Unsteady Velocity Field Research Articles

Unsteady flow analysis in a double-suction pump as turbine impeller based on finite-time Lyapunov exponent

Pump as turbine (PAT) is an excellent energy recovery device. Understanding the flow characteristics of the key component, the impeller, is essential for further optimization and design of PAT. To analyze the unsteady flow characteristics inside the impeller of a double-suction PAT from a Lagrangian perspective, numerical simulations were conducted using the shear stress transport k–ω turbulence model for the design conditions. The finite-time Lyapunov exponent (FTLE) method was employed to extract the two-dimensional and three-dimensional Lagrangian coherent structures (LCSs) of the impeller over one cycle of unsteady velocity field. Results indicate that with time, the scale of the FTLE field gradually decreases, suggesting enhanced flow stability, reduced mixing efficiency, smoother flow structures, and increased flow convergence. In the two-dimensional perspective, high FTLE values concentrate at the inlet region of the passage, pressure side of the blades, and outlet region of the passage, spreading gradually over the entire blade surface, while low FTLE values predominantly concentrate on the blade surface with a diminishing area. The flow separation occurs at the leading edge of the impeller, the suction side of the impeller and the inlet region of the flow channel. In the three-dimensional perspective, different LCSs show varied changes at specific FTLE values, reflecting the impact of FTLE variation on the distribution of LCSs and indicating the evolution of flow states in fluid dynamics. Each moment of LCS exhibits a growth–stability–dissipation status transition. The FTLE method effectively reveals the flow variations inside the impeller of a double-suction PAT, offering a new perspective and tool for analyzing the turbulent structures in the complex flow field of PAT.

Unsteady Swirl Distortion in a Short Intake Under Crosswind Conditions

Under crosswind operating conditions, the flow field of an aero-engine intake can be characterized by notable unsteady flow distortion. These distortions are typically associated with flow separation within the intake as well as with the ingestion of the ground vortex. This unsteady flow distortion can have a detrimental effect on the intake performance and potentially on the operability of the downstream compression system. Measurements of the unsteady velocity field within a model-scale intake under crosswind conditions were acquired using stereo particle image velocimetry (S-PIV). This work analyzes the S-PIV data to quantify the unsteady flow distortion, as well as the characteristics of the ingested ground vortex, in a short intake under crosswind conditions. The swirl distortion metrics were calculated for a range of crosswind velocities and intake mass flow capture ratios (MFCRs). The conditions at which the intake flow separates depend on crosswind velocity, ground clearance, the design of the intake, and the MFCR. Flow characteristics of both low MFCR diffusion-driven and high MFCR shock-induced separation were identified. The circumferential extent and intensity of the swirl distortion are strongly dependent on the crosswind velocity and mass flow rate. The swirl distortion caused by the diffusion-driven separation is greater than that due to the shock-induced separation. The diffusion-driven separation affects a larger portion of the intake aerodynamic interface plane with greater time-averaged and peak distortion levels compared to shock-induced separation. The ground vortex characterization at the aerodynamic interface plane showed a decreasing level of unsteadiness in vortex meandering with increasing MFCR.

Unsteady flow analysis in a pump as turbine impeller based on proper orthogonal decomposition and dynamic mode decomposition methods

Pump as turbine (PAT) is an efficient, simple, and cost-effective equipment combining pump and turbine and is one of the excellent energy recovery devices. It is helpful to master the flow characteristics of the key component impeller for the further optimization and design of the PAT. To analyze the unsteady flow features in the impeller of a double-suction pump operating as a turbine, numerical simulations were conducted using the shear stress transport (SST) k-ω turbulence model at the designed operating conditions. By utilizing proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods on the unsteady velocity field of a single cycle, the dominant modes up to the fourth order, along with their respective space–time information, can be extracted. The velocity field and vorticity field analysis were performed on the first four modes extracted using two different methods. Additionally, the vortex structures were extracted using the Ω method. The analysis demonstrates that the POD and DMD methods effectively decompose the intricate flow characteristics within the impeller into dynamic–static interference modes, fundamental modes, and dissipative modes. The dynamic–static interference mode is dominant, reflecting the flow characteristics influenced by the stationary components within the impeller. The vortex structure is mainly small tubular vortex and point vortex. The fundamental mode captures the steady flow field characteristics caused by the blade channel geometry. The vortex structure is mainly continuous tubular vortex and the diameter becomes larger. The dissipative mode reflects the flow separation generated on the blades by disturbances from the stationary components. The vortex structure is dominated by point vortex and discontinuous tubular vortex. Comparing the outcomes of the two modal analysis methods shows that the POD method has a distinct advantage in showcasing key changing nodes. In contrast, the DMD method is superior in isolating modes with a single frequency and in determining their stability.

Global dynamics and topology of two-phase mixing layer flow through simultaneous gas and liquid velocity measurements

This study reports the first time-resolved particle image velocimetry characterization of a planar two-phase mixing layer flow, whose velocity field is measured simultaneously in gas and liquid streams. Two parallel air and water flows meet downstream of a splitter plate, giving rise to an initially spanwise invariant configuration. The aim is to elucidate further the mechanisms leading to the flow breakup in gas-assisted atomization. The complete experimental characterization of the velocity field represents a database that could be used in data-driven reduced-order models to investigate the global behaviour of the flow system. After the analysis of a selected reference case, a parametric study of the flow behaviour is performed by varying the liquid ( $Re_l$ ) and gas ( $Re_g$ ) Reynolds numbers, and as a consequence also the gas-to-liquid dynamic pressure ratio ( $M$ ), shedding light on both time-averaged (mean) and unsteady velocity fields. In the reference case, it is shown that the mean flow exhibits a wake region just downstream of the splitter plate, followed by the development of a mixing layer. By increasing both $Re_l$ and $Re_g$ , the streamwise extent of the wake decreases and eventually vanishes, the flow resulting in a pure mixing layer regime. The spectral analysis of the normal-to-flow velocity fluctuations outlines different flow regimes by variation of the governing parameters, giving more insights into the global characteristics of the flow field. As a major result, it is found that at high $Re_g$ and $M$ values, the velocity fluctuations are characterized by low-frequency temporal oscillations synchronized in several locations within the flow field, which suggest the presence of a global mode of instability. The proper orthogonal decomposition of velocity fluctuations, performed in both gas and liquid phases, reveals finally that the synchronized oscillations are associated with a low-frequency dominant flapping mode of the gas–liquid interface. Higher-order modes correspond to interfacial wave structures travelling with the so-called Dimotakis velocity. For lower gas Reynolds numbers, the leading modes describe higher frequency fingers shedding at the interface.

Clustering of Floating Tracers in a Random Velocity Field Modulated by an Ellipsoidal Vortex Flow

The influence of a background vortex flow on the clustering of floating tracers is addressed. The vortex flow considered is induced by an ellipsoidal vortex evolving in a deformation. The system exhibits various vortex motion regimes: (1) a steady state, (2) oscillation and (3) rotation of the ellipsoidal vortex core. The latter two induce an unsteady velocity field for the tracer, thus leading to irregular (chaotic) tracer motion. Superimposing a stochastic divergent velocity field onto the deterministic vortex flow allows us to observe significantly different tracer evolution. An ellipsoidal vortex has ellipsoidal symmetry, and the tracer’s trajectories exhibit the same symmetry inside the vortex. Outside the vortex, the external deformation flow symmetry dominates. Diffusion scattering and chaotic advection give tracers the opportunity to leave the region of ellipsoidal symmetry and form a picture of shear flow symmetry. We use the method of characteristics to integrate the floating tracer density evolution equation and the Euler Ito scheme for obtaining the floating tracer trajectories with a random velocity field. The cluster area and cluster mass from the statistical topography are used as the quantitative diagnostics of a floating tracer’s clustering. For the case of a steady ellipsoidal vortex embedded into the deformation flow with a random velocity field component, we found that the clustering characteristics were weakened by the steady vortex. For the cases of an unsteady ellipsoidal vortex, we observed clustering in the floating tracer density field if the contribution of the divergent component was greater than or equal to that of the rotational (nondivergent) component. Even when the initial floating tracer patch was set on the boundary of the oscillating ellipsoidal vortex, we observed the formation of clusters. In the case of a rotating ellipsoidal vortex, we also observed pronounced clustering. Thus, we argue that unsteady ellipsoidal vortex regimes (oscillation and rotation), which induce chaotic motion of the nearby passive tracer’s trajectories, are still conducive to clustering of floating tracers observed in the density field, despite the intense deformation introduced by strain and shear.

Aerodynamic characterisation of porous fairings: pressure drop and Laser Doppler Velocimetry measurements

Wind tunnel measurements of pressure drop and steady and unsteady velocity field of a flow through fairing samples are described. 10 samples have been tested in pressure drop among which the velocity fields of 3 samples have been characterized by means of laser Doppler velocimetry. The samples are perforated plates, wiremesh plates or complex 3D geometries resulting from additive manufacturing methods. The Reynolds number of the experiments ranges from 55 000 to 117 000.

Experimental Flowfield Analyses of Installed Subsonic Jet–Pylon Interaction

This paper presents an experimental investigation into the flowfield of single-stream jets blocked by internal and external rigid nozzle structures. The jets studied include axisymmetric round and annular jets and asymmetric blocked pylon jets. The pylon nozzles tested have three different thicknesses, reducing the exit flow area by 5, 10, and 20%. Hot-wire anemometry is used to record the unsteady velocity field both at the nozzle exit and up to 10 jet diameters downstream. Installation effects, created by mounting a wing section close to the jet, and forward-flight effects are also considered. The nominal Mach numbers studied are and 0.6 for the jet flow, and , 0.1, and 0.2 for the flight stream. Results show that the nozzle blockages 1) redirect the jet toward the wing, 2) increase the entrainment rate in locations far downstream of the nozzle exit, 3) produce dominant effects compared to the change of entrainment induced by the presence of the wing, and 4) considerably increase the normalized turbulence intensity generated in in-flight conditions.

Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

Abstract

Flame-resolved transient simulation with swirler-induced turbulence applied to lean blowoff premixed flame experiment

This article presents a flame-resolved transient simulation of the Cavaliere et al premixed flame experiment [1] to investigate the mechanisms that lead towards lean blowoff/blowout (LBO). The computational domain includes the swirler to capture the unsteady turbulent 3D velocity field generated. The computational grid design intent is to minimize the use of the subgrid scale models in order to resolve most of the turbulence scales in both the fresh and the burnt gases as well as the flame front thickness throughout the computational domain, resulting in a structured mesh with a grid count of 236 million cells. A transient sequence corresponding to a step change of equivalence ratio Φ from 0.7 to 0.55 is modeled. The combustion chemistry mechanism consists of a single step overall reaction. The computational results are compared to experimental data and an overall good agreement is observed, except for the latest times of the LBO sequence. The validated computational results are analyzed with dynamic mode decomposition (DMD) technique, flow field visualizations, signals time-traces and space-time diagrams of a posteriori reconstructed OH fields to investigate the underlying mechanism leading to lean blowoff for this flame. In addition, an evaluation of known state of the art LBO mechanisms reported in literature is carried out. It includes the precessing vortex core, flame sheet holes, inner recirculation zone (IRZ) dynamics, and heat losses. The analysis shows that a key phenomenon leading to lean blowout for the present configuration is associated with the convective motion of cooler combustion products into the IRZ as the equivalence ratio is decreased.

Instantaneous pressure determination from unsteady velocity fields using adjoint-based sequential data assimilation

A sequential data assimilation (DA) method is developed for pressure determination of turbulent velocity fields measured by particle image velocimetry (PIV), based on the unsteady adjoint formulation. A forcing term F, which is optimized using the adjoint system, is added to the primary Navier–Stokes (N–S) equations to drive the assimilated flow toward the observations at each time step. Compared with the conventional unsteady adjoint method, which requires the forward integration of the primary system and the backward integration of the adjoint system, the present approach integrates the primary-adjoint system all the way forward, discarding the requirement of data storage at every time step, being less computationally resource-consuming, and saving space. The pressure determination method of integration from eight paths [J. O. Dabiri et al., “An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements,” J. Exp. Biol. 217, 331 (2014)] is also evaluated for comparison. Using synthetic PIV data of a turbulent jet as the observational data, the present DA method is able to determine the instantaneous pressure field precisely using the three-dimensional velocity fields, regardless of the observational noise. For the two-dimensional three-component (3C) or two-component (2C) velocity fields, which are not sufficient for pressure determination by the integration method due to the lack of off-plane derivatives, the present DA method is able to reproduce pressure fields whose statistics agree reasonably well with those of the referential results. The 3C and 2C velocity fields yield quite similar results, indicating the possibility of pressure determination from only planar-PIV measurements in turbulent flows. The tomography PIV measurements are also used as observational data, and a clear pressure pattern is obtained with the present DA method.

Experimental study of swirling flow from conical diffusers using the water jet control method

The actual requirements of the energy market enforce the hydraulic turbine to operate far from the best efficiency point. When hydraulic turbines operate at partial discharge, downstream of the runner (in the conical diffuser), the decelerated swirling flow becomes highly unstable. In these conditions a spiral vortex breakdown occurs, also known in engineering literature as the precessing vortex rope. The flow unsteadiness produced by the vortex rope results in severe pressure fluctuations that hinder the turbine operation or may cause accidents. We propose the water jet method for decelerated swirling flow with vortex rope from conical diffuser to mitigate the unsteadiness. The method involves injecting water at the inlet of the conical diffuser. Initial experimental investigations of the unsteady pressure field at conical diffuser wall reveal that the water injection method mitigates the pressure pulsations associated to the precessing vortex rope. In this paper, we investigate experimental measurements of the unsteady velocity field in a conical diffuser using LDA (Laser Doppler Anemometry). The main goal of the paper is to show how different water-jet discharge rates change the velocity field and the characteristics of the vortex rope in the wake.

Synchronization of dual diffusion flame in co-flow

In this study, the interaction of two adjacent diffusion flames (dual flame) were experimentally investigated using the direct imaging method and particle image velocimetry (PIV) measurements for varied distances between the two flames under the influence of the co-flow. The direct imaging method indicates the presence of various synchronization modes, such as merging, in-phase synchronization, amplitude death, anti-phase synchronization, and desynchronization, as the distance between the flames was increased. The dual flame synchronization was characterized using an image analysis of the time-series variation of flame heights summarized by the mean flame height, root-mean-square of the flame height, Strouhal number, and the cross-correlation coefficient of flame heights against the burner distance. Furthermore, the unsteady velocity fields of the synchronized flames were measured using PIV combined with the proper orthogonal decomposition (POD) analysis to extract the flow structure of the dual flame. The experimental results indicated that the in-phase mode is characterized by the formation of symmetrical vortices, whereas the anti-phase mode features the formation of asymmetrical vortices inside and outside of the flame. The POD analysis demonstrated higher fluctuating energy in the anti-phase mode than in the in-phase mode, which suggested the formation of a highly organized flame structure in the anti-phase mode.

Turbulence Amplitude Amplification in an Externally Forced, Subsonic Turbulent Boundary Layer

Experimental studies of the changes in turbulence characteristics inside a boundary layer due to external forcing were performed using hot-wire anemometry. The forcing was created by a periodically forced shear layer that was external to a compressible subsonic turbulent boundary layer. The convecting coherent structures in the shear layer create a concomitant unsteady pressure and velocity field and provide an external disturbance for the turbulent boundary layer on the wall of the tunnel close to the forced shear layer. Both the pressure and velocity fluctuations inside the boundary layer were simultaneously measured along with the forcing signal, and a phase-locked analysis was performed. Regions of amplified turbulence inside the boundary layer were observed. Near the wall, the region of amplified turbulence was slightly upstream or lagging of the external forcing and away from the wall it was downstream or leading the forcing signal. Analysis of the convective speeds in the region of amplified turbulence supported the existence of the critical layer inside the wake region of the boundary layer, and the critical layer is believed to be responsible for the amplified levels of the turbulence in the wake region. Various modulation and amplification correlation coefficients were computed and analyzed, and the results also indicated the presence of the critical layer. Examination of the phase-locked turbulence revealed similarities between the turbulence amplitude amplification results due to these externally forced experiments and modulation response of an internally forced, subsonic boundary layer in the literature.

The effect of an unsteady flow incident on an array of circular cylinders

In this paper we investigate the effect of an inhomogeneous and unsteady velocity field incident on an array of rigid circular cylinders arranged within a circular perimeter (diameter $D_{G}$) of varying solid fraction $\unicode[STIX]{x1D719}$, where the unsteady flow is generated by placing a cylinder (diameter $D_{G}$) upwind of the array. Unsteady two-dimensional viscous simulations at a moderate Reynolds number ($Re=2100$) and also, as a means of extrapolating to a flow with a very high Reynolds number, inviscid rapid distortion theory (RDT) calculations were carried out. These novel RDT calculations required the circulation around each cylinder to be zero which was enforced using an iterative method. The two main differences which were highlighted was that the RDT calculations indicated that the tangential velocity component is amplified, both, at the front and sides of the array. For the unsteady viscous simulations this result did not occur as the two-dimensional vortices (of similar size to the array) are deflected away from the boundary and do not penetrate into the boundary layer. Secondly, the amplification is greater for the RDT calculations as for the unsteady finite Reynolds number calculations. For the two highest solid fraction arrays, the mean flow field has two recirculation regions in the near wake of the array, with closed streamlines that penetrate into the array which will have important implications for scalar transport. The increased bleed through the array at the lower solid fraction results in this recirculation region being displaced further downstream. The effect of inviscid blocking and viscous drag on the upstream streamwise velocity and strain field is investigated as it directly influences the ability of the large coherent structures to penetrate into the array and the subsequent forces exerted on the cylinders in the array. The average total force on the array was found to increase monotonically with increasing solid fraction. For high solid fraction $\unicode[STIX]{x1D719}$, although the fluctuating forces on the individual cylinders is lower than for low $\unicode[STIX]{x1D719}$, these forces are more correlated due to the proximity of the cylinders. The result is that for mid to high solid fraction arrays the fluctuating force on the array is insensitive to $\unicode[STIX]{x1D719}$. For low $\unicode[STIX]{x1D719}$, where the interaction of the cylinders is weak, the force statistics on the individual cylinders can be accurately estimated from the local slip velocity that occurs if the cylinders were removed.

Unsteady measurement of core penetration flow caused by rotating geometric non-axisymmetry in a turbine rotor-stator disc cavity

The existence and causes of the deep ingress into the core region of a turbine rotor-stator disc cavity, or core penetration flow, generated by a rotating non-axisymmetric geometry have been investigated experimentally. In a low-speed, low-expansion ratio, single-stage, cold turbine test facility, time-resolved tangential and radial velocities in the cavity have been measured with 2-D hot-wire anemometers. In addition, time-resolved static pressures on the stator disc have been measured with fast response pressure transducers, and unsteady cavity velocity field in the absolute frame has been measured using Particle Image Velocimetry (PIV). Rotating geometric non-axisymmetry leads to an unsteady radial pressure gradient in the disc cavity. A time lag in the tangential velocity adjustment to the variation in the radial pressure gradient results in a net radial force, causing core penetration flow. A first-harmonic rotating geometric non-axisymmetry makes the core penetration flow to occur three times per revolution (twice when the cavity exit pressure increases and once when the cavity exit pressure decreases) and to revolve at the disc’s rotational speed. Core penetration flow due to the rotating geometric asymmetry is not affected by variations in the annulus flow coefficient or rotational Reynolds number but is weakened by increasing purge air flow rate.

High resolution LDA measurements in transitional oblique shock wave boundary layer interaction

Spatial development of a transitional Oblique Shock Wave Interaction at Mach 1.68 is presented. This type of flow is characterised by very small length scales (boundary layer thickness is smaller than 1mm), high velocities, reverse flows and a wide range of velocity fluctuations along the transition process. Unsteady velocity fields have been obtained using a high spatial resolution Laser Doppler Anemometry system, allowing quantitative measurements of the velocity fluctuations down to $$y/\delta =0.1$$ . A model to take into account the finite size of the probe volume on the mean and RMS velocity measurements is used and applied to the present measurements. Finally, the amplification of the velocity fluctuations along the transitional separated shear layer is described.

Application of Magnetic Resonance Imaging for Studying the Three-Dimensional Flow Structure in Blood Vessel Models

A possibility of using the 4D Qflow protocol, which is commonly applied for medical diagnostics by magnetic resonance imaging, for determining the structure of the three-dimensional fluid flow in the human blood circulation system is considered. Specialized software is developed for processing DICOM images taken by a magnetic resonance scanner, and the retrieved unsteady three-dimensional velocity field is analyzed. It is demonstrated that magnetic resonance measurements allow one to detect the existence of the swirling flow in blood vessel models and also to study the degree of its swirling (helicity) both qualitatively and quantitatively.

Proper Orthogonal Decomposition and Extended- Proper Orthogonal Decomposition Analysis of Pressure Fluctuations and Vortex Structures Inside a Steam Turbine Control Valve

In steam turbine control valves, pressure fluctuations coupled with vortex structures in highly unsteady three-dimensional flows are essential contributors to the aerodynamic forces on the valve components, and are major sources of flow-induced vibrations and acoustic emissions. Advanced turbulence models can capture the detailed flow information of the control valve; however, it is challenging to identify the primary flow structures, due to the massive flow database. In this study, state-of-the-art data-driven analyses, namely, proper orthogonal decomposition (POD) and extended-POD, were used to extract the energetic pressure fluctuations and dominant vortex structures of the control valve. To this end, the typical annular attachment flow inside a steam turbine control valve was investigated by carrying out a detached eddy simulation (DES). Thereafter, the energetic pressure fluctuation modes were determined by conducting POD analysis on the pressure field of the valve. The vortex structures contributing to the energetic pressure fluctuation modes were determined by conducting extended-POD analysis on the pressure–velocity coupling field. Finally, the dominant vortex structures were revealed conducting a direct POD analysis of the velocity field. The results revealed that the flow instabilities inside the control valve were mainly induced by oscillations of the annular wall-attached jet and the derivative flow separations and reattachments. Moreover, the POD analysis of the pressure field revealed that most of the pressure fluctuation intensity comprised the axial, antisymmetric, and asymmetric pressure modes. By conducting extended-POD analysis, the incorporation of the vortex structures with the energetic pressure modes was observed to coincide with the synchronous, alternating, and single-sided oscillation behaviors of the annular attachment flow. However, based on the POD analysis of the unsteady velocity fields, the vortex structures, buried in the dominant modes at St = 0.017, were found to result from the alternating oscillation behaviors of the annular attachment flow.

Temperature and Velocity of the Gas–Vapor Mixture in the Trace of Several Evaporating Water Droplets

The optical techniques (particle image velocimetry (PIV), laser-induced phosphorescence (LIP), planar laser-induced fluorescence (PLIF)) are used to study unsteady and inhomogeneous temperature and velocity fields of a gas–vapor mixture forming in the immediate vicinity of rapidly evaporating water droplets. Experiments involve various arrangements of several (two, three, and five) water droplets in a heated air flow. We establish the dependencies of the temperature and velocity of a gas–vapor mixture in the trace of each droplet on the heating time, velocity and temperature of the air flow, initial dimensions, and droplet arrangement scheme. Distinctive features of the synergistic effect of a droplet group on their temperature and aerodynamic traces are identified. Longitudinal and transversal dimensions of the aerodynamic and thermal traces of evaporating droplets are established. The length of the temperature trace of one droplet equals 10–12 of its radii, and the width of the temperature and aerodynamic trace of a droplet is no larger than its diameter.

Temperature and velocity fields of the gas-vapor flow near evaporating water droplets

Experimental studies of unsteady temperature and velocity fields of the gas-vapor flow in the immediate vicinity of evaporating water droplets were performed in the interests of developing high-temperature (over 300°С) gas-vapor-droplet applications. The formation time of virtually homogeneous (temperature variations of under 2–3°С) temperature fields of evaporating water droplets was established using Particle Image Velocimetry, Laser Induced Phosphorescence, Planar Laser Induced Fluorescence. We observed highly inhomogeneous and unsteady temperature and velocity fields of the gas-vapor mixture and determined the lateral and transversal dimensions of the aerodynamic and thermal traces of evaporating water droplets. The degree of impact of several parameters on the latter was evaluated: initial temperature (20–500 °C) and velocity of the incoming flow (0.5–5 m/s), as well as the initial droplet size (1–2 mm). The role of evaporation and convective heat exchange between a droplet and gases in forming of thermal and aerodynamic trace was analyzed. The heat flow density was found to vary nonlinearly with time (in the immediate vicinity of an evaporating droplet), and the impact of droplet trace temperature and velocity on the heat flow density was evaluated. Both advantages and limitations of the used techniques are established in terms of reliable plotting of unsteady temperature and velocity fields of gas-vapor mixture in the trace of evaporating water droplets, considering the heating lag of the latter.