Steady-state Flow Research Articles

On Intake–Compressor Interactions Within an Integrated Propulsion System

Abstract The integration of a propulsion system into the airframe can contribute to the overall aircraft performance and is beneficial for military applications due to a reduction of the aircraft radar cross section. On the other hand, engine integration calls for serpentine engine intake systems in which generally combined pressure-swirl distortions are provoked, which affect the performance of the propulsion system. The military engine intake research duct was designed to provoke a large-scale flow separation as well as a combined pressure-swirl distortion. The serpentine research duct is tested in both a remote- and close-coupled setup with the Larzac 04 turbofan engine to assess the aerodynamic interactions between the flow within the intake duct and the compression system. The upstream effect of the compression system on the steady-state duct flow is within the range of expectations. Less is known from the open literature with regard to the unsteady character of the flow in such a setup. Three distinct unsteady flow phenomena caused by the serpentine shape of the duct are identified up- and downstream of the low pressure compressor in the remote-coupled setup. An additional distinct low frequency unsteadiness is provoked with a configuration which features vortex generators for flow control. All phenomena are largely attenuated by the upstream effect of the compressor in the close-coupled setup. Nonetheless, the surge margin is massively reduced due to the inflow distortion and stall cells within the first stage of the low pressure compressor are visualized at high thrust settings of both the remote- and close-coupled setup, which are expected to impact the durability of the compression system.

Nondispersive ultraviolet monitoring of pulsed H2S gas delivery

This article describes time-resolved optical measurements of H2S partial pressure and mass flow in a pulsed gas delivery system approximating injection conditions encountered during atomic layer deposition. A high-speed nondispersive ultraviolet (NDUV) gas analyzer design is employed for in-line H2S detection in a gas delivery line with flowing carrier gas. An in-place analyzer calibration performed in a reference cell yields an H2S detection limit of ≈1.4 Pa (at 22 °C) at a sampling rate of 1 kHz. Flow measurements performed on the delivery line are used to evaluate the effects of adjustable delivery parameters on the time-dependent injection system output. Short pulse widths exhibit partial pressure transients attributed to flow development within the different volumes of the delivery system. After ≈1.0 s of injection, steady-state flow is established across flow elements. A partial pressure of H2S in the delivery line is found to vary linearly with upstream H2S pressure, consistent with choked flow. A stronger scaling of partial pressure is evident when the flow coefficient of the downstream metering valve is adjusted. Estimated steady-state H2S flow rates in the range of 0.05–0.21 mg/s are observed within a limited range of valve flow coefficients. However, further increases in the flow coefficient do not result in increased flow, likely due to conductance limitations in downstream flow system components. The utility of NDUV absorption measurements for high-pressure pulsed gas delivery systems is discussed.

Instability of isolator shocks to fuel flow rate modulations in a strut-stabilised scramjet combustor

Abstract Reynolds-Averaged Navier–Stokes (RANS) simulations, both steady and unsteady, are used to investigate supersonic, chemically reacting, flow fields inside a strut-stabilised supersonic combustion ramjet (scramjet) engine operating under different fuel flow rates. Fully supersonic, fully subsonic and mixed modes of operations inside the combustor, obtained at different fuel flow rates, are studied numerically through shock wave visualisations and top-wall static-pressure probing. The effect of changing fuel flow rates, imposed both suddenly and gradually, on the behaviour of shock waves and wall pressure profiles are studied in detail. For certain modes of combustion characterised by the presence of oblique shocks at the strut, shockwaves in the combustor respond predictably to an increase or decrease in fuel flow rate attaining the steady state flow fields as predicted by RANS simulations for those fuel flow rates. For certain other modes of combustion, characterised by the presence of shockwaves in the isolator and the absence of oblique shocks at the leading edge of the strut, shockwaves in the flow field appear unstable to fuel flow rate modulations. For such cases, any change in fuel flow rates, sudden or gradual, increase or decrease, causes the isolator shocks to immediately move upstream and eventually out of the isolator. A plausible physics-based explanation of the observed phenomena is presented.

Experimental evaluation of water surface profiles upstream and downstream of a culvert with and without an apron

Culverts are structures designed to facilitate the transfer of water beneath roadways, effectively connecting two areas within a catchment. Several critical parameters influence the design of a culvert and its surrounding environment. Among these, the flow conditions and the management of water levels at both the inlet and outlet are essential for the culvert's operation, particularly regarding its performance during flood events. This article examines the impact of variations in the longitudinal slope of the culvert and the elevation of the downstream bed—both with and without an apron—on the flow profile entering and exiting the culvert. To investigate this, a series of 80 experiments were conducted in a straight laboratory channel under steady flow conditions. The objective of these tests is to analyze the water level profiles both upstream and downstream of the culvert under various scenarios. The results indicated that increasing the culvert slope led to a rise in water level on the upstream side of the culvert. Specifically, the maximum water level upstream increased by 14 %, 56 %, and 65.1 % when the culvert slope was raised from zero to 2.5 %, 4 %, and 5.5 %, respectively. Additionally, the minimum water level upstream also increased by 19.1 %, 70.6 %, and 83.1 % under the same slope changes. The average maximum and minimum water levels for all scenarios were calculated and compared. The findings of this research will be valuable for analyzing water transfer both upstream and downstream of the culvert structure, as well as for enhancing hydraulic c alculations related to its performance.

Design optimization of floating offshore wind farms using a steady state movement and flow model

Abstract In this study, we demonstrate how to carry out the design optimization of floating offshore wind farms by considering the impacts brought by the movements of the floating wind turbines. A steady state movement and flow model is applied in the modelling process. This model is developed by building a turbine surrogate model for estimating the steady state movement and power production of floating wind turbines and incorporating it in an open-source static wind farm simulator, PyWake. Using this modelling methodology, layout optimization problems of floating offshore wind farms are solved by using algorithms like Random Search to maximize the energy yield while satisfying certain constraints. Case studies are carried out for two wind farms with met-ocean conditions from a real planned site in Scottland to show the potential of layout optimization for floating wind farms.

An equivalent analysis of unsteady sand transport in a wind tunnel

This study investigates the effect of unsteady wind on sand transport in a wind tunnel using sinusoidally varying wind velocity to represent the unsteady wind. By comparing sand transport fluxes under steady and unsteady winds, we demonstrate that cumulative sand transport flux varies sinusoidally with the sinusoidally varying wind velocity. In addition to the time-averaged wind velocity, the sand transport rate is also affected by the amplitude and period of wind velocity variations. We then propose an ‘equivalent’ steady aeolian sand transport process as a substitute for the actual unsteady transport process. In terms of wind velocity amplitude and period variations, an equivalent wind friction velocity factor u*′ is defined to capture differences caused by wind velocity variations with the same time-averaged wind velocity and friction velocity. Finally, a unified equation for aeolian sand transport is derived, demonstrating applicability for both steady and unsteady flow conditions. The results of this study contribute to a deeper understanding of aeolian sand transport under unsteady flow.

Predicting straw drinking ability of liquid foods by pipe-flow rheometry

Designing the straw drinking experience is increasingly important in consumer-oriented liquid food innovation. The perceived ’straw drinking ease’ of liquid foods could be assessed by sensory analysis. However, challenges arise in linking instrumental measurements to the subjective quantification of sensory attributes due to the complexity of perceptual behaviors in drinking. Here, we developed a pipe-flow rheometry approach to predict straw drinking ability with minimized reliance on panel tests. We measured the instantaneous flow of liquid samples within straws and compared their flow profiles based on different yielding behaviors. The dynamic flow processes were simplified into steady-state pipe flow, and perceived straw drinking ability was modeled as the shear viscosity of liquid foods at specific flow rates. A power-law relationship was found between viscosity at sample-specific shear rates and straw drinking ability, regardless of whether the liquid foods exhibit yield stress. This approach provides opportunities for directly addressing the straw drinking experience through simple laboratory measurements when developing texture modulation systems for liquid foods.

Water and carbon fluxes from a supra-permafrost aquifer to a stream across hydrologic states

Supra-permafrost aquifers within the active layer are present in the Arctic during summer. Permafrost thawing due to Arctic warming can liberate previously frozen particulate organic matter (POM) in soils to leach into groundwater as dissolved organic carbon (DOC). DOC transport from groundwater to surface water is poorly understood because of the unquantified variability in subsurface properties and hydrological environments. These dynamics must be better characterized because DOC transport to surface waters is critical to predict the long-term fate of recently thawed carbon in permafrost environments. Here, we used distributed Darcy’s Law calculations to quantify groundwater and DOC fluxes into Imnavait Creek, Alaska, a representative headwater stream in a continuous permafrost watershed. We developed a statistical ensemble approach to model the parameter variability and range of potential contributions of steady-state groundwater flow to the creek. We quantified the model prediction uncertainty using statistical sampling of in-situ, active-layer soil hydro-stratigraphy (water table, ice table, and soil stratigraphy), high-resolution topography data, and DOC data. Moreover, the predicted groundwater discharge values representing all possible hydrologic conditions towards the end of the thawing season were also considered given the potential variability in saturation. The model predictions were similar to and span most of the observed range of Imnavait Creek streamflow, especially during recession periods, and also during saturation excess overland flow. As the Arctic warms and supra-permafrost aquifers deepen, groundwater flow is expected to increase. This increase is expected to impact stream, river, and lake biogeochemical processes by dissolving and mobilizing more soil constituents in continuous permafrost regions. This study highlights how quantifying the uncertainty of hydro-stratigraphical input parameters helps understand and predict supra-permafrost aquifer dynamics and connectivity to aquatic systems using a simple, but scalable, modeling approach.

Numerical modelling of downstream scour in circular culverts: Impact of inlet blockages and variable flow conditions.

An accurate estimate of scour depth downstream of culvert outlets is essential for culvert design integrity. Inadequate designs can result in structural failures, leading to increased costs for maintenance and rehabilitation. The present research evaluates the efficacy of numerical models in predicting scour depth and its location downstream of circular culverts under variable flow conditions. Two hydrographs were created for unsteady flow, featuring nine different flow discharges, while steady flow conditions were analysed at flow rates of 14 l/s and 22 l/s. The study investigated circular culverts with inlet blockages of 0%, 15%, and 30%, comparing outcomes with predictions from the Flow-3D software using the renormalisation group (RNG) turbulence model. Extensive experimental data on circular culverts were utilised, with simulations performed using commercial software. This involved analysing the scour's downstream profile, its maximum depth, and its location, and comparing these metrics with actual observed data. The results revealed that the numerical model predictions closely corresponded to the experimental data, even though the simulated scour was generally less than that observed for steady and unsteady flows. The results showed that in unsteady flow conditions and for the discharge of 22 l/s, 30% blockage increased scour by 6.8% and 14.2%, respectively, compared to 15% blockage and non-blocked flow. This increase was 22% and 9.5% for the discharge of 14 l/s, respectively. In the steady case, when the flow rate was adjusted from 14 l/s to 22 l/s, there was a noticeable increase in scour depth downstream of the culvert. While blockage rates impacted the scour patterns significantly in unsteady flow scenarios, escalating blockage percentages did not lead to uniformly proportional increases in scour depth within steady flow environments.

Ground Behavior of Parallel Tunnels in Response to Variations in Groundwater Flow

With the steady expansion of urban development, the importance of tunnel design and construction has increased, particularly with respect to changes in the groundwater level. Excavation without considering groundwater variations can destabilize tunnels; and this problem has been exacerbated by recent climate change-induced groundwater level fluctuations. This study evaluates the impact of various factors, such as filler width, lateral earth pressure coefficient, and groundwater flow, on tunnels by analyzing the ground behavior around parallel tunnels in Korea. The findings reveal that an increase in filler width reduces settlement and displacement, while the coefficient of lateral earth pressure affects convergence displacement to a higher degree than other settlements. Moreover, steady flow conditions are observed to wield a more pronounced impact on ground behavior than unsteady ones. These findings emphasize the importance of thoroughly evaluating groundwater flow characteristics during tunnel excavation and provide essential data for the future design and construction of parallel tunnels.

Modeling phosphorus transport in soil columns amended with polyaluminum chloride and anionic polyacrylamide water treatment residuals: implications for stormwater bioretention systems

ABSTRACT Understanding phosphorus transport in soil columns amended with polyaluminum chloride and anionic polyacrylamide water treatment residuals (PAC-APAM WTRs) is crucial for the effective recycling of PAC-APAM WTRs into traditional soil-based stormwater bioretention systems. Phosphorus transport in columns containing three distinct soil types amended with PAC-APAM WTRs under saturated steady-state flow conditions was effectively modeled using three different models: the convection-dispersion equation (CDE) model with linear isotherm, the CDE model with Langmuir isotherm, and the chemical non-equilibrium two-site model (TSM). In Soils 1 and 2, amended with PAC-APAM WTRs, the primary mechanism governing phosphorus transport transitioned from instantaneous adsorption to two-site adsorption as flow rate increased. In contrast, Soil 3 amended with PAC-APAM WTRs was predominantly governed by two-site adsorption throughout the experiments. An increase in flow rate reduced the solid–liquid distribution coefficient and the fraction of equilibrium adsorption sites, resulting in decreased phosphorus adsorption and increased phosphorus mobility. This study strongly recommends the selection of soil amended with PAC-APAM WTRs that exhibits higher instantaneous phosphorus adsorption. Additionally, this study emphasizes the importance of appropriately designing the depth of the ponding layer, utilizing the TSM model, and refining modeling techniques to optimize phosphorus retention and mitigate pollution risks in stormwater management.

Fluid Force Reduction and Flow Structure at a Coastal Building with Different Outer Frame Openings Following Primary Defensive Alternatives: An Experiment-Based Review

A well-constructed tsunami evacuation facility can be crucial in a disaster. Understanding a tsunami’s force and the flow structure variation across various building configurations are essential to engineering designs. Hence, this study assessed the steady-state flow structure at building models (BM) incorporating outer frame openings, including piloti-type designs with a different width-to-spacing ratio of piloti-type columns following an embankment model (EM) with a vegetation model (VM). The experiments also demonstrated the outer frame opening percentage’s impact and orientation toward the overtopping tsunami flow at the BM. The results show that the arrangement of an opening on the outer frame and the piloti-type columns are critical in reducing the tsunami force concerning the experimental setup. Moreover, allowing a free surface flow beneath the BM implies that the correct piloti-pillar arrangement is crucial for resilient structure design. In addition, the three-dimensional numerical simulation was utilized to explain the turbulence intensity of the overtopping flow around the critical BM type. The derived resistance coefficient (CR) defined the drag and the hydrostatic characteristics at the BM due to the overtopping tsunami flow. Furthermore, for the impervious BM, the value CR was consistent with the previous studies, while the CR value for the BMs with an outer frame opening was directly coincident with the percentage of porosity.

A critical state μ(I)-rheology model for cohesive granular flows

The dynamic behaviour of granular media can be observed widely in nature and in many industrial processes. Yet, the modelling of such media remains challenging as they may act with solid-like and fluid-like properties depending on the rate of the flow and can display a varying apparent friction, cohesion and compressibility. Over the last two decades, the $\mu (I)$ -rheology has become well established for modelling granular liquids in a fluid mechanics framework where the apparent friction $\mu$ depends on the inertial number $I$ . In the geo-mechanics community, modelling the deformation of granular solids typically relies on concepts from critical state soil mechanics. Along the lines of recent attempts to combine critical state and the $\mu (I)$ -rheology, we develop a continuum model based on modified cam-clay in an elastoplastic framework which recovers the $\mu (I)$ -rheology under flow. This model permits a treatment of plastic compressibility in systems with or without cohesion, where the cohesion is assumed to be the result of persistent inter-granular attractive forces. Implemented in a two- and three-dimensional material point method, it allows for the trivial treatment of the free surface. The proposed model approximately reproduces analytical solutions of steady-state cohesionless flow and is further compared with previous cohesive and cohesionless experiments. In particular, satisfactory agreements with several experiments of granular collapse are demonstrated, albeit with shear bands which can affect the smoothness of the surface. Finally, the model is able to qualitatively reproduce the multiple steady-state solutions of granular flow recently observed in experiments of flow over obstacles.

Curved-pipe flow with boundary conditions involving Bernoulli pressure

In this article, we study the steady-state flow of the incompressible viscous fluid through a thin distorted pipe with an arbitrary central curve. We prescribe the inflow and outflow boundary conditions involving the Bernoulli pressure with a given pressure drop. Using the multiscale expansion technique with respect to the pipe's thickness, we construct the higher-order asymptotic approximation of the flow given by the explicit formulae for the velocity and pressure. We also perform a detailed error analysis justifying the usage of the proposed solution and indicating its order of accuracy. For more information see https://ejde.math.txstate.edu/Volumes/2024/63/abstr.html

Developing a machine learning-based methodology for optimal hyperparameter determination—A mathematical modeling of high-pressure and high-temperature drilling fluid behavior

Drilling fluids exhibit complex rheological behavior due to a non-linear response to shear rate variations and high sensitivity to changes in temperature, time, and pressure conditions. The prediction of drilling fluid rheological behavior is crucial for the success of oil well drilling, and it directly impacts the fluid's performance. The dataset used in this study was obtained from extensive rheometric tests of water-based and olefin-based drilling fluids in steady-state flow curves. The optimal hyperparameters were guided by performance metrics and compared with alternative models such as Power-law and Herschel-Bulkley rheological models. Different configurations with different hidden layers, using neuron sequences of 16, 32, and 64, learning rates of 0.001 and 0.01, and the ReLU activation function were used to improve the model's performance. Additionally, the paper delved into the impact of the number of training epochs on the accuracy of shear stress predictions. Finding this equilibrium was identified as a crucial factor in achieving precise results. The neural network model demonstrated remarkable accuracy when using the ML-C3 configuration, with MAE values of 0.535 and R2 of 0.987 in predicting the steady-state flow curves of drilling fluids, establishing itself as a powerful tool for forecasting the rheological behavior of these fluids under diverse operational conditions. The present research significantly contributes to the field of drilling fluid rheology and provides valuable insights for optimizing drilling operations in HPHT environments.

Numerical Simulation of the Diffusion of Electroactive Molecule in Biosimilar Hydrogel Media

Based on experimental data of cyclic voltammetry, the values of the diffusion coefficients for toluidine blue in alginate hydrogel, gelatine hydrogel and alginate-gelatine hydrogels were obtained. Using the experimental values of the coefficients in a numerical model, the values of the recovery of flows have been calculated showing them consistent with what was the experimental. It is proposed to use the period in time during which the value of the flow force reaches the value of steady state flow force as an indicator of the diffusion properties of the hydrogel medium. The findings of this study can be used for the development of methods for the evaluation of the diffusion properties of hydrogel media: bioinks and tissue-engineered structures.

Isothermal Flow Field Characterization of a Full-Scale Sector Combustor at Elevated Pressures

Abstract An experimental investigation in a sector (20 deg) of full-scale annular gas turbine combustor is performed. The sector combustor is optically accessible for the flow and flame visualization of the primary and exit zones of the combustor. The distinctive feature of the experimental setup is that it preserves the geometrical details of an annular combustor that includes the casing, dome and combustor liner. The combustor design features a series of primary and secondary dilution holes with multiple film cooling strips on the outer and inner liner. In the present study, the combustor is operated at inlet Mach numbers of 0.02–0.3 at operating absolute pressures of 1–5 bar. Static pressure measurements are performed at multiple locations in the rig to characterize the pressure drop across the combustor. Two-dimensional particle image velocimetry (PIV) is performed to measure the velocity fields of the primary and exit zones of the combustor simultaneously. The results show the presence of a central recirculation zone (CRZ), high-velocity annular jets, and a pair of dilution jets in the primary zone of the combustor. The steady-state flow structures are invariant of inlet Mach number and pressures. The relationship between the relative pressure drop across the combustor and the combustor inlet condition is obtained. Mass flowrate and momentum flux are calculated for the flow through the swirler, central recirculation zone, the primary dilution jets, and the exit zone. The paper shows how the flow structures in a realistic combustor change with variations in global combustor parameters.

Does sheath size matter: benchtop comparison of flow and pressure across variety of continuous flow endoscopes.

Laser enucleation utilizes purpose-built endoscopes for laser stabilization and continuous flow. No evaluation has been done with respect to flow or intravesical pressure with these scopes. We sought to evaluate the effect different endoscopes and sheath sizes on irrigation outflow and intravesical pressure. Using a benchtop model using a silicone bladder model, five outer/inner sheath combinations were assessed: Storz 28/26Fr, Storz 26/26Fr, Wolf 26/24Fr, Wolf 26/22Fr, and Wolf 24/22Fr. A urodynamics pressure transducer was inserted alongside the scope for bladder pressure measurement and outflow from scope to drain was measured using uroflowmetry device. Four 1-minute trials were recorded for each sheath and the steady state flow and pressure was recorded. The Storz 28F outer sheath and 26F inner sheath had the highest outflow (12.4 ± 0.5 mL/s, p < 0.01). The Wolf 24F outer and 22F inner had the lowest outflow (7.0 ± 0.0 mL/s, p < 0.01). The steady state bladder pressure was the lowest in the Storz 28/26 (1.5 ± 1.7cm H2O, p < 0.01)) and the greatest in the Storz 26/26 (24.2 ± 1.9cm H2O, p < 0.01). The Storz 28/26 combination had best outflow rate and lowest intravesical pressures in our benchtop study. Flow rates generally decreased with smaller sheath sizes and steady state bladder pressures increased as the difference between the outflow and inflow sheath size narrowed. These findings provide initial parameters that could guide sheath selection in future to optimize visualization and success of voiding trials.

CFD Simulations of the Molten Salt Fast Reactor

The molten salt fast reactor (MSFR) is a fast-spectrum molten salt reactor concept, where the fuel salt flows freely through a toroidal core (2 m high × 2 m in diameter). The flow through this core is turbulent (Reynolds number ≈ 5 × 10 5 ) and presents several recirculation areas. Several thermal-hydraulic studies of the steady-state MSFR flow have been performed, where the thermal power distribution was fixed and the Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES) approaches were used. Different geometries were considered, from 1/16th of the core to the full core. The RANS simulations were performed first. The use of symmetry boundary conditions in these simulations had a very limited impact on the results while greatly speeding up the calculations. In the LES formulation, however, the symmetry boundary conditions had a large impact on the velocity and temperature fields, and so could not be used. While the RANS fields and the LES mean fields differed quite heavily, no particular hot spots appeared in the LES fields. Analysis of the LES temperature evolution in the center of the core revealed fluctuations of ± 20°C at a speed of 100°C·s−1.

Horizontal well hydraulics in leaky confined aquifer near a stream: analytical solutions for induced drawdown and water budget components.

Horizontal wells have gained popularity as a technology for exploring water resources and remediating aquifers over the last decades, due to costs and numerous technical benefits compared to traditional vertical wells. This study presents a set of analytical solutions for drawdown distribution and various components of water budget contributing to flow toward a horizontal well in an aquifer-aquitard system interacting with a fully penetrating stream. It is assumed that the water level in the upper unconfined aquifer remains fixed at a specific elevation during the course of the pumping in the lower leaky aquifer. The water budget components account for inflows from aquifer storage, stream depletion, and leakage across the aquifer-aquitard interface. Analytical solutions to this three-dimensional, transient, non-axisymmetric Darcian flow model are given for both transient and steady-state flow conditions, relying on a four-fold integral transform technique that includes a Robin-type boundary condition at the aquifer-aquitard interface. It is shown how various components of water budget collectively counterbalance the effect of pumping discharge, confirming that the mass is conserved under both continuous and non-continuous pumping scenarios. Response maps are prepared to assess how different components of water budget react to changes in the well position. Furthermore, it is found that the components of water budget are most sensitive to the well-to-stream distance and anisotropy ratio of the leaky aquifer.