Non-dimensional Time Research Articles

Performance prediction of flame-retardant clothing using correlations and artificial neural networks: Optimizing firefighter safety

Flame-Retardant Clothing serves as a protective shield for firefighters that safeguards them from exposure to heat, flames and other thermal hazards. To achieve an optimal design for the clothing, it is essential to simultaneously account for all the factors affecting the performance of the clothing. The present study employs data from a numerical model to explore heat and moisture transport through clothing subjected to flame exposure. Seventeen non-dimensionless parameters associated with the heat and moisture transport in flame-retardant clothing are obtained. A correlation is developed to link the dimensionless second-degree burn time with other non-dimensional parameters. This correlation provides a means to predict the thermal protective performance (TPP) of the clothing. Additionally, an Artificial Neural Network (ANN) method is employed to determine the TPP of the clothing. Multi-layer feedforward backpropagation networks are utilized to predict the TPP under specified exposure conditions. The findings indicate that both the correlations and the ANN approach adopted in the present study demonstrated promising results. However, the ANN model predictions show better agreement with model data in comparison to the results derived from the developed correlations. The maximum percentage error in the predicted non-dimensional second degree burn time using ANN is limited to 10 %.

Machine learning-based prediction of scour depth evolution around spur dikes

ABSTRACT Spur dikes are pivotal elements in river training, serving to mitigate the dynamic alterations induced by river degradation and aggradation. Traditionally, scour prediction models have relied on regression techniques, but the advent of soft computing and machine learning has offered opportunities for enhanced accuracy. This study focuses on the development of hybrid machine-learning models, including eXtreme Gradient Boosting (XGBoost), random forest (RF), convolutional neural network–long short-term memory, and artificial neural network, optimized using genetic algorithms to predict both temporal scour depth variation and maximum scour depth around the initial spur dike in a series. The analysis reveals strong associations between scour depth and various parameters such as non-dimensional time, spacing, channel width, time-averaged velocity, and densimetric Froude number. The models are established through an iterative process involving four predictor combinations. Results demonstrate XGBoost as the top-performing model, consistently exhibiting superior performance with R2 of 0.99, root mean square error (RMSE) of 0.012, and mean absolute error of 0.008 during training, and R2 of 0.96, RMSE of 0.044, and Kling–Gupta efficiency of 0.98 during testing for predicting temporal scour depth. For non-dimensional maximum scour depth, it reached R2 of 0.99 and RMSE of 0.005 in training, with R2 > 0.91 across all combinations during testing. Although RF showcases commendable accuracy, it slightly lags in precision compared to XGBoost.

Heat transfer augmentation in a double lid-driven trapezoidal porous cavity with heated block using hybrid nanofluid

This study intends to understand the fundamental characteristics of hybrid nanofluids (HNF) in a porous cavity using computational modeling, which will aid in developing HNF within hydrodynamics and enable adaptability. The present research investigates the enhancement of the transmission of heat in a double lid-driven trapezoidal porous cavity containing a heated block, utilizing a HNF composed of aluminum oxide/copper-water (Al2O3/Cu-H2O) employing the Finite Element Method (FEM) based on Galerkin weighted residual (GWR). Additionally, the Darcy-Brinkman-Forchheimer comprehensive approach has been used to demonstrate fluid flow in the porous media. The governing parameters such as the Darcy number (10−4 ≤ Da ≤ 10−2), the porosity of the porous medium (0.6 ≤ ε ≤ 0.9), inclined angle (π/16 ≤ ϕ ≤ π/3), and solid volume fraction (0.001 ≤ δ ≤ 0.05) have been chosen to evaluate the impact within dimensionless time (0.1 ≤ τ ≤ 1). The simulation outcomes of flow and thermal fields are shown through streamlines, isotherms, average heat transfer rate at the hot surfaces, and average temperature inside the cavity. The outcomes of this study show that the HT rate rises by 41.02% when increasing the solid volume fraction (svf) from 0.1% to 5%. Also, it has been found that if the inclined angle is enhanced from π/16 to π/3 at non-dimensional time τ = 0.5, the average HT augmented by 63.16%.

Swelling Kinetics of Hydrogel Beads in Aqueous Glycerin Solutions.

This study examines the swelling kinetics of polyacrylamide hydrogel beads in aqueous glycerin solutions of different concentrations. The total absorbed mass of the hydrogel beads remains nearly constant, independent of glycerin concentration, but the swelling process is markedly slower with increasing glycerin concentration in the aqueous solutions. Absorption capacity curves exhibit universal kinetics when time is rescaled using a characteristic time proportional to the viscosity of the solutions. Additionally, a novel visualization technique is employed to observe the core-shell structure of the hydrogel beads at early times in the swelling process. The evolution of the core-shell structure indicates a constant front velocity, which also reveals universal behavior with the same nondimensional time, suggesting a viscous dominated transport of the solution penetrating the beads.

Experimental investigation of equilibrium and temporal scour around the round head of the rubble mound breakwater in case of breaking and non-breaking waves

In this study, local sediment movements caused by regular wave effects around the head section of rubble mound breakwater were investigated experimentally. The experiments were performed in a wave channel with a length of 33 m, a width of 3.6 m and a depth of 1.2 m. A plunger-type wave generator was located at the offshore side, generating regular waves of varying heights and periods. Uniform sandbed material of three different grain sizes was used, alongside two distinct breakwater slopes and six different wave characteristics. Experiments were performed under both breaking and non-breaking wave conditions. Time-dependent scour depth and water level measurements were determined by using measuring equipment working with an ultrasonic method. In the paper, new empirical relations were derived for temporal relative scour depths and the non-dimensional time scale parameter and the non-dimensional time scale parameter. The determination coefficient and scatter index of these derived relations were calculated and evaluated statistically. It was observed that the relations are in good agreement with those obtained from experiments. Additionally, the findings indicate that wave breaking significantly reduces the equilibrium scour depth.

Intermittency transition to azimuthal instability in a turbulent annular combustor

We experimentally study the transition from a state of combustion noise to azimuthal thermoacoustic instability in a laboratory-scale turbulent annular combustor. This combustor has sixteen swirl-stabilized burners to facilitate continuous and spatially distributed combustion along the annular region. Our approach involves simultaneous measurement of CH* chemiluminescence emission of the flame using two high-speed cameras and the acoustic pressure fluctuations using eight piezoelectric pressure transducers mounted on the backplane of combustor. We observe that the transition from combustion noise to azimuthal instability occurs through mode shifting, where the system switches from a longitudinal mode to an azimuthal mode as the equivalence ratio is decreased. Throughout this progression, the combustor exhibits various dynamical behaviors, including intermittency, dual-mode instability, standing azimuthal instability, and beating azimuthal instability. These dynamical states are determined from the acquired pressure signals by decomposing the acoustic pressure fluctuations into clockwise (CW) and counterclockwise (CCW) waves, enabling a reconstruction of the amplitude of acoustic pressure fluctuations, nature angle, (anti-)nodal line location, and spin ratio. The global heat release response is then examined during various dynamical states, contrasting their behavior at different non-dimensional time steps by phase-averaging the fluctuations of the heat release rate over the acoustic pressure cycle. Distinctive flame behaviors were observed based on the direction of pressure wave propagation, showcasing characteristic CCW spinning, standing, and CW spinning heat release patterns. Moreover, our examination of relative phase distributions during various dynamical states, computed by analyzing the phase of heat release rate fluctuations across all burners with respect to one burner, reveals the emergence of diverse patterns in the interaction of neighboring flames influenced by acoustic field.

Performance enhancement of a vortex ring thruster by adopting the Coanda effect

A vortex ring thruster (VRT) is a propulsion device in which a piston pushes fluid and thrusts it in reaction. As the fluid inside a VRT is moving, the boundary layer near the wall at the edge of the exit surface of a VRT separates and rolls up into a vortex ring. In this paper, we performed performance analysis on a regular VRT and a VRT enhanced by the Coanda effect (hereafter referred to as a CoVoRT) on axisymmetric geometry. A CoVoRT consists of two jets: a primary jet and a Coanda jet. The primary jet has a relatively large volume flow rate compared to the Coanda jet, and the Coanda jet attracts the surrounding fluid by flowing along the curved surface at a relatively small flow rate. The present study evaluates the propulsion performance in two ways using SNUFOAM. This software was developed based on OpenFOAM, which is an open-source computational fluid dynamics (CFD) toolkit and specialized for naval hydrodynamics. The first one quantifies the propulsion performance by calculating the ratio of energy input and energy output generated by two jets during a stroke of the piston motion. The second one is to observe the evolution and pinch-off process of a vortex ring with formation time, which is a non-dimensional time scale. The comparison of propulsion performance was conducted with changes in the curvature of the Coanda jet, changes in the length of the Coanda jet exit, and changes in the Coanda jet velocity and piston stroke ratio. For quantitative evaluation of propulsion performance, the propulsion performance evaluation index (PPEI) was introduced. The results showed that the PPEI of a CoVoRT was improved by about 50% compared to that of a VRT, and it was confirmed that the dynamic characteristics of a CoVoRT’s vortex ring were superior to those of a VRT in terms of propulsion performance.

Numerical modeling of local scour around a subsea pipeline on cohesive seabed under steady currents

The present study introduces a numerical model for simulating local scour around a subsea pipeline on a cohesive seabed, representing a pioneering endeavor in the development of such a numerical model. The flow dynamics around the pipeline are solved using Reynolds-Averaged Navier–Stokes (RANS) equations with the SST k–ω turbulent model. Sediment movement on cohesive seabed is assessed through erosion rates, determined by an empirical formula derived from experimental data, rather than sediment transport rates typically used for non-cohesive sediment. Three different erosion rate formulas—linear, power law, and stochastic—are investigated in the simulation of the scour process. The numerical simulations are validated using laboratory data with artificial and marine sediments, demonstrating a satisfactory level of agreement in predicting scour bed profiles. Nevertheless, it is recommended to utilize the erosion rate formula that is calibrated to the specific sediment type based on experimental data for precise numerical prediction of scour process. The study reveals that the equilibrium scour depth is approximately a linear function of the bed shear stress, and the nondimensional time scale is inversely proportional to the bed shear stress within the specified range. Subsequently, an examination of the scale effect on the scour process with cohesive sediment around a pipeline is conducted. The results indicate that the nondimensional equilibrium scour depth marginally increases with larger pipeline diameter on cohesive seabed, contrary to the observed trend for non-cohesive sediments.

Two-Dimensional Simulation of Dam Break with Partial Damage Condition using Ansys Software

The issue of dam failure has been a key contributor to massive catastrophes, as well as economic and physical destruction. Nevertheless, the effectiveness and accuracy of the simulation of a dam break model are still under debate. In this study, a simulation of a 2D model of the dam breaking half-filled water tank was carried out using Ansys software to evaluate the deformation and water pressure of dam break flow. Four sensors were installed to examine the changes in pressure of the water deformation. Deformation of water at a certain time of the dam break simulation and the pressure of water inside were analyzed and compared with the experimental result, which has been reported by Lobovský. Validation and verification of hydrostatic tests have been found to be in agreement with the current model simulation. An extensive set of data for the simulation is given access as supplementary materials for the direct result of the recent initiative. The results show that by excluding minor differences in wave shape and duration of water movement, the deformation of water exemplifies the same behavior as the experimental results. For experimental data, the non-dimensional time of the dam break event is ranged within 0 to 7.14828 ms while the pressure of water flow is within 0 to 3.0441 Pa. As for simulation results, the non-dimensional time of the dam break event is ranged within 0 to 202 ms whereas the pressure of water flow is within 0 to 0.54124 Pa. Thus, to strengthen the quality numerical model, future work should emphasize the initiative to incorporate the Smooth Particle Hydrodynamics (SPH) method with the goal of improving computational validity and efficiency.

Effects of channel height on the combustion efficiency and thermal performances of a micro Swiss-roll combustor

Micro combustors can be used as the heat sources for micro power generation systems. Recently, we developed a micro Swiss-roll combustor for non-premixed fuel and air. In the current work, the impacts of channel height (H2 = 7.5, 7.0, 6.5, and 6.0 mm) on the combustion efficiency of CH4, and the surface radiation efficiency of this combustor were numerically investigated under constant flow rates of the fuel and air. The results showed that both combustion efficiency and radiation efficiency varied non-monotonically with the decrease of channel height. The optimal channel height was found to be 6.5 mm under which a highest combustion efficiency of 99.05 % and a highest radiation efficiency of 27.03 % were obtained. These variation rules were theoretically analyzed in terms of the heat recirculation effect on fresh reactants, the buoyancy effect on flame structure and chemical reaction, and the non-dimensional residence time of the reactants (DaL). It was unraveled that the combustor with H2 = 6.5 mm achieved a best heat recirculation effect. In addition, the buoyancy effect was weakened as the channel height was decreased, resulting in a more symmetric flame structure in the vertical direction and a more intense chemical reaction. Furthermore, when the channel height descended from H2 = 7.5 mm to 6.5 mm, the region of DaL > 1 was broadened due to the intensified reaction, but narrowed as the channel height was further reduced to 6.0 mm due to increased flow velocity. The combined actions of these factors led to non-monotonic variations of combustion efficiency and radiation efficiency. The discoveries of the present study provided a guideline for optimal design of such kind of micro Swiss-roll combustors.

Wind-tunnel measurements of sensible turbulent heat fluxes over melting ice

Accelerated glacier melt and the loss of perennial snowfields have been associated with increased warming in polar regions, at rates up to four times faster than the rest of the world, thereby reinforcing the critical need for improved models (and predictions) of glacier melt. An essential requirement for such models is an improved understanding of the sensible heat fluxes over glaciers. Since their complexity makes them difficult to model, and direct measurements of sensible turbulent heat fluxes over real glaciers are both rare and impractical, the present work involves simultaneous hot-wire anemometry and cold-wire thermometry measurements of two components of velocity and temperature above a melting glacier model in a series of wind-tunnel experiments. Both single- and multi-variable statistics were used to compare the turbulent velocity field measured over melting ice with that of a similar flow in the absence of ice. The results demonstrate that the ice's presence reduces the magnitude of the Reynolds stresses and vertical velocity variance, but also increases the streamwise velocity variance. The transient evolution of temperature statistics throughout the melt process was also investigated and found to be similar when suitably non-dimensionalized. The velocity and temperature fields were furthermore evaluated at an equivalent non-dimensional time during the melt process, in which statistics of the temperature field, and joint statistics of the vertical velocity and temperature, were studied. The present work lays the foundation for future laboratory-scale replications of the flow above melting glaciers, and provides additional insight into turbulent heat transfer over melting ice.

Droplet impact dynamics on superhydrophobic surfaces with convex hemispherical shapes

Functional solid surfaces that can realize rapid shedding of liquid droplets have received significant research interest due to their close relevance to many industrial applications. Droplet impact on superhydrophobic surfaces with point-like protrusions has been demonstrated to take off as rings, which alters droplet impact dynamics and thus reduces contact time compared to flat surfaces. However, the essential role of the size ratio of protrusion-to-droplet (λ) for droplets impinging on such surface is rarely considered. Here, we numerically investigate droplet impact on superhydrophobic surfaces with convex hemispherical shapes using a phase-field model coupled with dynamic contact angles. The postimpact outcome regimes occurring for varied λ and Weber number (We) values, spanning 0 ≤ λ ≤ 1.44 and 0.69 ≤ We ≤ 33.68, are mapped on a We−λ diagram. Three distinct dynamic behaviours of droplet impact are identified: contactless bouncing, conventional bouncing, and ring bouncing. Detailed comparative analyses of these impact outcomes are also presented, including the evolution of droplet morphology, impact force, maximum impact pressure, pressure distribution, and velocity vector distribution. The results reveal a previously unknown phenomenon in contactless bouncing, where the impact force exhibits an initial increase followed by a subsequent decrease, while the maximum impact pressure remains approximately constant. Annular rotating retraction results in a longer contact time. Breakup occurs near the necked area, inducing a part of the droplet to depart from the surface as a jet. In addition, it is observed that the dimensionless maximum wetting area becomes independent of the λ and follows a scaling law of 0.67We3/5 if the We exceeds 2.75. Ring bouncing exclusively occurs within the range of 0.24 ≤ λ ≤ 0.96 and We ≥ 24.74, resulting in an approximate 50 % reduction in non-dimensional contact time compared to conventional bouncing. These findings favor the understanding of the underlying mechanisms governing droplet impact and thereby provide available guidance to the design of superhydrophobic surfaces.

RETRACTED – Reynolds-number scaling and convergence time scale in two-dimensional Rayleigh–Bénard convection

An equation for the evolution of mean kinetic energy, $E$ , in a two-dimensional (2-D) or 3-D Rayleigh–Bénard system with domain height $L$ is derived. Assuming classical Nusselt-number scaling, $Nu \sim Ra^{1/3}$ , and that mean enstrophy, in the absence of a downscale energy cascade, scales as $\sim E/L^2$ , we find that the Reynolds number scales as $Re \sim Pr^{-1}Ra^{2/3}$ in the 2-D system, where $Ra$ is the Rayleigh number and $Pr$ the Prandtl number. Using the evolution equation and the Reynolds-number scaling, it is shown that $\tilde {\tau } \gtrsim Pr^{-1/2}Ra^{1/2}$ , where $\tilde {\tau }$ is the non-dimensional convergence time scale. For the 3-D system, we make the estimate $\tilde {\tau } \gtrsim Ra^{1/6}$ for $Pr = 1$ . It is estimated that the total computational cost of reaching the high $Ra$ limit in a simulation is comparable between two and three dimensions. The predictions are compared with data from direct numerical simulations.

Particle deposition model for a fully developed turbulent channel flow

This study aims to develop a mathematical model for solid particle deposition under a fully-developed turbulent flow in a rectangular channel, considering the effect of the change in geometry over time. The present study introduces a mathematical approach to predict the equilibrium thickness/mass of the deposition, saturation and equilibrium times, and their corresponding non-dimensionalized parameters. Scaling analysis, and parametric study are reported. For a fixed Reynolds number Re, the particle deposition increases with non-dimensional relaxation time. In general, as more particles are deposited, the surface takes less time to become saturated and approach equilibrium faster. The saturation and equilibrium times decrease with an increase in non-dimensional particle relaxation time. For a fixed particle concentration, as the inlet velocity increases, the saturation and equilibrium time decreases, and the asymptotic deposited mass decreases.

Effect of iso-propanol additive on the impact dynamics of a Leidenfrost water droplet

This paper experimentally investigated the Leidenfrost dynamics of an impacting droplet of water and 2–8 vol% iso-propanol-water solutions in the film boiling regime up to 450 °C. A single millimetric droplet was released from a height of several centimeters to yield different impact velocities. The aim of the present study was to clarify the influence of iso-propanol additive on the dynamic Leidenfrost point temperature, maximum spreading factor and nondimensional residence time, which remains to be verified. Visualization study with high-speed imaging indicated that the droplet impact pattern depends on both surface temperature and iso-propanol additive. It was shown that the dynamic Leidenfrost point temperature increases with impact velocity, and was significantly elevated with a small amount of iso-propanol additive by approximately 40 °C at the same Weber number. Especially, the lowest value of the mixture droplet with the smallest impact momentum (430 °C at 0.44 m/s and We = 6.2–8.3) still surpassed the highest value of the water droplet with the largest impact momentum (410 °C at 1.33 m/s and We = 55.0) within the present test range. Meanwhile, the iso-propanol additive markedly enhanced the droplet spreading ability, which was speculated to be caused by lower surface energy. Results also demonstrated that the nondimensional residence time was highly dependent on the impact velocity, but was not significantly influenced by the iso-propanol additive. Empirical correlations of the maximum spreading factor and nondimensional residence time were proposed with satisfactory predictive accuracy and good universality.

Melting process of a phase change material using single and double elliptic charger applied in thermal storage for building application: A numerical study on effect of position and aspect ratio

Nowadays phase change materials are considered as very useful and innovative working medium that can be used in different engineering systems for various purposes, including the thermal stabilization regime in building elements, cooling of electronic systems, development of thermal energy storage devices and other fields. The present research deals with numerical analysis of phase change material melting behavior in a closed adiabatic cavity under an influence of one or two elliptical local heaters that can be considered as local charges for the working material. Using the finite element technique, the governing partial differential equations formulated using primitive variables and enthalpy-porosity formulation have been solved numerically. The computational results have been validated utilizing published experimental and numerical data. Influence of the local heaters position and its shape on evolution of melting process has been studied. It has been revealed that in the case of vertically oblong one elliptical heater the melting rate is the maximum, while for the case of circular charger one can find a minimum melting rate. It has been ascertained that more intensive melting occurs when the charger is placed near the bottom wall (Sv = 0.2) and for this case the non-dimensional charging time for MF = 1 is about 2. While for other cases less intensive meting can be found. Moreover, in the case of elongated chargers for vertical axis (Ar = 0.1) and for horizontal axis (Ar = 10) the melting occurs intensively, namely the non-dimensional charging time for MF = 1 is about 1.5, while the maximum values (at about 24) of the average Nusselt number during the melting process are for Ar = 0.5 and Ar = 1.0. The highest values of the average Nusselt number (at about 12) are related to the minimum melting time (at about 1.1) that can be found for cases 6 and 9 when two chargers are placed in central part or along the bottom line.

Strength and timing of primary and secondary vortices generated by a rotating plate

Accurate predictions of how vortices grow, evolve, and separate from aerodynamic objects are desirable for various applications ranging from autonomous aerial vehicles to wind turbines. Here, we present an experimental characterisation of the formation process of vortices created by the rotation of a thin rectangular flat plate. The plate is rapidly accelerated from rest up to a constant rotational velocity that was varied to explore the effect of the Reynolds number on the limit strength and the timing of successively generated vortices at the tip of the plate. The total non-dimensional positive circulation released at the tip of the plate during the entire rotation varies solely as a function of the angular position of the plate. Initially, all this circulation accumulates in a primary or starting vortex until this vortex separates after a constant non-dimensional time for all rotational velocities and different plate dimensions tested. An empirical model of the prediction of the limit strength of the primary vortex based on the constant non-dimensional formation is presented. The limit strength of the primary vortex is independent of the Reynolds number. After the primary vortex separates, a series of smaller secondary vortices form at the tip of the plate. These secondary vortices are discretely released at increasing time intervals. The timing of the release of the secondary vortices and their non-dimensional strength depend on the Reynolds number, and an empirical prediction model is presented.

Bagnold 충격수를 고려한 압축 팽창하는 갇힌 공기에 미치는 축척비 효과에 대한 상사 해석

A developed code based on the unified conservation laws of incompressible/compressible fluids is applied to analyze similarity in pressure oscillations caused by pulsating air pockets in sloshing tanks. It is shown that the nondimensional time histories of pressure show good agreements under Froude and geometric similarities, provided that there are no pulsating entrapped air pockets. However, the nondimesional period of pressure oscillation due to the pulsating air pocket becomes longer as the size of the sloshing tank increases. The discrepancy in the nondimensional period is attributed to the compressibility bias of the entrapped air. To get rid of the compressibility bias, the ullage pressure in a sloshing tank is adjusted based on the Bagnold’s impact number. The variation in the period of pressure oscillation according to the ullage pressure is explained based on the spring-mass system. It is shown that the nondimensional period of pressure oscillation is virtually constant when the ullage pressure is adjusted based on the Bagnold’s impact number, regardless of tank size. It is found that the Bagold’s impact number should be the same, if the time history of pressure is important while an entrapped air pocket pulsates.

Characterization of the Unsteady Wake Aerodynamics for an Industry Relevant Road Vehicle Geometry Using LES

A wall-resolved large eddy simulation (WRLES) study of the flow around a 15% scale model of the Nissan NDP, an electric concept vehicle developed by Nissan, at Re_H=100{,}000 is presented. First, wake asymmetries and the associated possibility of wake bimodality occurring are investigated by comparing the flow fields around “squareback” and cavity variants of the Nissan NDP. It is highlighted that there is no noteworthy long-term wake asymmetry in the spanwise direction for both configurations and that there is, instead, symmetric spanwise vortex shedding, as highlighted through the use of proper orthogonal decomposition (POD) post-processing. One can, therefore, exclude the existence of classical wake bimodality in the spanwise direction that has been observed for the Ahmed body. However, the wake does explore the vehicle’s rear space in the spanwise direction rapidly over non-dimensional time intervals of {mathcal {O}}(10). Meanwhile, there is a strong wake tilt in the vertical direction due to the presence of a ground, the vehicle geometry’s vertical asymmetry, and the detachment of a powerful hairpin vortex from the vehicle’s roof. When looking at POD of the flow field in a vertical plane, asymmetric vortex shedding, similar to that observed for the Ahmed body by Hesse and Morgans (2021) in the spanwise plane, is found. This suggests that wake bimodality in the vertical direction could occur for the Nissan NDP—the presented results are not conclusive, as the provided non-dimensional simulation duration of t^* sim 60 is insufficient for the bimodal phenomenon that occurs at t^* sim 1000. Additionally, the discernible impact of having a cavity at the rear of the NDP is to allow the wake to explore a larger vehicle base space (i.e. the wake is able to move more freely). This, coupled to a 5% reduction in rear base area, translates to a drag reduction compared to the “squareback” variant of 13.6%. Second, in a more qualitative analysis of simulation results, the effect of using a moving ground in simulation as compared to a stationary ground is assessed. This is only done for the cavity variant of the Nissan NDP. It is found that, for this vehicle geometry, a stationary ground is associated with the occurrence of low pressure clockwise rotating (when looking into the page of the vertical plane) vortices near the ground caused by the flow deceleration just aft of the vehicle base, where the flow moves from the vehicle under-body toward the wake’s far-field region. The consequence of this flow phenomenon is to simulate a 3.3% higher drag value with the stationary ground simulation as compared to the moving ground simulation. Thus, although the moving ground should be more representative of the real-world, the stationary ground simulation is more conservative in aerodynamic terms and should be used if developing the NDP vehicle completely digitally using a virtual twin. By over-design, the stationary ground variant namely ensures that the drag key performance indicator (KPI) is met.

Numerical study of flow establishment process of engine in a shock tunnel

In this paper, an unsteady numerical simulation of the full-scale flow field establishment process of a scramjet in shock tunnel is carried out. The simulation covers from the driving process of the shock tube to the flow field establishment of nozzle and engine, and combines the chemical reaction of air. The feasibility of the calculation method is verified by comparing the pressure from simulation results and the experimental ones that measured in the shock tube. The results show that in the shock tube, the total pressure at the nozzle inlet is formed by the incident shock wave, the shock wave reflected by the diaphragm and the shock wave train caused by the nozzle high pressure. After the nozzle flow field is established, the Mach number of the core flow reaches the design value of 9.0, and the total pressure of the core flow reaches 30 MPa. By comparing the results of flow fields, wall pressure distributions and drag coefficients with the steady case, we show that the flow in test section approaches steady state in 16 ms, which includes the shock tunnel and nozzle starting time. The non-dimensional characteristic establishment time of the engine is about 4 and it is closed to that of the flat plate case.