations from both corridor and local segment levels. At the corridor level, a fluid queue approximation is employed to model queuing dynamics. Assuming polynomial arrival and departure rates, critical system variables such as time-dependent delay, travel time, and queue length are analytically derived. To preserve the differentiability of traffic state variables, continuous space–time distribution functions are introduced to model traffic flow variables and partial differential equations. A computational graph is constructed to represent the nonlinear programming model in a layered structure, which is then solved using a forward–backward method. Comprehensive numerical experiments based on real-world and hypothetical datasets are designed to demonstrate the effectiveness of the proposed framework.

An Approximate Analytical Model of a Jet Flow with Mach Reflection and Pulsed Energy Supply at the Main Shock

The supersonic flow of a reactive gas mixture with Mach reflection of oblique shocks and pulsed energy supply at the Mach stem is considered within the framework of the Chapman–Jouguet theory. An approximate analytical model is proposed that quickly determines the shape and size of the shock-wave structure as well as the flow parameters in various flow regions. As an example of the application of the proposed analytical model, the “first barrel” of a highly overexpanded jet flow of an air-methane mixture with a high supersonic velocity, is studied. Flows of hydrogen–air and hydrogen–oxygen mixtures were also considered for comparison with preceding numerical results. The height of the triple point of the Mach reflection is determined in the presence of a change in the chemical composition of the mixture and an isobaric pulsed energy supply at the main shock.

Interpreting Concentrations Sampled in Long-Screened Wells with Borehole Flow: An Inverse Modeling Approach.

New approaches are needed to assess contaminant mass based on samples from long-screened wells and open boreholes (LSW&OB). The interpretation of concentration samples collected in LSW&OB is complicated in the presence of vertical flow within the well. In the absence of pumping (i.e., ambient conditions), the well provides a conduit for flow to occur between aquifer layers or fractures as a result of head differences. Under pumping conditions, vertical borehole flow may vary with depth depending on far-field heads and hydraulic conductivity; furthermore, if pumping fails to overcome ambient gradients, outflow from the well to the aquifer may occur. Concentration samples thus represent flow-weighted averages of formation concentrations, but the averaging process is commonly unknown or difficult to identify. Recognition of the importance of borehole flow has motivated the use of multi-level wells, packers, and well liners; however, LSW&OB remain common for numerous reasons, including cost, multi-purpose design requirements (e.g., pump-and-treat, water supply), logging, and installation of instrumentation. Here, we present a simple analytical model for flow and transport within a well and interaction with the surrounding aquifer. We formulate an inverse problem to estimate formation concentration based on sampled concentrations and data from flowmeter logs. The approach is demonstrated using synthetic examples. Our results (1) underscore the importance of interpreting sampled concentrations within the context of hydraulic conditions and aquifer/well exchange; (2) demonstrate the value of flowmeter measurements for this purpose; and (3) point to the potential of the new inverse approach to better interpret results from samples collected in LSW&OB.

Approximate Analytical Model of Jet Flow with Mach Reflection and Pulsed Energy Supply at the Main Shock

Approximate Analytical Model of Jet Flow with Mach Reflection and Pulsed Energy Supply at the Main Shock

Analytical Model for the Material Flow during Cold Rolling

Analytical Model for the Material Flow during Cold Rolling

Tunnel face stability model for layered ground with confined aquifers

Confined aquifers with high fluid pressures pose severe risks for the stability of the face of earth-pressure-balanced shields. This study presents a method to compute the limit face pressures in the layered ground with confined aquifers. Seepage analyses based on the finite element method (FEM) are conducted to investigate the underground water flow patterns in the above ground due to shield tunneling. These analyses show: (1) the presence of confined aquifers enhances the hydraulic gradient around the tunnel face; (2) the hydraulic heads display distinct distribution patterns in the confined aquifers and adjacent aquitards; (3) the hydraulic gradients exhibit abrupt jumps at the aquifer-aquitard interface. These characteristics are in strong contrast to the distribution functions assumed in existing studies. Therefore, a new analytical flow model is proposed based on the hydraulic fields obtained from the seepage analyses. An approach to evaluate necessary face pressures is constructed by combining the flow model and a limit equilibrium model (LEM). By comparing against the results from drained FEM analyses under seepage flow, this paper shows that the proposed LEM can reasonably represent the influences of confined aquifers on the critical face pressures and the collapse mechanism of soils in front of the tunnel face.

Full-scale spatio-temporal traffic flow estimation for city-wide networks: a transfer learning based approach

The full-scale spatio-temporal traffic flow estimation/prediction has always been a hot spot in transportation engineering. The low coverage rate of detectors in transport networks brings difficulties to the city-wide traffic flow estimation/prediction. Moreover, it is difficult for traditional analytical traffic flow models to deal with the traffic flow estimation/prediction problem over urban transport networks in a complex environment. Current data-driven methods mainly focus on road segments with detectors. An instance-based transfer learning method is proposed to estimate network-wide traffic flows including road segments without detectors. Case studies based on simulation data and empirical data collected from the open-source PeMS database are conducted to verify its effectiveness. For the traffic flow estimation of segments without detectors, the mean absolute percentage error (MAPE) is approximately 11% for both datasets, which is superior to the existing methods in the literature and reduces MAPE by two percentage points.

An analytical and meshless model for 3D transient flow in a confined aquifer with nonuniform thickness: Application to stream depletion due to groundwater extraction

This study proposes an analytical and meshless model for three-dimensional transient flow induced by multiple wells in a stream-confined aquifer system with arbitrary nonuniform aquifer thickness. The model involves allocating external image wells near the aquifer boundary. The aquifer drawdown is defined as Theis’ solution plus a simple series expanded by complementary error functions reflecting the boundary effects of the stream and impervious stratum. The solution for stream depletion rate (SDR) can be derived based on the drawdown solution. Results suggest the Dupuit assumption of no vertical flow is valid to estimate SDRs affected by the landward exponentially decreasing thickness. The SDR induced by multiple wells is the same as that by a single well if the total well discharge rate and stream-well distances in the multiple well case are identical to those in the single well case. The present solution outperforms a finite difference solution in computational efficiency.