Unsteady Process Research Articles

Complete Dynamics From Ignition to Stabilization of a Lean Hydrogen Flame With Thickened Flame Model

Abstract In recent years, attention has been paid to hydrogen thanks to its carbon-free nature and its interesting characteristics as an energy vector. Despite the large number of numerical analyses regarding hydrocarbon combustion in all the steady and unsteady processes, few papers that cover all those aspects are available in the literature for hydrogen flames. Therefore, a numerical methodology to explore the complete ignition sequence from the spark release to the flame stabilization is validated on a single-sector hydrogen burner. In this context, a preliminary direct numerical simulation (DNS) investigation of laminar spherical expanding flames is performed using different diffusive transport models to isolate their impact. The present work, carried out within the European project HESTIA, investigates the atmospheric test rig installed at the Norwegian University of Science and Technology operating with a lean, perfectly premixed, hydrogen–air flame stabilized on a conical bluff body. Four simulations are performed adopting the thickened flame model with an energy deposition (ED) strategy to assess the impact of preferential and thermal diffusion, as well as grid resolution, on flame dynamics. Three-dimensional (3D) flame structure visualization coupled with detailed particle image velocimetry (PIV)/OH-planar laser induced fluorescence (OH-PLIF) measurements allows the investigation of the key mechanisms involved during the ignition. The dynamic response of the flame through axial fluctuations once the ignition transient is concluded is reconstructed by the numerical strategy employed. Although the overall behavior is almost unchanged by including or not thermal diffusion effects, their local impact on the flame is evident leading to a better agreement with experimental data.

Non-equilibrium condensation flow characteristics of wet steam considering condensation shock effect in the steam turbine

A non-equilibrium condensation flow occurs in steam turbines, accompanied by condensation shock. At present, there are limited studies on the influence of condensation shock on the flow and condensation characteristics of wet steam, and the unsteady influence of condensation shock on the flow field of wet steam always have been ignored. In this paper, the unsteady flow characteristics of condensation were presented by considering the condensation shock effect. First, the condensation flow models and corresponding source terms were programmed and loaded with UDS (user-defined scalar) and UDF (user-defined function), respectively, and the governing equations were discretized using a high-resolution calculation method. The calculated results agreed well with the reported experimental results. Based on the models, the non-equilibrium condensation flow characteristics with inlet and outlet pressures in Laval nozzle considering the condensation shock effect were analyzed. Finally, during the unsteady phase change process, the effects of back pressure and saturation of the inlet on the liquid phase parameters were examined considering the condensation shock effect in the Dykas cascade. The results show that a decrease in the back pressure and an increase in the inlet pressure improve the condensation shock intensity in Laval nozzle. With the increase of condensation shock intensity, the nucleation rate increases. Moreover, in Dykas cascade, with the increase of back pressure from 48.8 kPa to 73.2 kPa, the maximum wetness decreases from 4.8 % to 2.1 %, whereas with the increase of relative saturation from 0.58 to 0.88, the maximum wetness increases from 2.4 % to 3.6 %. The results obtained in this paper are of significance to accurately analyze the actual situation of non-equilibrium condensation flow of wet steam and to develop methods for reducing wet steam loss in turbine stage.

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.

Unsteady numerical simulations of aircraft icing based on the dynamic grid method

In this study, an unsteady numerical simulation method based on dynamic grids was established to solve unsteady aircraft icing processes. The dual-time step method was used to achieve the time advancement of the transient airflow and droplets fields. The droplets trajectory was calculated using the Euler method, which incorporates a supercooled large droplets model. The transient evolution of the water film and ice layer on the substrate surface was considered in the icing thermodynamic model. The accuracy of the unsteady method for ice-shape prediction was verified via comparison and analysis of numerical examples. Additionally, the rime and glaze ice formation processes were explored, and the coupling effects of ice horn growth and the air convective heat transfer coefficient, water collection coefficient, and water film flow on the substrate surface were studied. The ice shapes calculated by unsteady and quasi-steady methods were compared. The results indicated that the latter predicts a larger icing range than the former. Moreover, there may be more obvious distinctions between these two methods in predicting glaze ice.

Progress of Experimental Studies on Oblique Detonation Waves Induced by Hyper-Velocity Projectiles

Oblique detonation waves (ODWs) are hypersonic combustion phenomena induced by oblique shock waves. When applied to air-breathing engines, ODWs offer high thermal cycle efficiency, adaptability to a wide range of flight Mach numbers, and the advantage of a short combustion chamber, making them highly promising for hypersonic propulsion applications. Despite numerous numerical studies on the heat release and multi-wave flow mechanisms of ODWs, practical applications of oblique detonation engines (ODEs) remain limited due to several technical challenges. These challenges include generating the required high-velocity test environments, achieving effective fuel and oxidant mixing, and measuring the flow field structure in hyper-velocity and high-temperature flows. These limitations hinder the development of ODEs, underscoring the importance of experimental research, particularly for understanding the initiation and propagation mechanisms of ODWs. One of the primary experimental techniques involves inducing oblique detonation using high-velocity models. This method is extensively used to study the initiation process, shock structure, initiation criteria, and ODW propagation. It is advantageous because the state of the experimental mixture is controllable, and the model state can be precisely measured. This paper reviews studies on oblique detonation induced by hyper-velocity projectiles, presenting advances in experimental methods, detonation wave structures, unsteady processes, and initiation characteristics. Additionally, we discuss the deficiencies in existing studies, noting that the current measurement methods fall short of the requirements for observing the ODW initiation process, propagation process, and fine structure. The application of advanced combustion diagnostic techniques and the exploration of the relationship between initiation processes and criteria are crucial for advancing our understanding of ODW initiation and stabilization mechanisms. Finally, we summarize the current state of experimental facilities and measurement techniques, providing suggestions for future research on the measurement of shock waves and chemical reaction zones.

Extinction of Ammonium Perchlorate: Similarity Between Rapid Depressurization and Low-Pressure Deflagration Limit

ABSTRACT The extinction of Ammonium Perchlorate (AP) monopropellant due to two transient processes, namely rapid depressurization and Low-Pressure Deflagration Limit (LPDL), was studied. The critical depressurization rate was determined experimentally using silica grease on the sides of the AP pellet to reduce convective heat loss. The critical depressurization rate was found to lie between 1820 and 1950 MPa/s. The computed critical depressurization rate was found to be 1450–1500 MPa/s with variable thermal properties in the condensed phase. The extinction of AP due to LPDL was studied using different heat fluxes imposed on the surface. Case I involved the constant heat flux imposed on the surface and suddenly reduced to zero, while case II involved constant heat flux imposed on the surface and linearly reduced to zero. The combustion stability was checked for both cases, and it was found that the combustion remains in a stable regime. For case I, the AP did not burn below 5.0 MPa when the imposed heat flux of 3 MW/m2 was suddenly reduced to zero in 0.1 s. However, for case II, the AP was found to burn up to 1.6 MPa when the imposed heat flux of 3 MW/m2 was linearly reduced to zero in 0.5 s. The extinction boundaries of two unsteady processes, extinction by rapid depressurization and extinction due to LPDL, were determined, and the two processes were shown to have similar physical behavior.

Deep Low‐Frequency Earthquake Reveals Unsteady Fluid Flow Beneath Tengchong Volcano Field in Southeast Tibet

AbstractDeep low‐frequency earthquakes (DLFE) are observed beneath volcanoes worldwide but are limited to island arc volcanoes, hotspot volcanoes, and rift zones. Here we show DLFEs in the Tengchong Volcano Field, southeast Tibet, located ∼300 km from the Indo‐Burma volcanic arc, by analyzing a 12‐year continuous seismic data set. The earthquakes were at a depth of ∼12 km, near the sidewall of the magma body detected by the magnetotelluric survey. The features of isotropic focal mechanism, episodic occurrence, and possible non‐power‐law scaling, with no detectable geodetic deformation, as well as the petrological signatures of the Holocene eruption product, suggest that the earthquakes were likely associated with the weak intermittent magma flows near the magma body. This finding may demonstrate the existence of unsteady magmatic processes in the margin of the Indo‐Eurasia collision zone, which could indicate unneglectable volcanic hazards, underestimated geothermal resources, and mineralization processes in similar regions.

Computational fluid dynamic model for the prediction of the unsteady operation process of a non-dispersive gold extraction from wastewater

The current study tries to investigate gold extraction in a membrane extractor in unsteady mode. The model was successfully validated using experimental results. The results showed that the diffusive flux on the zone close to the membrane surface is dominant in the first minutes of extraction but later the convective flux is the main flux, particularly at the centre of the shell side. The extraction time of one hour was not ample to extract all gold from the aqueous solution when the volume of solutions was 2000 mL and 3000 mL. Finally, the change in feed flow rate in the range of 30–55 cm3/min did not have a significant influence on the gold extraction time. However, the outlet dimensionless concentration of gold after one hour was increased from 0.24 to 44 with the increase of feed flow rate from 30 cm3/min to 55 cm3/min.

Mathematical modeling of unsteady process of cold storage within a container filled with nanomaterial incorporating Galerkin method

This research focuses on simulating the freezing involving a mixture of H2O and alumina nano-powders. It sheds light on the complex relationship between the characteristics of nano-powders and freezing dynamics, offering valuable insights applicable to various fields, including cryopreservation and thermal energy storage. By utilizing the Galerkin approach and incorporating an adaptive grid, the research introduces an elliptic container with a cold surface and strategically placed rectangular fins. The investigation examines how the characteristics of nano-powders, particularly their size (dp) and concentration (ϕ), influence different scenarios. Notably, changes in powder size have a significant effect on freezing time, initially decreasing by approximately 20.22 % before increasing by 19.1 %. Moreover, the sensitivity of powder size decreases with lower powder concentrations. For example, at ϕ = 0.02, an augment in dp primarily reduces the time by about 11.72 %, followed by an increase of 10.98 %. The most substantial improvement occurs when ϕ is optimized, resulting in a remarkable 41.27 % reduction in freezing time.

Lightweight insulating oil-well cement filled with hollow glass microspheres and numerical simulation of its unsteady heat transfer process

Lightweight insulating oil-well cement filled with hollow glass microspheres and numerical simulation of its unsteady heat transfer process

Tip-leakage-flow excited unsteadiness and associated control

Tip leakage flow in turbomachinery inherently generates intense unsteady features, named self-excited unsteadiness, which significantly affects the operating stability, aerodynamic efficiency, and noise but has not been well understood. A zonalized large eddy simulation is employed for a linear cascade, with wall-modeled large eddy simulation active only in the tip region. The simulation is well validated with advantages demonstrated for effectively reducing the computational cost while maintaining an equivalent prediction accuracy in the region of interest. The time-averaged and spatial-spectral characteristics of tip leakage vortex (TLV) structures are systematically discussed. The self-excited unsteady processes of TLV include the tip gap separation, the tip leakage and jet-mainstream interaction, the primary tip leakage vortex (PTLV) wandering motion, and the induced separation near end wall. The Spectral Proper Orthogonal Decomposition (SPOD) is used to examine the dominant frequencies and their coherent structures. It is found that these unsteady features change from a single high frequency to multiple lower frequencies due to the PTLV breakdown. The SPOD and correlation analyses reveal that the self-excited unsteadiness originates initially from unsteady vortex separation in the tip gap and is then fed by the interactions between the tip leakage jet and mainstream. The associated unsteady fluctuations are convected along the tip leakage jet trajectory, causing the wandering motion of PTLV core. Based on the revealed unsteadiness sources, a micro-offset tip design is proposed and shown to be an effective solution to reducing the tip flow unsteadiness. This work improves the understanding of tip-leakage-flow dynamics and informs the control of the associated unsteady fluid oscillation and noise.

Effect of a high-gradient magnetic field on particle concentration distribution in a magnetic fluid seal: Rivalry of the diffusion and magnetophoresis

In this paper, the unsteady process of particle concentration distribution in a magnetic fluid is studied. Diffusion and the effect of a high-gradient magnetic field in a magnetic fluid seal (MFS) are taken into consideration. It is crucial to take into account how particle mobility and diffusion coefficient vary on particle concentration in order to determine the possibility and time of the formation of a close packing of particles. The Carnaghan-Starling approximation was employed. It is demonstrated numerically that the geometry of the MFS, namely its gap width and pole base width, as well as the magnitude of the magnetic field strength under the pole tooth of the MFS, both influence the time of the formation of a close packing of particles. This period can be regarded as the MFS's uptime. Depending on the design of the working gap, the uptime seal for magnetic fluid based on vacuum oil may require between two weeks and six months. The uptime seal also becomes shorter when the carrier fluid's viscosity decreases.

Lattice Boltzmann model for incompressible flows through porous media with time-fractional effects

Anomalous transport has been commonly observed in the fluid flow through a complex porous medium, where the evolution exhibits a complex memory-like behavior. Classical integer-order models fail to depict anomalous transport phenomena, while fractional calculus has been proved effective in describing such behavior due to its ability to characterize long memory processes. In this paper, the time-fractional generalized Navier-Stokes (N-S) equations are formulated to model anomalous transport in porous media at the representative elementary volume (REV) scale by incorporating the Caputo fractional derivative of time into the widely employed generalized N-S equations. An innovative lattice Boltzmann (LB) model is presented for solving the time-fractional generalized N-S equations. We validate the proposed LB model by conducting a numerical example with analytical solutions, and observe a good agreement between the LB results and the analytical solutions. The proposed LB model is utilized for simulating Poiseuille flow, Couette flow, and cavity flow in porous media. Unlike the previous studies, which focus on the steady state of these flows, the present work focuses on the unsteady process from the initial state to the final steady state. It is found that time-fractional effects play a significant role in the unsteady processes of these flows. As the fractional order decreases, the flows undergo a slower evolution process and the impact of Darcy number on the unsteady process becomes increasingly noticeable. The Reynolds number has a significant impact on the velocity profile in the steady state, but it has relatively little effect on the duration of the unsteady process.

NUMERICAL SIMULATION OF TURBULENT FLOW AROUND DARRIEUS AND SAVONIUS ROTORS

The study of unsteady processes during the flow around the rotors of vertical-axis wind turbines was carried out based on the Navier-Stokes equations. General definition of the coupled problem on vertical-axis wind turbines rotors aerodynamics and dynamics is formulated. The solution to the system of initial equations is obtained using an implicit finite-volume numerical algorithm based on the method of artificial compressibility and multi-block structured grids. A code for the calculation of vertical-axis wind turbines rotors aerodynamic and power characteristics is developed on the base of Reynolds averaged Navier-Stokes equations for incompressible fluids. Two types of Darrieus and Savonius rotors with different geometric parameters and number of blades were calculated. The influence of Reynolds numbers, tip-speed-ratios and solidity on the power characteristics of the rotors has been established.

Vortex shedding from a square cylinder interacting with an undular bore wave train

In this work, we studied the wave-induced vortex generation and shedding from a semi-submerged vertical square cylinder interacting with an upcoming undular bore wave train under a shallow water configuration. This unsteady and rapid process was investigated by means of numerical and experimental approaches. A numerical simulation, solving the full turbulent viscous Navier–Stokes equations, was carried out in order to study and characterize both the undular bore wave properties and the vortex dynamics triggered during this unsteady interaction. Starting with fluid at rest, the undular bore was generated by the impulsive translational motion of a piston wavemaker at laboratory scale in both a numerical and an experimental wave tank. When the undular bore impinges on the cylinder, filamentary vortex structures were formed at the four cylinder's edges synchronized with the propagating wave motion, leading to the vortex shedding phenomena at a frequency that matched the wave instantaneous frequency. These vortices extended along the entire cylinder span under the water column, from the free surface to the seabed. At the trailing edge of the cylinder, a pairing process of two shed vortices was observed, similar to a Lamb–Oseen vortex pair. These vortices were present during the whole undular bore wave train dynamic forcing. An overall agreement was found with the experimental version of the bore–cylinder interaction, carried out in a physical wave tank. Laser sheet bore profiling and particle image velocimetry measurements of the velocity field confirmed undular bore properties, the onset of vortex formation, subsequent shedding, and pairing in the experiments performed in similar conditions with the numerical approach.

Efficacy of dispersing nano-powders on rate of cold storage during solidification considering transient conduction

This study conducts a simulation of the freezing through a container featuring finned sinusoidal geometry. The application of the Galerkin method effectively captures the intricate dynamics of unsteady processes, showcasing a significant enhancement by introducing nanoparticles to augment the system's thermal conductivity—an essential element for optimizing conduction efficiency. The numerical approach underscores the importance of employing an adaptive grid in unsteady scenarios, tailoring the grid based on the solid front's position due to heightened scalar gradients. Various powder diameters (dp) and fractions (φ) are systematically investigated, elucidating their distinct impacts on process duration. Results reveal that an initial increase in dp causes to a decrement in period by 19.93%, followed by a subsequent rise of 49.06%, specifically for scenarios with a 0.04 nanoparticle concentration. The incorporation of nanoparticles yields a noteworthy 41.13% decrease in solidification time when optimal powder sizes are utilized. In contrast, the solidification time without additives is 278.95s, reduced to 164.19s with the introduction of optimally sized powders.

Flow physics during durge of an axial-centrifugal compressor

Aerodynamic instability design is one of the crucial elements when designing a compressor. Unstable phenomenon such as surge harms the compressor in both performance and structure integrity. The complex unsteady flow process during instability strongly relates to the compressor design. This paper investigates the transient instability process using URANS on a three-stage-axial and one-stage-centrifugal combined compressor under its off-design conditions. Results show that the compressor suffers two surge patterns. The mild surge happens first, with a higher frequency than the traditional mild surge. Then, with the decrease of valve opening, the deep surge is initiated, and the axial stages work at the peak pressure ratio because the mass flow rate is limited by the choked radial diffuser. Moreover, analysis of aerodynamic loads reveals that IGV and the first rotor have the largest unsteady force among all blade rows. According to the flow field, the rotor root and stator tip suffer the most serious impulse caused by reversed flow during surge conditions.

Gas dynamics at starting and terminating phase of a supersonic exhaust diffuser with a conical nozzle

This research investigates the process of starting and breakdown of second throat diffuser during high-altitude test of conical nozzle with a high expansion ratio. The subscale experimental setup includes a conical nozzle with an expansion ratio of 53, plus a second throat diffuser with a contraction ratio of 1.85, using compressed air as the working fluid. Numerical simulation has been employed to identify the flow physics during the unsteady process of diffuser startup and breakdown. According to the results, the starting process is divided into three distinct stages. In the first stage, the exhausted flow from the nozzle enters the vacuum chamber, leading to an increase in vacuum chamber pressure. The second stage, corresponding to the period before full flow establishment in the conical nozzle, exhibits a relatively constant slope. In the final stage, associated with the transition from over-expanded to under-expanded states, the slope of the rate of evacuation development descends. Next, the vacuum degradation in termination process has been analyzed, and it has been found to include three stages: high slope, middle slope, and low slope. The flow physics during the start process, similar to the results observed in other conical nozzles, exhibits only a Mach reflection structure. However, during the termination process, the flow physics involve a combination of both structures, including Mach reflection and Cap Shock. The results indicate that during the start, an internal shock only interacts with the separation shock, and no special change occurs in the Mach reflection structure. In contrast, during the termination process, unlike what has been reported in previous studies on conical nozzles, the structure of cap shock waves and restricted shock separation patterns are also observed. Another distinction between the starting and termination processes is related to the pressure distribution in the diffuser wall. The wall pressure at the diffuser inlet during the termination process has been reported to be 90% higher than during the starting process.

Power Generation Limits in Thermal, Chemical and Electrochemical Systems

Power generation limits are evaluated via optimization for various energy converters, such like thermal, solar, chemical, and electrochemical engines, in particular fuel cells. Thermodynamic analyses lead to converters’ efficiencies, which help to solve problems of optimal upgrading and downgrading of resources. While methods of static optimization, i.e. differential calculus and Lagrange multipliers, are sufficient for steady processes, dynamic optimization applies the variational calculus and dynamic programming for unsteady processes. In reacting systems chemical affinities constitute prevailing components of an overall efficiency, thus flux balances are applied to derive power in terms of active parts of chemical affinities. Methodological similarity is observed when treating power limits in flow thermal machines and fuel cells. The examples show power maxima in fuel cells and prove suitability of a thermal machine theory to chemical and electrochemical systems. The main novelty of contribution in the fuel cell context consists in introducing an effective change of Gibbs free energy between products p and reactants s which takes into account lowering of voltage and power caused by the incomplete conversion of the overall electrochemical reaction.

Research on the distribution of heat fluxes during infrared drying of grain material

Purpose. To develop mathematical models of unsteady heat and mass transfer during the infrared (IR) drying process, and to create an algorithm for calculating the variable power of IR energy input to ensure quality drying of thermolabile material. Methods. The methods of mathematical modeling used to describe the unsteady drying process of thermolabile material in a dryer are based on the formalized description in the form of nonlinear inhomogeneous differential equations, taking into account the change in the power of IR energy input during the drying process. Results. A dependency for calculating the perceivable power of the IR source by the grain, based on the given process mode parameters, has been obtained. The drying kinetics of the grain, derived from formula (10), more accurately characterizes the process from a physical point of view than the drying equation (8) with a constant coefficient kck. It was established that three characteristic periods of the drying process can be traced in the graphical dependencies: I – heating; II – constant drying rate; III – falling drying rate. The calculation of heat fluxes for downward cross-ventilation of the grain layer, where air washes over IR heaters and reflectors and heats up to 35 °C, is presented. It was found that in the implementation of the process with a downward airflow, it is necessary to supply 20–25 % less radiant energy to the material at the same drying exposures according to the graphical dependencies. Conclusions. A mathematical description of the unsteady drying process of thermolabile material in a dryer, considering the change in the power of IR energy input during drying, has been formulated. An algorithm for calculating parameters that can be used for process identification and optimization of the operating parameters of existing grain dryers has been developed. Keywords: drying, grain material, mathematical model, diffusive transfer, moisture content, temperature, speed.