Quasi-steady Model Research Articles

State-space aerodynamic model reveals high force control authority and predictability in flapping flight.

Flying animals resort to fast, large-degree-of-freedom motion of flapping wings, a key feature that distinguishes them from rotary or fixed-winged robotic fliers with limited motion of aerodynamic surfaces. However, flapping-wing aerodynamics are characterized by highly unsteady and three-dimensional flows difficult to model or control, and accurate aerodynamic force predictions often rely on expensive computational or experimental methods. Here, we developed a computationally efficient and data-driven state-space model to dynamically map wing kinematics to aerodynamic forces/moments. This model was trained and tested with a total of 548 different flapping-wing motions and surpassed the accuracy and generality of the existing quasi-steady models. This model used 12 states to capture the unsteady and nonlinear fluid effects pertinent to force generation without explicit information of fluid flows. We also provided a comprehensive assessment of the control authority of key wing kinematic variables and found that instantaneous aerodynamic forces/moments were largely predictable by the wing motion history within a half-stroke cycle. Furthermore, the angle of attack, normal acceleration and pitching motion had the strongest effects on the aerodynamic force/moment generation. Our results show that flapping flight inherently offers high force control authority and predictability, which can be key to developing agile and stable aerial fliers.

On Aerodynamic Models for Flutter Analysis: A Systematic Overview and Comparative Assessment

This work reviews different analytical formulations for the time-dependent aerodynamic load of a thin aerofoil and clarifies numerical flutter results available in the literature for the typical section of a flexible wing; inviscid, two-dimensional, incompressible, potential flow is considered in all test cases. The latter are investigated using the exact theory for small airflow perturbations, which involves both circulatory and non-circulatory effects of different nature, complemented by the p-k flutter analysis. Starting from unsteady aerodynamics and ending with steady aerodynamics, quasi-unsteady and quasi-steady aerodynamic models are systematically derived by successive simplifications within a unified approach. The influence of the aerodynamic approximations on the aeroelastic stability boundary is then rigorously assessed from both physical and mathematical perspectives. All aerodynamic models are critically discussed and compared in the light of the numerical results as well, within a comprehensive theoretical framework in practice. In all cases, results accuracy depends on the aero-structural arrangement of the flexible wing; however, simplified unsteady and simplified quasi-unsteady aerodynamic approximations are suggested for robust flutter analysis whenever the wing’s elastic axis lies ahead of the aerofoil’s control point.

Swirl\u2013nozzle interaction experiment: quasi-steady model-based analysis

Measurements of sound due to swirl–nozzle interaction are presented. In the experiment a swirl structure was generated by means of unsteady tangential injection into a steady swirl-free flow upstream from a choked convergent–divergent nozzle. Ingestion of swirl by the choked nozzle caused a mass-flow rate change, which resulted in a downstream-measured acoustic response. The downstream acoustic pressure was found to remain negative as long as the swirl is maintained and reflections from the open downstream pipe termination do not interfere. The amplitude of this initial acoustic response was found to be proportional to the square of the tangential mass-flow rate used to generate swirl. When the tangential injection valve was closed, the mass-flow rate through the nozzle increased, resulting in an increase of the downstream acoustic pressure. This increase in signal was compared to the prediction of an empirical quasi-steady model, constructed from steady-state flow measurements. As the opening time of the valve was varied, the signal due to swirl evacuation showed an initial overshoot with respect to quasi-steady behavior, after which it gradually decayed to quasi-steady behavior for tangential injection times long compared to the convection time in the pipe upstream of the nozzle. This demonstrates that the acoustic signal can be used to obtain quantitative information concerning the time dependence of the swirl in the system. This could be useful for understanding the dynamics of flow in engines with swirl-stabilized combustion.Graphic abstract

Numerical investigation of temperature effect on water hammer with cavitation in copper pipe rig

The paper investigates temperature effect on water hammer in an isothermal pressurized copper pipe rig, for single and two phase flow. The study concerns pressure wave’s intensity, celerity and attenuation. Also, the cavities volume created during low pressure periods is inspected. The mathematical model of hyperbolic equations is described by the dynamic and continuity equations, which have been transformed by the characteristics method (MOC) into ordinary differential equations. Water hammer solver was built considering two different models of cavitation and column separation, the discrete vapor cavity model (DVCM) and the discrete gas cavity model (DGCM). In addition of the quasi-steady friction model, two unsteady friction models were incorporated into the code, the convolution based model proposed by Vardy & Brown and the instantaneous acceleration model proposed by Brunone. The simulations concern temperature range within 4°C to 95°C. Although the single and the two phase water hammer don’t behave with the same manner, the results obtained with the different models, show a significant influence of the temperature.

Exchange between drainage systems and surface flows during urban flooding: Quasi-steady and dynamic modelling in unsteady flow conditions

The accurate modelling of urban flooding constitutes an integral part of flood risk assessment and management in residential and industrial areas. Interactions between drainage networks and surface runoff flows are commonly modelled based on weir/orifice equations; however, this approach has not been satisfactorily validated in unsteady flow conditions due to uncertainties in estimating the discharge coefficients and associated head losses. This study utilises experimental data of flow exchange between the sewer flow and the floodplain through a manhole without a lid to develop two alternate approaches that simulate this interaction and describe the associated exchange flow. A quasi-steady model links the exchange flow to the total head in the sewer pipe and the head losses in the sewer and the manhole, whilst a dynamic model takes also into account the evolution of the water level within the manhole at discrete time steps. The developed numerical models are subsequently validated against large-scale experimental data for unsteady sewer flow conditions, featuring variable exchange to the surface. Results confirmed that both models can accurately replicate experimental conditions, with improved performance when compared to existing methodologies based only on weir or orifice equations.

Effect of moving boundaries on the modeling of heat and mass transfer from an evaporating spherical drop

The effect of unsteadiness of the energy and vapor transport within the gas phase from an evaporating drop is studied by solving a moving boundary problem taking into account the effect of drop temperature variation and radius shrinking. The effect of convection is also taken into account in a simplified way by means of the film theory approach, which yields a double moving boundary problem. A proper change of the reference system leads to the numerical solution of a partial differential equation system with fixed boundaries. A comparison with the commonly adopted quasi-steady model allows to point out the effect of ambient temperature and pressure, convection and chemical species, by quantifying the discrepancies between the two predictions for sixteen different compounds, Reynolds number ranging between 0 and 20 and gas pressure up to 20 bar. The simplified approach used in this paper was chosen to maintain the same simplifying assumptions of the widely used quasi-steady model, with the only exception of the drop shrinking. Therefore, the discrepancies between the two predictions can solely be ascribed to the unsteadiness caused by the interface movement, allowing to quantitatively point out this specific effect.

Deviations from classical droplet evaporation theory.

In this article, we show that significant deviations from the classical quasi-steady models of droplet evaporation can arise solely due to transient effects in the gas phase. The problem of fully transient evaporation of a single droplet in an infinite atmosphere is solved in a generalized, dimensionless framework with explicitly stated assumptions. The differences between the classical quasi-steady and fully transient models are quantified for a wide range of the 10-dimensional input domain and a robust predictive tool to rapidly quantify this difference is reported. In extreme cases, the classical quasi-steady model can overpredict the droplet lifetime by 80%. This overprediction increases when the energy required to bring the droplet into equilibrium with its environment becomes small compared with the energy required to cool the space around the droplet and therefore establish the quasi-steady temperature field. In the general case, it is shown that two transient regimes emerge when a droplet is suddenly immersed into an atmosphere. Initially, the droplet vaporizes faster than classical models predict since the surrounding gas takes time to cool and to saturate with vapour. Towards the end of its life, the droplet vaporizes slower than expected since the region of cold vapour established in the early stages of evaporation remains and insulates the droplet.

Development of nonlinear framework for simulation of Typhoon-induced buffeting response of Long-span bridges using Volterra series

This paper presents a nonlinear time-domain analysis framework to simulate the buffeting response of long-span bridges subjected to the typhoon winds. The analysis framework separates the aerodynamic forces generated on the bridge deck into low- and high-frequency components modelled by the quasi-steady and Volterra series-based wind load models, respectively. The aerodynamic nonlinearity and non-stationary wind effects existing in the wind-bridge interaction are incorporated in the analysis framework in terms of the ① static force coefficients measured at low-frequency effective angle of attack, ② flutter derivatives identified at varying angles of attack, ③ higher order fluid memory terms of the Volterra series and ④ time-varying mean wind speed. The efficacy of the proposed framework is verified by presenting the numerical example of a suspension bridge fully immersed in the typhoon winds with aerodynamic characteristics sensitive to the effective angle of attack. The dynamic analysis results show good agreement in the simulation of the typhoon-induced buffeting response of the bridge deck. Moreover, the simulation results are also compared with the measurements, and the existing linear and nonlinear wind load models to elucidate the efficiency of the proposed framework.

Numerical simulation of heat and mass transfer during sublimation drying of porcine aorta

Freeze-drying is an effective method for aortal preservation. However, there are few studies on heat and mass transfer of aortal freeze-drying. In this study, the contactless weighing device was used to monitor freeze-drying process. The radiation view factor of the aortal segment was estimated, and the quasi-steady state model was used to analyze heat and mass transfer, there was a certain amount of heat flux in the frozen layer, which provided sublimation heat for internal sublimation interface. By theoretical calculation, the vapor diffusion coefficient was determined. The unsteady state model was used for numerical simulation. The simulated result of free water removal ratio was consistent with experiment result. Both heat flux density and mass flux density decreased non-linearly in the early stage, but approximately linearly in the late stage. The velocity of inner and outer sublimation interfaces was almost the same. The nodes temperature gradually increased and finally approached the heating temperature, and the temperature gradient of both dried and frozen layers decreased gradually with drying time. The water vapor pressure gradient was smaller near the aortal wall and larger in the middle region.

Code development and analysis on the operation of liquid metal high temperature heat pipes under full condition

Heat pipe cooled reactor (HPR) is an innovative solid-core reactor which utilizes heat pipes to extract heat from the core to the energy conversion system. In this paper, a mathematical model for high-temperature heat pipes from a frozen state to a steady state is developed based on experimental data. The model is simplified and solved numerically. The two-dimensional transient heat conduction model of the wall and wick and the one-dimensional quasi-steady compressible vapor flow model are coupled to simulate the operation of a heat pipe when vaporization and condensation occur at the liquid–vapor interface. And the equivalent heat capacity model and the rarefied vapor model are introduced to simulate the process of heat pipe startup from a frozen state. Numerical results indicate that the model of heat pipe can predict the operation of high-temperature heat pipe with an error of less than 1.04% at steady state and 23.4% during the startup. Based on the simulation results, the velocity of vapor decreases with the heat transfer power in the steady state and the velocity of potassium vapor is 58.4% of sodium vapor velocity under the same operation condition. During the startup, when the rarefied-continuum interface located in the end of the evaporator section, the maximum vapor velocity occurs which is 1.3 times of steady velocity. This work makes it possible to predict the operation of a high-temperature heat pipe and provides a reference for the design and application of HPR.

Shock motion inside a varying cross-section channel and consequences on the downstream flow

Using numerical simulations shock wave physics in a constant area channel behind a convergent or divergent channel is investigated. It is found that shock wave propagation in the downstream uniform area region is influenced by the post-shock flow unsteadinesses. A detailed flow description is provided and a quasi-steady model for determining the waves intensity at large times is proposed. Moreover, this study points out the limits of the use of Whitham's theory in a variable area channel.

Latent heat storage integration into heat pump based heating systems for energy-efficient load shifting

Integrating latent heat thermal energy storage (LHTES) units into building heating systems has been increasingly investigated as a heat load management technology. A conventional LHTES integration method for heat pump based heating systems is to connect the heat pump’s condenser for charging the LHTES unit. This integrating layout however usually leads to increased electricity input to the heating system. To underline this issue and provide solutions, this paper presents three new LHTES integrating layouts where the LHTES unit is connected with the de-superheater of the main heat pump (Case 2), the condenser of a cascaded booster heat pump cycle (Case 3), or a combination of using both the de-superheater and the booster cycle (Case 4). In the context of a multi-family house in Stockholm, a quasi-steady state heating system model was developed to evaluate the new integrating layouts, which were benchmarked against the baseline heating system without storage (Case 0) and the conventional integrating layout using the main heat pump condenser (Case 1). Hourly electric power input to the heating system was modelled for calculating the performance indicators including the heating performance factor, the operational expense and justifiable capital expense, and the indirect CO2 emissions. Two load shifting strategies were simulated for an evaluation period of Week 1, 2019: 1) charge during off-peak hours (8 pm to 6 am) and 2) charge during daytime hours (10 am to 7 pm). The simulation results of the off-peak charging strategy show that, in Cases 2–4, the heating performance factor is 22%-26% higher than Case 1 and the operational expense can be reduced by 2%-5% as compared with Case 0. The savings in the operational expense can justify the capital expense of 11 k-25 k Swedish Krona (SEK) for the LHTES systems in Cases 2–4 assuming a 15-year operation. Furthermore, the advantage of using the daytime charging strategy is principally the mitigation of CO2 emissions, which is up to 14% lower than the off-peak charging strategy. In summary, higher energy efficiency for heating is validated in the three new proposed integration layouts (Cases 2–4) against the condenser charging layout.

Aerodynamic Characterization of a Full-Scale Compact Car Exposed to Transient Crosswind

The transient surface pressure over a full-scale, operational compact automotive vehicle—a Volkswagen Golf 7—exposed to transient crosswinds with relative yaw angles of β = 22-45° has been characterized. Experiments were performed at the BMW side-wind facility in Aschheim, Germany. Measurements of the incoming flow in front of the car were taken with eleven five-hole dynamic pressure probes, and separately, time-resolved surface pressure measurements at 188 locations were performed. Unsteady characteristics (not able to be identified in quasi-steady modelling) have been identified: the flow in separated regions on the vehicle’s leeward side takes longer to develop than at the windward side, and spatially, the vehicle experiences local crosswind as it gradually enters the crosswind. The total effects of these localized unsteady pressure characteristics have also been predicted to affect the vehicle globally, with the evaluation of the transient forces and moments—through pressure integration—exhibiting unsteady characteristics of overshoots, undershoots, and temporal lag; relative to steady crosswind. These results provide new insight into both the characteristics and the causes of the unsteady crosswind response of a real, operational vehicle operating in real-world conditions. This insight can be used in the design of future vehicles to make them less sensitive to unsteady gusts. Further these results can be used to develop and validate numerical and reduced-scale experimental methods that can test and assess new vehicle geometry designs during the early stages of vehicle development.

A CFD data-driven aerodynamic model for fast and precise prediction of flapping aerodynamics in various flight velocities

Abstract

Hybrid quasi-steady thermal lattice boltzmann model for investigating the effects of thermal, surfactants and contact angle on the flow characteristics of oil in water emulsions between two parallel plates

In this work, a two-dimensional hybrid quasi-steady thermal lattice Boltzmann model with temperature-dependent interfacial tension, surfactant and contact angle modules, is used to study the combined multi-physics effects on oil in water (O/W) systems flowing between two-parallel oil-wet plates. The proposed model is used to execute a parametric study for investigating the effects of the droplet radius, source terms, temperature, and surfactants parameters such as concentrations, elasticity, and diffusion coefficients on the flow characteristics of oil in water (O/W) emulsions inside microchannels. Flow conditions such as droplet Reynolds number0.41≤Re≤48, Webber number0.041≤We≤28 dimensionless surfactant surface concentration0.1≤Γ∗≤0.5, and surface Péclet number0.011≤Pes≤31are used in the simulations. The presence of surfactant noticeably enhances the droplets' transportation inside the channel, due to increased droplets' contact angle and deformation. Contaminated droplets with surfactant retain a greater bulk mass center velocity than clean ones to the tune of 2–5 times depending on the simulation conditions. The rise in temperature has a major impact on improving the suspended phase bulk velocity and power number ratio (system's efficiency indicator) for cases with and without surfactant. However, the presence of surfactant at elevated temperatures ameliorates the amount of useful work absorbed by the droplets from the flow significantly. Using specific conditions from the parametric study such as high temperature and surfactants characterized by low diffusion coefficient, results in an effective droplets breakup. The daughter droplets depart from the channel walls by shear lift, which enhances the suspended fluid transportation and increases the power number ratio up to 5.7 times.

Effects of side ratio on energy harvesting from transverse galloping of a rectangular cylinder

Rectangular cylinders have been identified as ideal bluff bodies for galloping-based energy harvesting, while a systematic study of the effects of the side ratio (i.e., the ratio between the cylinder width and the cylinder height) remains unavailable. This study investigates the influences of the side ratio on the piezoelectric energy harvesting from the transverse galloping of a rectangular cylinder based on a representative electro-aero-mechanical model, in which the aerodynamic force is calculated by the quasi-steady theory. The existing experimental aerodynamic coefficients for rectangular cylinders with side ratios of 0.62–3.0 are utilized as inputs of the quasi-steady aerodynamic force model. The influences of the side ratio and load resistance on the onset velocity, displacement, and power output of the galloping-based energy harvester are investigated. The results show that the onset velocity of galloping is dependent on the load resistance while this dependency becomes less significant with increasing the natural frequency. The onset galloping velocity of the energy harvester decreases with increasing the side ratio, and the lowest onset velocity is achieved by a rectangular cylinder with a side ratio of around 2.50. The largest vibration amplitude is achieved by the cylinder with a side ratio of 1.62 or 2.0 at low flow velocities, while the largest vibration amplitude is always achieved by the square cylinder at high flow velocities. Therefore, the side ratio of a galloping-based energy harvester should be designed according to its working environment: the optimal side ratio is around 1.0 if the harvester is expected to work at relatively high reduced flow velocities, while the optimal side ratio is around 1.62–2.0 if the harvester is expected to be effective at relatively low reduced flow velocities. These conclusions can provide references for designing galloping-based energy harvesters with rectangular cylinders as bluff bodies.

Flow-induced periodic snap-through dynamics

Abstract

The Simulation of Different Combustion Stages of Micron-sized Aluminum Particles

In this study, a quasi-steady combustion model of an aluminum particle is established, which is more accurate to simulate the physical combustion process. Detailed gas-phase reaction mechanism and surface reaction mechanism are considered. Moreover, the particle temperature is not constant in this work, which is calculated in different combustion stages. The judgement standard of each combustion stage is from observational data in the experiment and the simulation results of combustion durations of each stage, and distribution of ambient temperature and gas-phase species profiles are in good agreement with experimental results. The calculation results show that in the first stage, burning rate of the particle is the fastest, and in the second stage, particle temperature can drop to more than 100 K below the boiling point for the large particles, which is slightly below the boiling point for small ones. As the combustion stage changes, Da number is going to keep going down, which will lead to the transition of combustion method from diffusion-limited control to kinetic-limited control for an aluminum particle.

Performance Analysis and Optimization of a Vertical-Axis Wind Turbine with a High Tip-Speed Ratio

In this work, the aerodynamic performance and optimization of a vertical-axis wind turbine with a high tip-speed ratio are theoretically studied on the basis of the two-dimensional airfoil theory. By dividing the rotating plane of the airfoil into the upwind and downwind areas, the relationship among the angle of attack, azimuth, pitch angle, and tip-speed ratio is derived using the quasi-steady aerodynamic model, and aerodynamic loads on the airfoil are then obtained. By applying the polynomial approximation to functions of lift and drag coefficients with the angle of attack for symmetric and asymmetric airfoils, respectively, explicit expressions of aerodynamic loads as functions of the angle of attack are obtained. The performance of a fixed-pitch blade is studied by employing a NACA0012 model, and influences of the tip speed ratio, pitch angle, chord length, rotor radius, incoming wind speed and rotational speed on the performance of the blade are discussed. Furthermore, the optimization problem based on the dynamic-pitch method is investigated by considering the maximum value problem of the instantaneous torque as a function of the pitch angle. Dynamic-pitch laws for symmetric and asymmetric airfoils are derived.

Heat source model for electron beam welding of nickel-based superalloys

Abstract An adapted heat source model is developed for transient thermal numerical analysis of electron beam welded nickel-based alloy with increased susceptibility to hot cracking. The model enables the consideration of heat redistribution due to beam deflection phenomena. The modeling concept is validated by the appropriate theoretical models and in addition, experimental studies especially performed for this purpose. Special attention is given to the calibration of heat source model parameters. The calibration procedure is based on a statistical approach involving a combination of novel analytical solutions and quasi-steady state finite element models. The model parameter field is statistically analyzed, and a prediction algorithm is developed using optimization algorithms from the six sigma theory. The reliability and practicability of the model is demonstrated by validation weldments. The work is dedicated to precisely calculating the temperature field in the high temperature region around the weld pool and thus to provide a more detailed explanation of the formation of hot cracks when welding turbine materials commonly used in industry and aircraft constructions.