Steady-state Flow Simulations Research Articles

A deep learning-based surrogate model for trans-dimensional inversion of discrete fracture networks

Fractures and their geometrical patterns are usually required to analyze the mechanical and flow properties of porous media in the subsurface. Fracture characterization is therefore regarded of crucial importance for optimizing production management or achieving maximum storage capacity. In this research, we propose to invert the fracture networks under the Bayesian framework for the uncertainty quantification. In particular, the number of fractures in the modelling system is treated as unknown, leading to a trans-dimensional inverse problem, and the reversible jump Markov chain Monte Carlo algorithm is applied to sample the model space with possible model moves proposed in the sampling process. A deep learning network is further applied as a surrogate model in the sampling process for increasing the computational efficiency, instead of using the physical forward simulator. We apply the proposed methodology to estimate the spatial distribution of fracture networks based on the head measurements from the steady-state flow simulation. The prior distributions of fracture parameters such as position, orientation and length are described using the discrete fracture networks approach that is deeply rooted in stochastic modelling. Due to the high non-uniqueness, the correct spatial distribution of fracture patterns cannot be successfully recovered in this case study, even a good match between observed and simulated head data is reached. More analysis could be performed in the future with the production historical data or more informative priors.

Stochastic inversion of fracture networks using the reversible jump Markov chain Monte Carlo algorithm

Characterization of fracture networks is essential in the production optimization or storage calculation for enhanced geothermal systems or geologic carbon storage. A novel inversion approach is proposed for estimating the fracture networks in this research. The discrete fracture network technique is adopted to probabilistically describe various fracture parameters such as trace length, midpoint position or azimuthal angle. The reversible jump Markov chain Monte Carlo algorithm is applied to explore the target posterior distribution of model parameters of differing dimensionality, in which the number of fractures is assumed to be unknown. More specifically, the birth-death strategy is utilized to perturb the fracture number iteratively in the sampling process. The proposed methodology is applied with two different types of observational datasets, namely the head records from steady-state flow simulation and the acoustic impedance obtained from seismic inversion. The sampling results can successfully recover the fracture geometry in the observed domain, and the number of fractures in the system can be retrieved as well. Benchmarked on multiple Markov chain trials, the technique of parallel tempering can greatly improve the convergence efficiency and increase the diversity of sampled posterior models, through the random swapping of model states across the whole temperature ladder.

Investigation of REV scale and anisotropy for 2D permeable fracture Networks: The role of geological entropy

To investigate the intrinsic association between geometrical properties and permeability of anisotropic fractured media, a methodology of geological entropy is applied to anisotropic fracture networks for the evaluation of seepage fields. By integrating the synthetic effect of fracture geometrical parameters (e.g., trace length, spacing, dip angle, and aperture), the global connectivity of fracture networks is quantified by the entropy scale (Hs), while the directional entropy scale (Hs,α) is used to characterize the local geometrical anisotropy in arbitrary orientations. A series of hydraulic representative elementary volumes (REVs) of fracture patterns with various geometrical properties are acquired based on continuum analysis. The permeability in the continuum scale is obtained from steady-state flow simulations. Sensitivity analyses are performed to understand the geometrical dependence of permeability parameters regarding entropy indices. It is found that a systematic increase in trace length, spacing, and dip angle is correlated with an increase, decrease, and equilibrium in entropy, respectively, which corresponds to a change in hydraulic REV sizes that can be expressed as a power-law function related to the Hs. Moreover, Hs,α can well explain the permeability anisotropy resulting from the spatial order of fracture networks, and a unified mathematical relationship for the effective permeability coefficients in arbitrary orientations versus the Hs,α is proposed, independent of variations in fracture patterns and scales. The results indicate that geological entropy, related to the geometrical properties and spatial distribution of fractures, is appropriate to characterize the permeability of anisotropic systems.

Wing Sails: Numerical Analysis of High-Performance Propulsion Systems for a Racing Yacht

With the increasing popularity of yachting sports and races comes the need to develop a more advanced and efficient propulsion device. Significant improvement can be made when using a mainly lift-driven propulsion source, known as a wing sail. This idea, dating back as far as the mid-70s, is nowadays regaining interest as a propulsion system in multihull, high-performance racing vessels (for instance, the AC50 and AC72 America’s Cup yacht classes). This article documents 2D and 3D numerical analyses of wing sail systems imitating those of an AC72 racing yacht class. It depicts methods employed in two- and three-dimensional steady-state flow simulations, compares systems equipped with various geometries of mainsails, and details a comprehensive examination of the airflow around the vessel using spatial analyses. Numerical calculations were carried out using ANSYS CFX and ANSYS Fluent (with overset feature) for 2D and 3D models, respectively. All simulations were conducted under conditions similar to those acting on the real system, i.e., high Reynolds number (order of magnitude 106 to 107) and atmospheric boundary layer (in the 3D model).

Sequential Direct and Inverse Modeling of Underground Flows in the Upper Cheliff Alluvial Aquifer, Algeria

The Upper Cheliff plain lies 125 km south-west of Algiers, capital city of Algeria. It is characterized by its unconfined aquifer contained in a heterogeneous filling of Mio-Plio-Quaternary age. Nowadays, this aquifer is severely exploited to meet the domestic, industrial and agricultural needs in the region. Groundwater resources management by means of numerical modeling is highly required in order to improve our knowledge of the hydrogeological operation of this aquifer. In this work we implemented an approach based on a sequential solving of the direct and inverse problems. In the case of the direct problem, steadystate flow simulations revealed the persistence of large discrepancies between the measured and calculated piezometric levels, which reflect the heterogeneity of the aquifer. The zonation provided by the direct method, based on the conceptual model, is then fed in the inverse method. The latter, in addition to its speed and its convergence, made it possible to reduce the disparities with measurements as noted in the direct method. The main results highlight a heterogeneous hydraulic conductivity distribution which reaches its highest values in the central and north-western sectors of the aquifer, whereas the lowest values are found in the eastern, northern and southern sectors of the aquifer. Furthermore, calculation of the groundwater flow budget by the inverse model showed that rainfall recharge is the main input into the aquifer with 462.5x103 m3/day, whereas the most important outlet of the aquifer is the Cheliff Wadi with a flow rate of 627x103 m3/day.

Experimental and Analytical Investigations of Wire-Partially Insulated Parallel Plate Electrode Type Electrohydrodynamic Fan

As an alternative to conventional mechanical fans, EHD fans and/or EHD gas pumps, which generate less noise, were investigated for cooling systems, such as in electronic equipment and automobiles. Wire-parallel plate electrode type EHD fans, which have greater design freedom and potential for practical application, have been suggested. This study clarifies the characteristics of a wire-partially insulated parallel plate electrode type EHD fan under DC positive applied voltage. In order to understand the characteristics of the EHD fan more deeply, visualizations of the air flow in the flow channel and the exit area were conducted by using PIV and CFD analyses. In the experiment, air at atmospheric pressure and room temperature was used as a working fluid. The experimental results for fan characteristics of the EHD fan, such as the velocity profile, cross-sectional average velocity, volumetric flow rate in the flow channel or at the exit area, power, and so on, are considered in detail. In addition, the flow visualization and the instantaneous and time-averaged velocity profiles from the PIV analysis are discussed. A comparison with the experimental results described above, and differences of flow regime for different locations, are also presented and discussed. Furthermore, a two-dimensional steady state flow simulation by means of CFD analysis was conducted and its experimental results analyzed.

Determination of the maximum allowable active powerflow in the section taking into account the thermal conditions of power transmission lines

Subject of research: This paper assesses the possibility of introducing into the task of calculating maximum and emergency allowable active power flow, taking into account the thermal modes of overhead lines when planning electric power regimes. 
 Purpose of research: determine the effect of thermal processes in power lines on the maximum allowable active power flow in controlled sections of electric power systems.
 Methods and objects of research: Such factors influencing active power flow as ambient air temperature, which is currently corrected by the Russian Power System Operator, wind speed, solar radiation and direct heating from flowing current are considered. Simulation of steady state flow in the software package RastrWin3 and Mathcad for a 2-bus scheme with mode only taking into account the ambient temperature and the calculations of steady state flow were already taking into account variations in weather parameters, taking into account possible restrictions on the maximum load due to the modes of operation of the power system (technical feasibility generating equipment was not taken into account in the work under consideration).
 Main results of research: the result of calculation, it is clearly seen that when taking into account the thermal conditions of overhead power lines, the allowable active power flows differ by 1626 % from the values determined only when taking into account the ambient temperature.

Thermo‐Hydro‐Chemical Simulation of Mid‐Ocean Ridge Hydrothermal Systems: Static 2D Models and Effects of Paleo‐Seawater Chemistry

AbstractDecades of research have resulted in characterization of the ocean floor manifestations of mid‐ocean ridge (MOR) hydrothermal systems, yet numerical models accounting for the connections between heat transfer, hydrology and geochemistry have been slow to develop. The Thermo‐hydro‐chemical code ToughReact can be used to describe the coupled effects of fluid flow, heat transfer, and fluid‐rock chemical interactions that occur in MOR systems. We describe the results of 2‐dimensional simulations of steady state flow in fractured diabase with mineral‐fluid chemical reactions. Basal heating and specified permeability yield maximum temperature of 400°C. Total fluid flux and high fracture flow velocities are in accord with observations. Fluid chemistry, mineralogical changes and 87Sr/86Sr ratios can be compared to observations to assess and calibrate models. Simulated high temperature fracture fluids have Mg and SO4 near zero, elevated Ca and 87Sr/86Sr of about 0.7040. Total alteration is 10%–50% for simple models of spreading. Anhydrite forms mainly near the base of the upwelling zone and results in substantial local fracture porosity reduction. A calibrated model is used to predict how Sr isotopes and other features of altered oceanic crust would be different in the Cretaceous (95 Ma) early Proterozoic (1,800 Ma) and Archean (3,800 Ma), when seawater may have had high Ca and Sr concentrations, lower pH, higher temperature, and lower Na, Mg, and SO4. The simulations are offered as a start on what ultimately may require a longer‐term community effort to better understand the role of MOR thermo‐hydro‐chemical systems in Earth evolution.

On the application of higher-order Backward Difference (BDF) methods for computing turbulent flows

The Backward Differentiation Formulae (BDF) of orders one to six are implemented in an in-house three-dimensional finite-volume (FVM) compressible flow code that operates on unstructured meshes. The lower-upper symmetric Gauss-Seidel (LUSGS) implicit relaxation technique based on the splitting of convective Jacobians is used to obtain a variable-order stable implementation in the solver. The temporal order of accuracy of the implemented schemes is verified using the Method of Manufactured Solutions (MoMS). Practical engineering flow problems are simulated to investigate the operational stability of BDF methods so that these can be used as a cheaper alternative to multi-stage methods in RANS, hybrid RANS-LES, and LES implementations. Steady-state flow simulations of supersonic flow over a flat plate and high Reynolds number flow over a NACA-0012 airfoil show that algorithm with BDF schemes of orders 1-5 is stable at high CFL numbers (700-1000) and produces a converged solution. Stokes' second problem and a high-resolution delayed detached eddy simulation (DDES) of flow over a 3D circular cylinder using the BDF1-BDF6 methods demonstrate the use of these higher-order temporal schemes in unsteady laminar and turbulent flows. It is concluded that BDF methods of orders 3-5 can be practically employed to achieve higher levels of temporal accuracy in flow simulations when the level of spatial accuracy is also high (ENO/WENO schemes, spectral methods, etc.) in hybrid RANS-LES, LES or DNS. Even without higher-order spatial accuracy, the same BDF schemes can be used in Adaptive Time-stepping (ATS) methods to obtain prescribed temporal accuracy efficiently by algorithmically switching between the different schemes.

Reducing the Effects of Water Hammer Phenomenon in Pipelines by Changing the Closing Rate of Line Break Valve (LBV)

Line break valves in pipelines are using to prevent environmental hazards caused by the entry of the fluid into the surrounding. The operation of these valves leads to sudden changes in pressure and velocity, resulting in the occurrence of the water hammer phenomenon. The water hammer pressure will cause serious problems such as the destruction of pipelines and transmission line equipment and tools. Due to the salinity of water, when a fracture occurs, the amount of water that enters the surrounding is environmentally essential, so the use of several LBVs is vital. This paper investigated a water transmission line with a total length of 337 km that transfers saline water from Khoor Moosa to Azadegan plain. This study discussed the closing of the valve at different rates and the solution to reduce its destructive effects. WaterGEMS V8i software and Hammer V8i software are respectively using to perform a steady flow simulation and damping flow analysis for this phenomenon. The results obtained from the steady-state flow simulation is the initial conditions in the damping flow calculations. Then, by reducing the closing rate of the valve in 6 different scenarios, the volume of air chambers decreased. Finally, the results led to creating a linear relationship between the valve closing rate and the capacity of the air chamber. The optimal model for this rate depends on reducing the construction cost as well as the environmental hazards caused by discharged water.

Research on Computational Method of Supersonic Inlet/Isolator Internal Flow

In this research, a CFD solver is developed for solving the 2D/3D compressible flow problem: the finite volume method based on multi-block structural grids is used to solve the compressible Reynolds averaged Navier–Stokes equations (RANS). Included in the methodology are multiple high-order reconstruction schemes, such as the 3rd-order MUSCL (Monotone Upstreamcentered Schemes for Conservation Laws), 5th-order WENO (Weight Essentially Non-Oscillatory), and 5th-order MP (Monotonicity-Preserving) schemes. Of the variety of turbulence models that are embedded, this solver is mainly based on the shear stress transport model (SST), which is compatible with OpenMP/MPI parallel algorithms. This research uses the CFD solver to conduct steady-state flow simulation for a two-dimensional supersonic inlet/isolator, incorporating these high-precision reconstruction schemes to accurately capture the shock wave/expansion wave interaction and shock wave/turbulent boundary layer interaction (SWTBLI), among other effects. By comparing the 2D/3D computation results of the same inlet configuration, it is found that the 3D effects of the side wall cannot be ignored due to the existing strong lateral flow near the corner. To obtain a more refined turbulence simulation, the commercial software ANSYS Fluent 18.0 is used to carry out the detached eddy simulation (DES) and the large eddy simulation (LES) of the same supersonic inlet, so as to reveal the flow details near the separation area and boundary layers.

The relationships between permeability and geological entropy of fracture networks

A systematic approach has been proposed to estimate the relationship between the permeability and geological entropy of two-dimensional fracture networks. The relative entropy index is developed as a measure of multiple properties of two-dimensional fracture networks, including fracture density, length, orientation and spatial distribution. In order to understand geological entropy dependence of the permeability, a computational method combining fracture network generation and steady-state flow simulation is employed. Based on the results of detailed numerical simulations, the relative entropy index and permeability increase simultaneously as the fracture density and length are independently increased. A simple closed-form empirical expression of the logarithmic dependence of the normalized permeability on the relative entropy index is proposed.

ML-LBM: Predicting and Accelerating Steady State Flow Simulation in Porous Media with Convolutional Neural Networks

Fluid mechanics simulation of steady state flow in complex geometries has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of steady state flow in such porous media requires significant computational resources to solve within reasonable timeframes. This study outlines an integrated method combining predictions of fluid flow (fast, limited accuracy) with direct flow simulation (slow, high accuracy) is outlined that reduces computation time by an order of magnitude without loss of accuracy. A convolutional neural network (CNNs) is trained with various configurations on simulations in 2D and 3D porous media to estimate steady state velocity fields. Permeability estimation (as an average of the field) is accurate, but the velocity fields themselves are error prone, unsuitable for further transport studies. This estimate can either be used as an indicative prediction, or as initial conditions in direct simulation to reach a fully accurate result in a fraction of the compute time. Using Deep Learning predictions (or potentially any other approximation method) to accelerate flow simulation to steady state in complex structures shows promise as a technique to push the boundaries fluid flow modelling.

The Effect of Ramp Location in a Strut Based Scramjet Combustor under non reacting flow field

The scramjet engine is considered to be the high-speed propulsive system for hypersonic air-breathing vehicles. Researchers focus on various geometries of strut injectors to enhance the mixing and combustion efficiencies of the scramjet combustor. This paper reveals the non-reacting flow characteristics of various ramp locations in a scramjet combustor with strut injection. The ramps are symmetrically placed at three different locations upstream of the strut within the combustor. Air enters into the combustor inlet with Mach number 2, and the fuel is injected at the sonic velocity from the strut. The 2D supersonic flow characteristics are numerically investigated using ANSYS 18.0 software. The steady-state flow simulations are performed in this study. The flow field is modelled using RANS equations, and the k-ω SST turbulence model and default constants are chosen to investigate the flow characteristics within the combustor. The flow characteristics of the ramp based DLR scramjet combustors are compared with the baseline DLR scramjet model. The computational results are validated with the experimental data. The shock wave interaction from the ramps enhances the distribution of hydrogen in the lateral direction of the flow than the baseline strut configuration. The ramps create recirculation regions that could enhance fuel-air mixing. The ramp induced strut based DLR scramjet engine provides increased total pressure loss of the baseline DLR scramjet.

Numerical Investigation of Single-Strand Slab Casting Tundish Flow with Heat Transfer and Inclusion Transport

In continuous casting process, cleanliness of steel can be improved and maintained by promoting the inclusion separation inside the tundish by various means; tundish flow optimization using arrangement of flow control devices inside the tundish is one among them. Three-dimensional computational fluid dynamics simulation of tundish flow is an efficient way to investigate the arrangement of flow control devices. In the present work, three-dimensional isothermal steady-state flow simulations, residence time distribution analysis and inclusion transport simulations of tundish flow are conducted. All the simulation results are validated with experimental measurements reported in literature. Subsequently, the simulations are extended for a non-isothermal flow of the existing tundish in the plant and an additional flow control device, namely a weir with appropriate dimensions is proposed which indicated better steel flow in the tundish with more inclusion separation efficiency as compared to the existing bare tundish.

Hydrodynamic analysis of a low head prototype Francis turbine for establishing an optimum operating regime using CFD

Hydraulic turbines need to operate at regimes other than designed ones. Off-design functioning of these turbines yields an inefficient and uneconomical operation of hydro projects. Performance and energy losses at different possible operating conditions need to be evaluated before finalizing the design of water turbines for satisfactory operations. Moreover, hydraulic turbines are unique machines designed for unique set of operating conditions and cost a huge percentage of the overall cost of the project. This work is compiled with twofold objectives; derivation of complete performance characteristics of a 48m head prototype Francis turbine in order to establish an optimum operating regime and, determination and analyses of head loss at different components of the turbine. Steady state flow simulations for four different load operations (60%, 80%, 100% and 120%) have been carried out using computational fluid dynamics. It is found that the optimum regime of operation lies within the speed factor range of 0.412-0.48 along with discharge factor range of 0.27-0.329 and maximum efficiency is obtained as 90.64% at full load operation. Maximum head loss in critical components of the turbine such as runner and draft tube is found as 12.7% at speed factor of 0.568 and 26.31% at 0.202 speed factor respectively. Also, the maximum total head loss in all the components is found as 47.8% at 60% load and 0.609 speed factor. It is concluded that the functioning of the turbine at higher speed factors is more detrimental than that at lower speed factors. Requirement of performance improvement at off-design conditions (especially at 60% load operation) is also suggested in order to widen the range of optimum operating regime. Obtained computational results are validated with experimental results and a strong agreement is found between the two.

Non-Darcian flow effect on discharge into a tunnel in karst aquifers

The groundwater flow in karst aquifers is prone to become non-Darcian due to the presence of karst conduits, and this effect may become more pronounced during tunnel construction. Prediction of discharge into tunnels in karst aquifers remains a challenging task because of the complex nature of non-Darcian flow and the uncertainty of aquifer's properties. This study aims to evaluate the effect of non-Darcian flow on the discharge into a tunnel in karst aquifers in Guizhou Province, China, where a large proportion (~86%) of borehole packer tests evidences the flow in non-Darcian regime. An integrated method combining packer test data interpretation, statistical correlation and inverse modelling is proposed to determine the non-Darcian flow properties of the aquifer system. Numerical simulations of steady-state flow show that the predicted discharge based on the Forchheimer's equation agrees better with measurements than that based on the Darcy's law by ~27%. The region with the most pronounced non-Darcian effect occurs at the intersection between the tunnel and a karstified fault connecting to an underground river, and the occurrence of non-Darcian flow leads to an increase in hydraulic gradient, but a reduction in discharge into the tunnel. This work presents a framework that combines aquifer properties estimation and numerical simulations for more accurately evaluating the discharge and seepage erosion risk induced by tunnel construction in karst aquifers.

A Three-Dimensional Thermo-hydrodynamic Simulation of Compact Cross-Flow Plate Heat Exchanger

This study is dedicated to the thermal analysis and thermo-hydrodynamic simulation of an air-to-air plate heat exchanger in order to solve its routine problem in industry. The compact type of cross-flow plate heat exchanger, in which corrugated plates pile up tightly and delicately brazed to each other, has been used in many situations and has many applications from food industries to petroleum and military. Routinely, after a certain lifespan, the brazed joints are detached and cause a mixture of hot and cold fluids as well as highly reduction of heat exchanger performance. This problem leads to increase the system maintenance significantly. Apart from the imposed cost and time for its maintenance, which is indeed a crucial problem? Finally, to have a better understanding, a threedimensional numerical investigation on thermo-hydrodynamic analysis of conjugate heat transfer was performed using computational fluid dynamics techniques. Forced convection heat transfer for fluid flow and conduction through solid material were considered as well. For simulation of steady state flow of Newtonian fluid, the governing equation was discredited by finite volume method and solved by the semi-implicit method for the pressure-linked equation. It was also found that both temperature and temperature gradient play an important role in this problem.

A Simulation Based Study of Flow Velocities across Cross Flow Turbine at Different Nozzle Openings

The present work reports CFD based investigation of the effect of design parameters on the flow velocities of a cross flow turbine (CFT). Best described as an impulse type turbine with partial admission of air, cross flow turbines meet the demand for an efficient turbine to run at low head that is also easy to manufacture. The design of cross–flow turbine is unique due to the generation of power during two stages. This type of turbine is often used in small hydropower plants located in less–developed countries. The design parameters of CFT that can be varied to increase overall efficiency and power output of the turbine are water inlet angle, blade angle at inlet and outlet. In the present work the design parameters are varied for different nozzle openings and simulated using CFD. A full 3-D steady state flow simulation of the cross-flow turbine is performed including casing, runner and nozzle assembly.

A Practical Approach to Operational Hydrodynamic Slug Analysis in Pipelines

Abstract Hydrodynamic slugs in pipelines are usually analysed by using steady-state flow simulation software as a first approximation and then modelled in transient simulation software in order to get more accurate values. In this work, the ILF approach for hydrodynamic analysis is presented by using an empirical and a mechanistic method for steady-state simulations and by using a transient approach. For both, steady-state and transient simulations commercial software is applied. Furthermore, a new pseudo-transient approach as an alternative to the Lagrangian slug tracking scheme that is currently tested is presented. A set of operational hydrodynamic slug examples illustrates the use and accuracy of both commercial simulation programs and the newly developed pseudo-transient approach. Finally, a set of considerations for the hydrodynamic slug analysis in pipelines is proposed as a guide for accurate estimation of the slug properties.