Incoming Velocity Research Articles

Research on Deployable Wings for MAVs Bioinspired by the Hind Wings of the Beetle Protaetia brevitarsis.

Deployable hind wings of beetles led to a bio-inspired idea to design deployable micro aerial vehicles (MAVs) to meet the requirement of miniaturization. In this paper, a bionic deployable wing (BD-W) model is designed based on the folding mechanism and elliptical wing vein structure of the Protaetia brevitarsis hindwing, and its structural static and aerodynamic characteristics are analyzed by using ANSYS Workbench. Finally, the 3D-printed bionic deployable wing was tested in a wind tunnel and compared with simulation experiments to explore the effects of different incoming velocity, flapping frequency, and angle of attack on its aerodynamic characteristics, which resulted in the optimal combination of the tested parameters, among which, the incoming velocity is 3 m/s, the flapping frequency is 10 Hz, the angle of attack is 15°, and the lift-to-drag ratio of this parameter combination is 4.91. The results provide a theoretical basis and technical reference for the further development of bionic flapping wing for MAV applications.

Effects of Leading-Edge Blowing Control and Reduced Frequency on Airfoil Aerodynamic Performances

Abstract Airfoil leading-edge fluid-blowing control is computationally studied to improve aerodynamic efficiency. The fluid injection momentum coefficient Cμ (the ratio of injection to incoming square velocities times the slot's width to airfoil's half chord length) varies from 0.5% to 5.4%. Both static and dynamic conditions are investigated for a NACA0018 airfoil at low speed and Reynolds number of 250 k based on the airfoil's chord length. The airfoil is dynamically pitched at a reduced frequency (the pitching tangential speed to the freestream speed ratio), varying between 0.0078 and 0.2. Reynolds-averaged Navier–Stokes (RANS) and unsteady RANS (URANS) is used in the simulations as based on the Transition SST and Spalart–Allmaras models, generally achieving good agreement with experimental results in lift and drag coefficients and in the pressure coefficient distributions along the airfoil. It is found that oscillating the airfoil can delay stall, as expected, in dynamic stall (DS). Leading-edge blowing control can also significantly delay stall both in static and dynamic conditions as long as sufficient momentum is applied to the control. On the other hand, for a small Cμ such as 0.5%, the leading-edge control worsens the performance and hastens the appearance of stall in both static and dynamic conditions. The airfoil's oscillation reduces the differences between pitch-up and pitch-down aerodynamic performances. Detailed analysis of vorticity, pressure, velocity, and streamline contours is given to provide plausible explanations and insight to the flow.

Periodic approaching flows and pollutant dispersion of a single-sided generic building with natural ventilation

In real urban environments, wind velocities often exhibit significant time-dependent variations. However, the impact of these fluctuations on ventilation performance is not frequently addressed in the literature. To accurately predict the building ventilation performance, this paper intends to elucidate the influence of the unsteady approaching flow. Four distinct inflows, characterized by periodic sinusoidal fluctuations, are evaluated using large-eddy simulation (LES). A single-sided building model with natural ventilation is constructed and validated through a wind tunnel experiment. Four periodic inflows consist of combinations of two frequencies (f = 0.1 and 0.3 Hz) and two amplitudes (A = 0.06 and 0.09). This paper mainly compares the results of airflow patterns and ventilation performance with those of stable inflows. The results indicate that periodic inflows cause greater fluctuations in the velocity fields on the leeward side. At higher frequencies and lower amplitudes, the vertical distribution of indoor bottom vortices is relatively dispersed. It shows that periodic flows lead to noticeable changes in the ventilation rate, with a deviation between instantaneous and average Q* ranging from 13.8% to 16.5%. Compared to the stable inflow, the impacts of periodic inflows on ventilation performance vary over time; 6% and 9% variations in incoming velocities result in deviations of up to 17.5% in ventilation rates. The frequencies and amplitudes of the periodic inflows do not exhibit a linear relation with ventilation rate. Therefore, it is prudent to be cautious about adopting averaged incoming wind velocities in predicting ventilation performance. This study helps in the more accurate prediction of single-sided natural ventilation.

Vortex shedding behind porous flat plates normal to the flow

This work examines the influence of body porosity on the wake past nominally two-dimensional rectangular plates of fixed width $D$ in the moderate range of Reynolds numbers $Re = UD/\nu$ (with $U$ the incoming velocity and $\nu$ the kinematic viscosity) between 15 000 and 70 000. With porosity $\beta$ defined as the ratio of open to total area of the plate, it is well established that as porosity increases, the wake shifts from the periodic von Kármán shedding behaviour to a regime where this vortex shedding is absent. This change impacts the fluid forces acting on the plate, especially the drag, which is significantly lower for a wake without vortex shedding. We analyse experimentally the transition between these two regimes using hot-wire anemometry, particle-image velocimetry and force measurements. Coherence and phase measurements are used to determine the existence of regular, periodic vortex shedding based on the velocity fluctuations in the two main shear layers on either side of the wake. Results show that, independent of $Re$ , the wake exhibits the classical Kármán vortex shedding pattern for $\beta <0.2$ but this is absent for $\beta >0.3$ . In the intermediate range, $0.2<\beta <0.3$ , there is a transitional regime that has not previously been identified; it is characterised by intermittent shedding. The flow alternates randomly between a vortex shedding and a non-shedding pattern and the total proportion of time during which vortex shedding is observed (the intermittency) decreases with increasing porosity.

On the low-frequency flapping motion in flow separation

Transitional separating flow induced by a rectangular plate subjected to uniform incoming flow at Reynolds number (based on the incoming velocity and half plate height) 2000 is investigated using direct numerical simulation. The objective is to unveil the long-lasting mystery of low-frequency flapping motion (FM) in flow separation. At a fixed streamwise-vertical plane or from the perspective of previous experimental studies using pointwise or planar measurements, FM manifests as a low-frequency periodic switching between low and high velocities covering the entire separation bubble. The results indicate that in three-dimensional space, FM reflects an intricate evolution of streamwise elongated streaky structures under the influence of separated shear layer and mean flow reversal. The FM is an absolute instability, and is initiated through a lift-up mechanism boosted by mean flow deceleration near the crest of the separating streamline. At this particular location, the shear bends the vortex filament abruptly, so that one end is vertically struck into the first half of the separation bubble, whereas the other end is extended in the streamwise direction in the second half of the separation bubble. These two ends of vortex filament are mutually sustained and also stretched by the vertical acceleration and streamwise acceleration in the first and second halves of the separation bubble, respectively. This process periodically switches the low-velocity (or high-velocity) streaky structure to a high-velocity (or low-velocity) streaky structure encompassing the entire separation bubble, and thus flaps the separated shear layer up and down in the vertical direction. A ‘large vortex’ shedding manifests when the streaky structure switches signs. This large vortex is fundamentally different from the spanwise vortex shedding residing in the shear layer originated from the Kelvin–Helmholtz instability and successive vortex amalgamation. It is also believed that the three-dimensional evolution of streaky structures in the form of FM is applicable for both geometry- and pressure-induced separating flows.

Numerical Simulation on Aerodynamic Characteristics of Transition Section of Tilt-Wing Aircraft

The tilt-wing aircraft has attracted widespread attention due to its excellent performance. However, its aerodynamic characteristics during the tilt transition section are characterized by unsteadiness, nonlinearity, and strong coupling, making it difficult to control. Using computational fluid dynamics (CFD) methods and moving overset grids to control the tilt-wing motion, the momentum source method is employed to replace actual propellers. The influence of the propeller on the aerodynamic characteristics of the tiltrotor at different tilt angles is investigated under incoming flow velocities of 8 m/s and 45 m/s in steady conditions. Additionally, the differences between steady and unsteady calculations of the tilt transition section are investigated at incoming flow velocities of 8 m/s, 15 m/s, 30 m/s, and 45 m/s in unsteady conditions. The research results indicate the following information: 1. the slipstream from the propellers significantly enhances the lift, drag, and stall angle of attack of the tilt-wing aircraft but reduces the lift-to-drag ratio; 2. there are noticeable differences in the forces acting on the tilt-wing aircraft between steady calculations with fixed tilt angles and unsteady calculations with continuous tilting.

Experimental studies on simultaneously reducing flow drag and noise of a circular cylinder with a downstream porous material plate

Pressure drag and noise level are two key parameters related to flow past a bluff body, thus various active and passive methods have been developed to reduce the drag and noise. The paper presents a passive method of simultaneously reducing the pressure drag and aerodynamic noise associated with flow past a smooth circular cylinder by placing a porous material plate (PMP) downstream the cylinder. Multi-points instantaneous wall pressure and far-field acoustic pressure have been measured in an anechoic wind-tunnel facility. The experimental results confirm that the PMP is effective to reduce both the pressure drag and the noise level, showing an attractive advantage compared with the impermeable splitter plate and porous coating. Parametric studies reveal effects of the pores per inch (PPI) of PMP, PMP-cylinder spacing and incoming flow velocity on the pressure drag and noise level.

Enhancing Wind Turbine Blade Preventive Maintenance Procedure through Computational Fluid Dynamics-Based Prediction of Wall Shear Stress

Wind turbine blades are essential parts of wind energy systems and are frequently exposed to harsh environmental elements, such as strong winds, turbulence, and corrosive atmospheric elements. Over time, these circumstances may result in serious harm to blades, such as delamination and erosion, which may negatively affect the wind turbine’s functionality and durability. Accurate prediction of various types of damage is crucial to improve the toughness and lifespan of wind turbine blades and to maximize the overall effectiveness of wind energy systems. This article presents a novel computational fluid dynamics (CFDs)-based method for analyzing the distribution of wall shear stress on turbine blades, aimed at publicizing the yearly maintenance procedure. The investigation results from the CFDs, when compared with the current situation in a wind turbine farm in Thailand, confirmed that our wall shear stress modeling accurately predicted wind turbine damage. A maximum wall shear stress level higher than 5.00 Pa in the case of PA 90°, incoming air velocity 10.00 m/s, and 15 rpm was the main contribution to presenting the erosion and delamination from current drone inspection in wind turbine farms. In conclusion, these findings demonstrated the potential of using CFDs to predict wind turbine blade delamination and erosion, thereby significantly contributing to the development of specific and accurate yearly preventive maintenance. The proposed CFDs-based approach should serve as a sustainability tool for local human development, benefiting wind turbine engineers and operating technicians by providing them with a deeper understanding of the local flow conditions and wall shear stress distribution along wind turbine blades. This enables them to make informed decisions regarding blade design and maintenance.

Numerical Study of Cavitation Characteristics through Butterfly Valve under Different Regulation Conditions

Butterfly valves are widely used in the pipeline transportation industry due to their safety and reliability, as well as their low manufacturing and operation costs. Cavitation is a common phenomenon in the butterfly valve that can lead to serious damage to a valve’s components. Therefore, it is important to investigate the generation and evolution of cavitation in butterfly valves. In this study, LES and the Zwart model were used as the turbulence and cavitation models, respectively, to simulate cavitation through a butterfly valve. The influence of the valve opening degree and inlet flow velocity on dynamic cavitation through the butterfly valve were studied. Furthermore, the cavitated flow field was examined, along with the performance coefficients of the butterfly valve. With the increase in the incoming flow velocity, the high-speed jet zone over a large-range and low-pressure zone appeared inside the downstream of butterfly valve, which affected its stability and the cavitation generation through the valve. Furthermore, the flow coefficient decreased with the increase in vapor volume. In addition, the results indicated that cavitation was more easily induced for smaller valve opening degrees, and the interaction between cavitation and solid walls was stronger. Due to the existence of cavitation, the flow characteristics of butterfly valves are seriously affected.

Exploring Vortex–Flame Interactions and Combustion Dynamics in Bluff Body-Stabilized Diffusion Flames: Effects of Incoming Flow Velocity and Oxygen Content

An afterburner encounters two primary features: high incoming flow velocity and low oxygen concentration in the incoming airflow, which pose substantial challenges and contribute significantly to the deterioration of combustion performance. In order to research the influence of oxygen content on the dynamic combustion characteristics of the afterburner under various inlet velocities, the effect of oxygen content (14–23%) on the field structure of reacting bluff body flow, flame morphology, temperature pulsation, and pressure pulsation of the afterburner at different incoming flow velocities (0.1–0.2 Ma) was investigated in this study by using a large eddy simulation method. The results show that two different instability features, BVK instability and KH instability, are observed in the separated shear layer and wake, and are influenced by changes in the O2 mass fraction and Mach number. The oxygen content and velocity affected the oscillation amplitude of the downstream flow. As the O2 mass fraction decreases, the flame oscillation amplitude increases, the OH concentration in the combustion chamber decreases, and the flame temperature decreases. Additionally, the amplitude of the temperature pulsation in the bluff body flame was primarily influenced by the temperature intensity of the flame and BVK instability. Moreover, the pressure pulsation is predominantly affected by the dynamic characteristics of the flow field behind the bluff body. When the BVK instability dominated, the primary frequency of the pressure pulsation aligned with that of the temperature pulsation. Conversely, under the dominance of the KH instability, the temperature pulsation did not exhibit a distinct main frequency. At present, the influence of oxygen content and incoming flow rate on the combustion performance of the combustion chamber is not clear. The study of the effect of oxygen content on the combustion characteristics of the combustion chamber at different incoming flow rates provides a reference for improving the performance of the combustion chamber and enhancing the combustion stability.

The existence and nonlinear stability of stationary solutions to outflow problem for a reduced gravity two and a half layer model

The main concern of this paper is to study large-time behavior of solutions for an outflow problem to the reduced gravity two and a half layer model in a half space. We establish the existence of stationary solutions and further obtain the large time asymptotic stability of small-amplitude stationary solutions provided that the initial perturbation is sufficiently small. Moreover, we obtain the convergence rate of the solution toward the stationary solution in some weighted Sobolev spaces only for the supersonic case. The proof is based on the basic energy method. A key point for the proof of convergence rates is to capture the positivity of the temporal energy dissipation functional and boundary terms with suitable space weight functions either algebraic or exponential depending on whether or not the incoming far-field velocity satisfy some additional conditions.

New Jet impingement flow-scale sets wall approach, Proximity limits & wall-jet heat transfer

A new scale is here identified as dominant in laminar jet impingement flow and heat transfer, namely, the height of the stagnation zone, zw. This being the point at which the jet “senses” the approaching wall, which corresponds to the location of marginal static pressure rise above the impinged plate. It is shown that this new profile-specific scale emerges from the virtual origin concept in Glauert's wall-jet solution, and physically constrained expressions are derived for both. Reynolds analogy is then conducted for the cases of uniform-heat-flux and -wall-temperature. This leads to a new prediction of the wall-jet heat transfer, valid upon convergence to quasi-self-similarity – within a diameter or two of the stagnation point. The convergence distance depends on incoming velocity profile and flow rate, as captured by the new virtual origin expression. The analysis also reveals that the convergence to self-similarity is delayed in the uniform heat flux case, even though eventually heat transfer is about one-third higher.The new scale also led to a successful description of the deceleration during wall-approach, as an interpolation between near-wall (Homann solution) and far-field (inviscid flow) asymptotes. Consequently, the new scale is shown to give the proximity limits for nozzle-to-plate distance. This being the distance at which the incoming jet becomes distorted due to constriction and back-pressure. Here found to correspond to around 2/5 of the stagnation zone height.All these findings are confirmed and validated through simulations, experimental measurements and literature data; and simple expressions are derived for prediction and design purposes.

Turbulence generation in the transitional wake flow behind a sphere

Turbulence generation in the transitional flow in the wake behind a sphere is studied with numerical simulations. The filtered Navier–Stokes equation and the large eddy simulation method are employed as the governing equation and the numerical method, respectively. The ΩR̃ vortex identification method is used to trace the evolution of vortices in the wake flow. The energy gradient theory is used to analyze the spike formation in the wake flow. The simulation results show that the vortex structure in the wake flow is the type of hairpin vortices, which is similar to that in a boundary layer flow. Ejection and sweep motions exist around the hairpin vortices. There are two most unstable regions in the wake where turbulence “burst” is first produced, one is near the center of the vortex head and the other is between the two vortex legs. There is a high-pressure zone above the vortex head due to the decrease in the streamwise velocity, and a soliton-like coherent structure exists in this area. The mechanism of turbulence generation in the wake is the discontinuity of the streamwise velocity, which makes the Navier–Stokes equation be singular. This singularity leads to the formation of the “negative spike” in the streamwise velocity. The amplitude of the “negative spike” reaches up to 60% of the incoming velocity, which is close to the situation in a boundary layer flow on a flat plate. It is concluded that the mechanism of turbulence generation in the wake flow is the same as that in the boundary layer flow.

An improved porous media model for simulating the flow–nets interaction

This study presents an improved porous media model for simulating the interaction between the fixed aquaculture nets and flow. The fluid motion is computed based on the Reynolds time-averaged Navier–Stokes equations on the regular Eulerian mesh. The porous media model simulates the nets, where the interface between the complex shapes of the nets and the fluid is determined by the continuous forced immersed boundary (IB) method. The fluid volume fraction is defined and embedded in the porous media coefficients and porosity equations to set the porous media parameters at IB. Several cases validate the model, including the flow interactions with the single net panel, gravity net cage, and offshore aquaculture platform. Meanwhile, the effects of incoming velocity, attack angle, solidity, and the shape of the net on the simulation are investigated. The numerical model can reasonably predict the hydrodynamic of the nets with a relative error of less than 8%. Moreover, the computational efficiency of the hydrodynamic of complex shaped nets is significantly improved, with a maximum of about 11.54 times.

The incipient motion safety factor of sediment considers the coupling between the surface and subsurface flows under multi-motion modes

The incipient movement of sediment particles in natural rivers under the action of water scour has remained a key issue in river sediment movement research. In this study, we establish a mathematical coupling model between surface and subsurface flows for investigating the interface velocity. The Navier-Stokes equation and Darcy's law are employed to describe surface and subsurface water flows, respectively. The interface velocity U between surface and subsurface flows is derived by introducing the Beavers–Joseph boundary conditions. Furthermore, based on the force equilibrium of a single particle, combined with three incipient modes, namely, sliding, rolling, and saltation, analytical solutions are derived for the critical instantaneous bottom velocity u0, and mean incoming velocity. The derived analytical solutions exhibit a higher computational accuracy than existing flume test data and classical flow velocity model results, with relative errors less than 12 %. Furthermore, the incipient motion state of sediment particles can be directly assessed by defining the critical incipient safety factor for particle motion (i.e., k = U/u0). Sensitivity analysis of the safety factor for sediment particle motion reveals a nonlinear positive correlation with the slope angle, riverbed permeability, riverbed porosity, and hydraulic gradient, while indicating a linear positive correlation with the water depth. However, a nonlinear negative correlation is observed with the B-J coefficient, relative exposure degree, and sediment particle dry bulk density. The safety factor shows a rapid decrease followed by a stabilizing trend with increasing B-J coefficient. Additionally, the safety factor first increases and then decreases with increasing in sediment particle size.

Investigations on bifurcation behavior of wind turbine airfoil response at a high angle of attack

Design load and vibration for parked conditions are gaining in importance for large-scale modern wind turbines with increasing flexibility, especially edgewise vibration when the blade is at a high angle of attack. In this work, flow-induced vibration of the wind turbine airfoil at 90 degrees of attack angle is studied with the fluid-structure interaction (FSI) simulation. The unsteady aerodynamic force due to flow separation and vortex shedding at the high angle of attack causes the chordwise vibration of the airfoil. When the vortex shedding frequency fv gets close to the chordwise natural frequency fn of the airfoil, vortex-induced vibration (VIV) of high amplitude occurs accompanied with the frequency lock-in phenomenon. In the post lock-in regime, it is found that period-3 and torus bifurcation occur successively and the vibration response becomes aperiodic. Dynamic mode decomposition(DMD) technique is used to investigate the mechanism of bifurcation from the perspective of energy balance, through analyzing the vorticity field in the wake and pressure distribution on the airfoil surface. For the certain incoming velocity in the post lock-in regime, since the frequency of the DMD mode f=2fv/3 is close to the natural frequencyfn, both the vibration of frequency 2fv/3 and fv get excited, leading to the onset of bifurcation. The Lissajou curves are obtained through reconstructing the transient pressure of each DMD mode, which indicates that energy transfer mainly exists in modes f=fv. In addition, the reconstructed Lissajou curves based on the leading DMD modes agree well with the original time-domain Lissajou curves.

Thermal boundary layer modelling for heat flux prediction of bubbles at saturation: A priori analysis based on fully-resolved simulations

This study presents and investigates uni-directional thermal sub-layer enhancement techniques within the context of an interface tracking method for simulating bubbly flows at saturation. Current discretisation methods on structured and fixed Cartesian grids tend to spread the bubbles' interface region, creating a trade-off between the freely moving nature of the bubble to the detriment of accurately capturing the discontinuous aspect of the interface and variations of properties and fluxes crossing it. Although robust techniques have been described in the literature to ensure energy conservation, less research has been undertaken to develop a methodology to retrieve the non-linear behaviour of quantities in the interface vicinity at a reasonable computational cost. In this study, the discretised bubble surface is used as a basis for addressing several quasi-static radial sub-problems that are bounded by an interfacial constant saturation temperature and a CFD temperature field value. A first approach, based on an analytical solution fitted at each time step using underlying Eulerian field values, has been developed to incorporate near-interface physics. This includes the tangential effect, incoming fluid velocity, and local mean curvature (first order surface approximation). A semi-analytical approach needs to meet certain assumptions to be valid. This is due to its derivation from a simplified plane boundary-layer development or from a spherical diffusion problem which limits its applicability range. Therefore, a second approach based on a uni-directional sub-resolution fed carefully by interpolated velocity and tangential source terms demonstrates promising results as it aligns with the principal variations of the solution. Both methodologies have been applied onto DNS data of a steady rising bubble configuration at low and moderate Reynolds {3.6;62.5} and Prandtl {1;2.5;5} numbers with a constant interfacial temperature after an extensive analysis of the advection-diffusion terms hierarchy. The key aspects to maximise the effectiveness of the sub-resolution method have been clearly identified and discussed. The Sub-resolution shows better applicability to our case study on moderately large thermal layers. The newly predicted interfacial temperature gradient and temperature profile could be re-employed for Eulerian fluxes correction.

Spatiotemporal Evolution of Wind Turbine Wake Characteristics at Different Inflow Velocities

In this paper, the spatiotemporal evolution of wind turbine (WT) wake characteristics is studied based on lattice Boltzmann method-large eddy simulations (LBM-LES) and grid adaptive encryption at different incoming flow velocities. It is clearly captured that secondary flow occurs in the vortex ring under shear force in the incoming flow direction, the S-wave and the Kelvin–Helmholtz instability occur in the major vortex ring mainly due to the unstable vortex ring interface with small disturbance of shear velocity along the direction of flow velocity. The S-wave and Kelvin–Helmholtz instability are increasingly enhanced in the main vortex ring, and three-dimensional disturbances are inevitable along the mainstream direction when it evolves along the flow direction. With increasing incoming flow, the S-wave and Kelvin–Helmholtz instability are gradually enhanced due to the increasing shear force in the flow direction. This is related to the nonlinear growth mechanism of the disturbance. The analysis of the velocity signal, as well as the pressure signal with a fast Fourier transform, indicates that the interaction between the vortices effectively accelerates the turbulence generation. In the near-field region of the wake, the dissipation mainly occurs at the vortex at the blade tip, and the velocity distribution appears asymmetric around the turbine centerline under shear and the mixing of fluids with different velocities in the wake zone also leads to asymmetric distributions.

Wind-driven smoke dispersion in rooftop photovoltaic fires: An experimental investigation with helium smoke

In 2022, global photovoltaic (PV) deployed capacity increased by 240 GW, reaching a cumulative capacity 1.185 of terawatts, accompanied by anticipated 34,247 PV-inducted fires. The dispersion of fire smoke from rooftops with PVs raises significant safety concerns regarding residents’ exposure. Therefore, it is essential to investigate the phenomenon of smoke dispersion generated by rooftop PV fires, particularly through rooftop openings such as skylights. However, there are limited studies on this topic in the literature. This study conducts small-scale tests in a wind tunnel to examine rooftop PV fire smoke dispersion using a novel smoke-helium similarity and scaling law. A parametric analysis is carried out, aiming to guide the fire protection design of the building. It examines the smoke dispersion generated from rooftop PV fires, considering a variety of rooftop angles, incoming wind velocities, as well as heat release rates (HRR). According to the findings, residents exposed to rooftop PV fire smoke must evacuate within 4 min. Moreover, descending to lower levels may not be a safe means of escape. The scenario with a 15° rooftop angle is deemed fatal. Conversely, rooftop angles of 45° and 60° are considered the most reliable layout for rooftop PV. As incoming wind velocity decreases from 7.75 m/s (full-scale 30 m/s) to 2.58 m/s (full-scale 10 m/s), smoke dispersion increases across the rooftop opening (e.g., skylight) as the rooftop angle increases from 0° to 30°. Smaller HRRs of rooftop PV fires correspond to more reliable fire protection.

Two three-dimensional super-Gaussian wake models for hilly terrain

With the increase in wind farms in hilly terrain, it is particularly important to explore the downstream wake expansion of wind turbines in hilly terrains. This study established two complex terrain-applicable super-Gaussian wake models based on the Coanda effect and the wind speed-up phenomenon. Then, by considering the wind shear effect and the law of mass conservation, two three-dimensional (3D) super-Gaussian wake models were obtained. The 3D super-Gaussian models were used to describe the shape of the wake deficit and could reflect the wake changes in the full wake region. The introduction of the Coanda effect could reflect the sinking of the wind turbine wake on the top of a hilly terrain. And considering that the wind speed-up phenomenon could better reflect the incoming velocity distribution of the actual hilly terrain. The validation results demonstrated that the prediction results of the 3D super-Gaussian wake models had negligible relative errors compared to the measured data and could better describe the vertical and horizontal expansion changes of the downstream wake. The models established in this study can assist with the development of complex terrain models and super-Gaussian models, as well as providing guidance for power prediction and wind turbine control strategies in complex terrain.