One-dimensional Flow Research Articles

Estimation of channel and flood plain roughness using HEC-RAS model: A case study of the Veseočica River, Bosnia and Herzegovina

Modeling flow in open channels is essential for determining channel capacity and predicting flood events. The key segment for creating flood hazard and risk maps is a high-quality hydraulic model of the flow in the main bed with its tributaries. Several software packages have been developed for hydrodynamic simulations of flood events. In addition to the geometric characteristics of the watercourse, the equations of a one-dimensional flow model include a parameter that connects all influences that provide resistance to the flow of water. Determining the roughness of a natural channel is one of the most demanding procedures for the development of hydraulic models. Therefore, it is necessary to calibrate and validate the Manning coefficients of the channel roughness using simulation models. In the present study, the estimation of channel and floodplain roughness for the Veseočica River in Bosnia and Herzegovina was performed using the HEC-RAS hydrodynamic model. After calibration and verification of the model, flood hazard maps were created for flood waves with return periods of 20, 100, and 500 years. ArcGIS and HEC-GeoRAS software tools were used to create the flood risk maps.

Parametric Influence on Rotating Detonation Combustion: Insights from Fast Reactive Euler Simulations

A two-dimensional unsteady reactive Euler solver is employed to model rotating detonation combustion (RDC). A baseline case is chosen, and several combustor geometric and design parameters are varied individually in order to assess their effect on flowfield structure, exhaust flow properties, and performance. The parameters of interest are the perimeter and axial lengths of the combustor annulus, mass flux, outlet throat area, air injector throat area, and equivalence ratio. Quantification of the isentropically available work (IAW) in the exhaust flow is employed as a performance criterion. IAW is primarily affected by mass flux and outlet throat area through the effects of one-dimensional flow and, to a lesser degree, by perimeter and axial length through changes in the fraction of the flow that experiences irreversible shock processing. For all cases in the present study, this fraction appears to be solely determined by the ratio of detonation height to axial length. This ratio is also highly correlated to the angle of the oblique shock and the strength of the flow fluctuations. The predicted wave speed is between 90 and 95% of the Chapman–Jouguet velocity for a range of equivalence ratios between 0.6 and 1.4.

Nonstationary one-dimensional flows of a two-temperature dissociating gas: Group analysis and invariant solutions

Modern problems such as detonation engines and hypersonic reentry are reviving interest in the point explosion theory, which gives simple gasdynamics models of similar processes. This work is devoted to the study, using group analysis methods of mathematical properties of gasdynamics equations with thermochemical nonequilibrium, which is a typical problem in the theory of a point explosion. For this purpose, the system of equations under study was slightly corrected without distorting the physical meaning. This made it possible to obtain self-similar solutions. Solutions of two different models describing: a second-order endothermic dissociation reaction with vibrational exiting and a first-order exothermic reaction with spontaneous decay, are given in the paper. The problem of strong explosion of linear charge was considered. As in the classical case, the solution of the problem is reduced to integrating a system of ordinary differential equations in self-similar variables. The calculations show that the solutions to the modified system of equations is physically consistent and adequately describes the known effects of thermochemical nonequilibrium behind the wave front.

Simulation of Relaxation Processes in Hypersonic Flows with One-Temperature Non-Equilibrium Model

Steady-state one-dimensional flows of five-component air behind a normal shock wave are considered with a one-temperature model. A mathematical model is formulated to describe the relaxation of a five-component air mixture with a one-temperature non-equilibrium approximation. A numerical study of non-equilibrium flows of a reacting five-component air mixture behind shock waves at different heights and velocities of free flow is performed. The contribution of different types of reactions to the overall relaxation of the mixture is discussed, and the distributions of macro-parameters of the flow behind the shock wave front are calculated. The lengths of the relaxation zones behind the shock wave front are compared at different initial conditions. Calculations are performed for the standard model of atmosphere.

Cross-scale coupling analysis method for OTSG in SFR and its application

The once-through steam generators (OTSG) in sodium-cooled fast reactor (SFR) are characterized by full-regime flow boiling heat transfer, coupled heat transfer on both sides and complex structure with a large dimensional span. This makes the computational fluid dynamics (CFD) and 3D refinement modeling methods to analyze the 3D temperature field of OTSG containing large-scale heat transfer tube bundles generally face the problems of high computational difficulty, low solution efficiency and poor solution stability. In this paper, based on the full-regime flow boiling heat transfer model and the flow pattern discrimination model, a one-dimensional full-regime flow boiling heat transfer model from subcooled water to superheated steam on the water side (tube side) and its cross-scale coupling solution model with the three-dimensional refined CFD model on the sodium side (shell side) are established. The effectiveness of the coupling analysis model was verified by comparative analysis with experimental data of the Indian 19-tube Steam Generator Test Facility (SGTF). The independent coupling of the water side of each heat transfer tube in the OTSG with the sodium side 3D fluid domain is realized. The results show that the cross-scale coupling method using the one-dimensional full-regime flow boiling heat transfer model for the water side and the three-dimensional CFD model for the sodium side can accurately predict the temperature distribution, the main heat transfer characteristic points on the full height of each heat transfer tube, and can obtain the temperature difference between different heat transfer tubes and tube walls. The maximum error between the calculated results and experimental data for the distribution of sodium temperature along the axial direction of the tubes is less than 3%. The cross-scale coupled solution method avoids the direct adoption of the three-dimensional multiphase flow model, which significantly improves the efficiency and stability of the solution of the three-dimensional temperature field of OTSG. This study provides an efficient 3D refinement numerical analysis method for the design and safety verification of OTSG.

Extending the Pressure-Time Method to Pipe With Variable Cross-Section With Three-Dimensional Numerical Simulations

Abstract The flowrate in hydraulic turbines can be measured using the pressure-time method specified by the IEC 60041 standard. This method assumes a one-dimensional (1D) flow and is limited to straight pipes with a uniform cross section and specific restrictions on length (L > 10 m) and velocity (U × L > 50 m2 s−1). However, in low-head hydropower plants, the intake typically has a variable cross section and small length, making it challenging to use this method. This paper presents the development of a methodology that extends the applicability of the pressure-time method for variable cross section by using three-dimensional computational fluid dynamics (3D CFD). A combination of 3D CFD and 1D pressure-time methods is employed iteratively to estimate the kinetic energy correction factor. The obtained time-dependent values are then used in the 1D pressure-time method to calculate the flowrate. The new methodology is applied with experiments performed on a test rig with a reducer. The obtained results illustrate the significantly different kinetic energy correction factor obtained than those obtained using constant or quasi-steady assumptions. The proposed methodology changes the mean deviation compared to the reference flowmeter from −0.83% (underestimation of flowrate) to ±0.1%, increasing the method's accuracy.

Modelling Air Flow through Pneumatic Valves: A Brief Review with an Experimental Case Study

Compressible flow models are commonly used for describing air flow through pneumatic valves. Because of the difficulties in predicting viscous losses, these models ultimately rely on experimental determination of coefficients. Different equations have been proposed for different fluid speeds, having the sonic fluid velocity as a reference mark. However, one might question whether a much simpler approach, where the fluid is considered as incompressible, would still give good results within the typical range of industrial applications. Moreover, practically all models presuppose that the valve output pressure decreases in time, as in a discharge process. This paper reviews some representative one-dimensional compressible flow models and discusses the appropriateness of using equations based solely on discharging flows. Two experimental circuits, where an air reservoir is pressurized and, subsequently, decompressed, are used for comparison between different flow models. It is shown that a simpler set of equations still produces acceptable results for practical pneumatic applications.

Asymmetric Flow Phenomena Affecting the Characterization of the Control Plant of an Altitude Test Facility for Aircraft Engines

As an indispensable part of the engine manufacturer supply chain, the eco-efficiency of altitude test facility (ATF) operations must improve. Automation is a key enabler in this context since it not only increases precision and reproducibility but also allows for reducing the test time and energy consumption. A suitable controller and reliable validation are crucial to ensure the stability and appropriate response of the control system. Both aspects necessitate a thorough understanding of the control plant, expressed in a numerical model. These models have to be suitable for control system design and validation while covering asymmetric flow phenomena that occur in the pipe system and detailing the nonlinear system dynamics to a high degree of accuracy. One-dimensional network models, state-space models, highly resolving numerical models, and data-driven models are relevant applications for this task. We compare the results of state-of-the-art one-dimensional network models which mainly imply symmetric flow conditions with those of three-dimensional Reynolds-averaged-Navier–Stokes (RANS) simulations which cover asymmetric flow phenomena. The findings show that the assumptions of idealized, axis-symmetric flow in the one-dimensional flow elements do not hold true for the complex flows in an altitude test facility. In a second step, we have compared the results of one-dimensional simulations with in-service measurements taken during ATF test campaigns. Deviations were observed, which become explainable based on the insights gained from the comparison with the RANS simulation. The findings reveal that the one-dimensional simulation-based approach is insufficient to adequately reflect the plant and subsequently for validation due to the observed asymmetric flow phenomena. To overcome this limitation, the application of an empirical first-order transfer function using system identification methods is proposed. Its applicability is successfully demonstrated for the exhaust gas section of the ATF. Subsequently, essential criteria for the design of a suitable control concept for the outlet condition are derived.

Analysis of the choking condition of one-dimensional diabatic flows with wall friction

The choking condition of a one-dimensional steady-state diabatic flow, with wall friction, of a perfect gas through a constant cross-section pipe has been analysed by applying a recent analytical solution. Such a choking condition can be achieved for an initially subsonic flow and a supersonic one, even when the heat flux goes from the fluid to the wall. Entropy–enthalpy diagrams have been analysed, and a universal choking condition for compressible diabatic flows with wall friction has been determined. The analytical solution of a supersonic flow, in which a normal shock occurs, has been obtained for a diabatic flow with wall friction and compared with the results of a numerical model.

Flow irreversibility and heat transfer effects on turbine efficiency

The quantification of the flow irreversibilities is crucial to developing future turbomachinery. Traditionally, design correlations and efficiencies are based on comparisons to isentropic relations to quantify the deviation from an “ideal” case. However, isentropic relations typically assume one-dimensional adiabatic flow, representing a significant departure from the actual situation in turbines operating with large levels of heat transfer. In this paper, the aerothermal losses and power generation in reversible processes are derived for three-dimensional compressible flow considering heat transfer effects. A new definition of the power potential in a reversible process is proposed that can be used to perform detailed budgeting of the losses. The proposed new loss framework can be adopted locally, which enables the precise identification of the loss source. New aerodynamic and aerothermal efficiency expressions are proposed to assess shaft power extraction in combination with heat exchange. The new method enables designers to identify the regions with high loss generation in steady and also in unsteady flow conditions, offering new avenues to evaluate the loss generation mechanisms during the design phase. Therefore, our new tool is essential to developing reduced-order models for the design of future fluid machinery.

A semi-implicit finite volume scheme for blood flow in elastic and viscoelastic vessels

A novel staggered semi-implicit finite volume method for the simulation of one-dimensional blood flow in networks of elastic and viscoelastic vessels is proposed. The one-dimensional blood flow model is split into three subsystems: one containing the nonlinear convective terms, a second one for the viscoelastic terms and a final subsystem for the pressure-related terms. An explicit approach is then employed to discretize the convective subsystem, while the viscous and pressure terms are treated implicitly. This leads to a CFL-type time step restriction which depends only on the bulk velocity of the flow and not on the speed of the pressure waves or on the visco elasticity. As such, the method is computationally efficient in case of low speed index, which is equivalent to a low Mach regime for the Navier-Stokes equations. To extend the proposed methodology to the case of networks, a novel and very simple 3D approach for the treatment of junctions is proposed. Each junction is represented by a unique three-dimensional primal cell and the Euler equations are employed to approximate the velocity and pressure unknowns. A multidimensional numerical flux then takes into account the elementary information of the junction geometry, namely normal vectors and areas of the incident vessels, when approximating the blood flow at the cell interfaces embedded in the 3D cell. As such, the final scheme, based on guaranteeing mass and momentum conservation through the junction, is able to capture reflecting waves properly considering the effect of the different incident angles of vessels at a junction. The proposed methodology is carefully validated in the context of single elastic and viscoelastic vessels and small networks showing a good agreement with available analytical, experimental and numerical data.

Symmetry and scaling in one-dimensional compressible two-phase flow

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. Here, we focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

Self-Similar Flows with a Shock Wave Advancing toward the Center or Axis of Symmetry

We study one-dimensional flows of an ideal (inviscid and non-heat-conducting) perfect gas with an adiabatic exponent γ behind a shock wave moving toward the center (ν = 3) or axis (ν = 2) of symmetry in a cold gas at rest. Flows with a reflected shock wave and flows terminating with simultaneous arrival of a shock wave and a piston, which has compressed the gas into a point or line, to the center of symmetry are admitted.

New Analytical Expressions of Concentrations in Packed Bed Immobilized-Cell Electrochemical Photobioreactor

An electrochemical photobioreactor with a packed bed containing transparent gel granules and immobilized photosynthetic bacterial cells is shown with a one-dimensional two-phase flow and transport model. We consider the biological/chemical events in the electrochemical photobioreactor, the intrinsically connected two-phase flow and mass transport, and other factors. This model is based on a system of nonlinear equations. This paper applies Akbari-Ganji’s and Taylor series methods to find analytical solutions to nonlinear differential equations that arise in an immobilized-cell electrochemical photobioreactor. Approximate analytical expressions of the concentration of glucose and hydrogen are obtained in liquid and gas phases for different parameter values. Numerical simulations are presented to validate the theoretical investigations.

Calibration of a Near-Wall Differential Reynolds Stress Model Using the Updated Direct Numerical Simulation Data and Its Assessment

In the article, a differential Reynolds stress model is recalibrated using turbulent channel flow direct numerical simulation data in the range of friction Reynolds numbers 550–5200. The calibration aims to produce a RANS sublayer model for use within the hybrid RANS/LES framework. The model is designed to capture the average field of a thin near-wall part of a boundary layer as accurately as possible. An a posteriori procedure is employed in which one-dimensional channel flow calculations are performed for all variations of the model coefficients at each stage of the optimization procedure. The coefficients are initialized with their original values and then optimized by minimizing the appropriately chosen norm. An improved representation of the mean velocity profile and peak Reynolds stress values is demonstrated. Both models—baseline and recalibrated—are implemented in an in-house CFD code, and several simulations, including a channel flow, a flat plate boundary layer and a boundary layer separation from a rounded step, are performed. The latter benchmark flow is also simulated in hybrid RANS/LES mode. The updated model is compared to the original one, demonstrating improvements over the baseline model in the cases it was designed for.

Enhanced prediction of the decongealing performance of aero-engine oil coolers with various fin types and operating conditions using lumped model

Freezing of the flight environment of an aircraft occasionally causes the congealing of oil in the oil coolers. Although decongealing tests and re-designs require longer durations, many studies have examined the cooling loss arising from this phenomenon. Numerical simulations for the decongealing process are computationally expensive, and experiments under typical operating scenarios are costly. In this paper, an efficient one-dimensional flow and thermal approach is proposed, with transient simulations under realistic decongealing scenarios involving a standard fuel cooled oil cooler. With the objective function being the maximization of the heat transfer and minimization of the pressure drop, different cooler configurations with various internal fins were examined for both design and off-design conditions. The proposed lumped model provides a similar accuracy with a lower calculation cost compared to an earlier model. It also ensures better stability and easier code modifications. The current study demonstrates an optimum heat transfer and pressure drop with improved total decongealing performance when offset-strip fins on both the oil and fuel sides (ΔP: 23.9 psi, Tout: 12.3 °C) or an offset-strip fin on the oil side and a wavy or pin fin on the fuel sides (ΔP: 34.2 psi, Tout: 11.4 °C) are applied.

Analysis of pressure surges under various flow patterns in the tunnel of an underwater rock plug blasting system using different transition process models

Abstract The pressure surge at the moment of blasting seriously threatens the safety of pipeline structures and other buildings. This article established two numerical simulation models of the hydraulic transition process and water–air two-phase flow based on the one-dimensional transient flow theory and considering the actual flow characteristics of water and air. The hydraulic characteristics and blasting parameters of the blasting system were studied under two different conditions of the tunnel with and without the pressure flow. The observed parameters of an actual blasting engineering prototype verified the accuracy of the mathematical model. The maximum pressure of pressure blasting was 2.55 times as high as hydrostatic pressure. The maximum pressure of non-pressure blasting was 1.77 times as high as hydrostatic pressure. Pressure blasting impact was 2.17 times greater than nonpressure blasting. Discrepancies between actual and simulated data for gushing and overflow heights ranged from 9 to 14%. The model can provide a reference for blasting engineering on the simulation calculation of hydraulic characteristics such as impact pressure, overflow time, and overflow of the underwater rock plug blasting system.

Adiabatic wall temperature in the supersonic flow of moist air with spontaneous condensation

The expansion of moist air in supersonic nozzles is accompanied by spontaneous condensation of water vapor due to a sharp decrease in flow temperature and pressure. However, in the near-wall boundary layer due to the viscous dissipation, moist air temperature decreases slightly in comparison with initial one. This leads to the fact that the vapor remains overheated in the near-wall region and condensation does not spread to its entire depth. Droplets formed in the core flow as a result of condensation can penetrate into the near-wall region due to turbulent diffusion and evaporate due to higher temperature in the near-wall region. This process causes cooling of the near-wall gas layers and, consequently, a decrease in the adiabatic wall temperature. A decrease in the adiabatic wall temperature relative to the stagnation temperature leads to a decrease in aerodynamic heating and, consequently, in the heat flux from the gas to the body. In this paper, measurements of the adiabatic temperature of the supersonic nozzle wall for moist air flow with condensation are presented. Temperature measurements were made using an infrared thermal imager. Initial moisture content varied in the range of 1.5–20.2 g/(kg. dry air) and initial relative humidity in the range 20–90%. It is shown that in the region behind the zone of spontaneous condensation (“condensation shock”), adiabatic wall temperature depends on the initial moisture content and can be either greater or less than the value of a single-phase (dry air) flow with identical initial flow parameters. Estimates of the flow parameters behind the condensation region are obtained using one-dimensional diabatic flow equations and experimental static pressure distributions along the nozzle length. The correlation between the initial moisture content, the average droplet size and the temperature recovery factor is shown.

Spectral cocycle for substitution tilings

AbstractThe construction of a spectral cocycle from the case of one-dimensional substitution flows [A. I. Bufetov and B. Solomyak. A spectral cocycle for substitution systems and translation flows. J. Anal. Math.141(1) (2020), 165–205] is extended to the setting of pseudo-self-similar tilings in ${\mathbb R}^d$ , allowing expanding similarities with rotations. The pointwise upper Lyapunov exponent of this cocycle is used to bound the local dimension of spectral measures of deformed tilings. The deformations are considered, following the work of Treviño [Quantitative weak mixing for random substitution tilings. Israel J. Math., to appear], in the simpler, non-random setting. We review some of the results of Treviño in this special case and illustrate them on concrete examples.

Method for efficient calculating earth pressure of retaining wall considering plant transpiration

An accurate estimation of earth pressure on retaining walls is imperative to achieving its design. This paper presents an analytical method framework that considers the effect of plant transpiration relative to the traditional calculation approaches. Specifically, a closed-form solution for one-dimensional steady unsaturated flow considering plant transpiration is incorporated into a representation of effective stress to obtain the changes in matric suction, and effective stress. The representations are used to extend Hooke’s law and Rankine’s earth pressure theory to determine at-rest, active, and passive earth pressures. Subsequently, the analytical method is used in a series of analysis case studies on the influence of root architecture types, transpiration rates, and soil types on earth pressure, to reveal that it can rapidly obtain the earth pressure. Notably, the effect of plant transpiration on earth pressure is significant. Furthermore, it is found that soil types and transpiration rates have a larger influence than root architecture types. Collectively, the research not only reveals the effect of plant on earth pressure for retaining wall, but also provides a theoretical basis for further exploration of the contribution of plants to the stability of retaining wall.