Streamwise Velocity Component Research Articles

Combined Large-Eddy and Direct Numerical Simulations of a Planar Jet with Heated Co-Flow with Medium and Low Prandtl Fluids

In the present work, we have applied a combined dynamic large-eddy simulation (LES) and direct numerical simulation (DNS) approach for a three-dimensional planar jet in a turbulent forced convection regime (Re = 18000) with a heated co-flow. Results from LES are compared with Reynolds Averaged Navier-Stokes (RANS) simulations and experimental data. We have analyzed flow and heat transfer features for four values of the characteristic Prandtl numbers (Pr = 0.71, 0.2, 0.025, and 0.006), which are representatives of air, He-Xe gas mixture, Lead-Bismuth Eutectic (LBE), and sodium, respectively. The latter two low-Prandtl fluids have been considered because of their role as primary coolants in advanced fast pool-type reactor prototypes (such as the Multi-purpose Hybrid Research Reactor for High-tech Applications (MYRRHA) at SCK•CEN, Belgium). We have provided detailed insights into instantaneous and long-term time-averaged behavior of the velocity and temperature fields (the first- and second-order moments). Furthermore, we have analyzed profiles of characteristic velocity and temperature time scales and dissipation rates, as well as the power spectra of the streamwise velocity component and temperature at several characteristic locations. The mean temperature profiles demonstrated rather low sensitivity for various values of the Prandtl number. In contrast, profiles of the temperature standard deviation exhibited larger variations, decreasing in magnitude with lower Prandtl values. Here presented results of the high fidelity numerical simulations (dynamic LES/DNS) for the low-Prandtl working fluids can be used for further development, testing, and validation of the advanced RANS-type turbulence models.

Coherent structures in turbulent mixed convection flows through channels with differentially heated walls

The occurrence and shape of turbulent structures in mixed convection flows through a differently heated vertical channel are investigated in terms of thermally induced attenuation and amplification of turbulent velocity, pressure, and temperature fluctuations using direct numerical simulations. It is shown that the wall-normal momentum transport is decreased and increased near the heated and cooled wall, respectively, and that this leads to a reduced and elevated production of turbulent velocity fluctuations in the streamwise velocity component in the aiding and opposing flow, respectively. The corresponding flow structures are smoother, faster and warmer in the aiding flow and aligned along the main flow, while the colder structures in the opposing flow are more frayed and less directed. The warmer flow structures in the aiding flow are overall more stable than the colder structures in the opposing flow. Besides, the study reveals that the position of the maximum temperature fluctuations moves toward the heated wall, so that the sweeps produced at the two walls are affected differently by the former. As a consequence, the distance and time period over which the fluctuations develop in the aiding flow are shorter than in the opposing flow. It is further shown that vortex structures oriented in the streamwise direction usually arise with an offset to the right or left above a sweep or an ejection, whereby the decreasing values of the correlation coefficients with increasing Grashof number indicate a weakening of the vortex structures. Since none of the evaluated vortex criteria, that is, the distributions of the vorticity, λ 2 - value or Rortex-value correlate well with the evaluated minima of the pressure fluctuations, they do not allow a clear identification of the vortex structures. Finally, analyzing the budget of the turbulent kinetic energy it is confirmed that the velocity fluctuations are only indirectly influenced by the buoyancy force. Thus, the attenuation and amplification of the turbulent velocity fluctuations is reflected in the reduction and exaggeration of the Reynolds shear stresses in the aiding and opposing flow, respectively.

Investigation of the Flow Structures for Two Tandem Arrangement of Torpedo-Like Geometries

Experimental studies on autonomous underwater vehicles for a torpedo-like geometry are limited in the literature. In this study, flow structures of a streamlined torpedo-like geometry having an elliptical nose and tampered stern at a length to diameter aspect ratio of L/D=5 for a single and double tandem arrangement with various spacings have been investigated using Particle Image Velocimetry (PIV) method in a closed loop water channel. Reynolds number defined for length of the geometry (L=200 mm), free stream water velocity of 100 mm/s was taken as Re=20000, the spacing (G) between two identical torpedo-like geometries is changed from 0 to 120 mm. Instantaneous 1000 images and their time-averaged results are comparatively presented for all configurations of the torpedo-like geometry. It is demonstrated that the tandem arrangements depending on the dimensionless spacing ratios (G/L) between 0 to 0.6 are significantly different from the single torpedo-like geometry for the flow patterns of instantaneous and time-averaged velocity field, dimensionless streamwise velocity component and streamline topology. For the contacting case in which the following model nose is placed on the trailing-edge of the front model, wake region of the back geometry is similar to the single model wake but the all of time-averaged flow patterns elongated and symmetrical flow patterns are slightly deformed. When flow area is provided between two models for spacing ratios of 0.15≤G/L≤0.30, chaotic and rotational flow patterns occur due to the impinging separated flow patterns from the front geometry to the nose of the downstream one. As the gap distance increases to the largest value at G/L=0.6, the wake region of both the single and tandem arrangement becomes almost identical. More detailed information for the flow characteristics of the examined torpedo-like geometry can be determined by using computational fluid dynamics after validation with PIV results in the present study.

Fluid–structure–thermal interaction of a self-fluttering membrane in turbulent channel flow

This study investigated the fluid–structure–thermal interaction of a fluttering membrane in turbulent channel flow at three different modes (straight mode, unsaturated flutter mode, and saturated flutter mode) and increasing Reynolds number. Using a high-speed camera at 2 kHz and a data-acquisition system at 51.2 kHz, the deformation shapes of a piezoelectric membrane and the temporal voltage variations were simultaneously recorded. Unlike the fluttering membrane in a parallel, unconfined flow, the flutter amplitude of the membrane in the channel exhibited an asymptotic behavior with the Reynolds number and eventually reached a saturated state. Different from the membrane characteristics at the unsaturated flutter mode, the membrane at the saturated flutter mode exhibited a dramatic fluttering behavior, with large flutter amplitude and front stationary points. Furthermore, the statistical flow quantities and the heat transfer performance were examined. The variations in the streamwise and vertical velocity components were closely related to the pressure loss and the heat transfer enhancement, respectively. In addition, the thermal enhancement factor was largest at the unsaturated flutter mode because of the high friction factor. Finally, through membrane shape identification, the spatiotemporal evolutions of flow–structure dynamics were captured. The relationships between the streamwise velocity and the pressure loss and between the vertical velocity and the heat transfer enhancement were further investigated phase by phase. According to the vorticity distributions, two small vortices occurred at the saturated flutter mode, which enhanced the heat transfer performance.

Characterization of flow field and combustion dynamics in a novel pressurized side-wall quenching burner using high-speed PIV/OH-PLIF measurements

A novel, pressurized side-wall quenching (SWQ) burner test rig enabling investigations on flame-wall interactions (FWI) of a fully premixed V-shaped flame at conditions mimicking some characteristics of practical devices, e.g. increased pressures and Reynolds numbers, is introduced within this study. Two operating cases featuring turbulent flow conditions at atmospheric and 3 bar operating pressure are defined and characterized based on velocity fields and flame front positions provided by simultaneous high-speed particle image velocimetry (PIV) and planar laser-induced fluorescence of the OH radical (OH-PLIF). For non-reacting conditions, profiles of mean velocities and mean velocity fluctuations are measured in addition to near-wall flow fields at locations where FWI occurs for chemically reacting conditions. For reacting conditions, near-wall flows are characterized in the vicinity of the quenching zone. Based on measured fluctuations of the streamwise velocity component, the turbulent flame is classified at the transition from the wrinkled to the corrugated flamelet regime. Using the derived flame front positions, the instantaneous flame-wall interaction is classified into SWQ-like, head-on quenching (HOQ)-like and multi-zone quenching events and the transition between these scenarios is identified by means of OH-PLIF image sequences. A statistical analysis of the flame front topology is performed based on the flame brush and deduced frequency distributions. Statistically significant differences between both operating cases are confirmed by chi-squared homogeneity tests.

On 3D structure of a circular cylinder wake

The 3D structure of the wake behind a circular cylinder in a cross-flow is studied experimentally using stereo PIV technique, Reynolds number was around 5 thousands. The statistical characteristics along the cylinder axis are effectively constant and thus 2D, however instantaneous flow-field in the wake is fully 3D. Within the wake dynamical flow, the streamwise vortices and spots of streamwise velocity component pulsations are detected.

Experimental Investigation of 3D Dynamical Effects in a Wake behind Circular Cylinder

A circular cylinder in crossflow is subjected to the study of 3D dynamical structure of its wake. The typical dynamics is characterized by quasi-periodic behaviour called Kármán – Bénard vortex street with the typical frequency in dimensionless form known as Strouhal number. The experimental study relies on stereo Particle Image Velocimetry method, the plane of measurement is perpendicular to the flow in the distance 3.8 cylinder diameters in streamwise direction. Reynolds number was around 5 thousand. The structure and dynamical behaviour of the wake along the cylinder axis is studied in details. On the top of the known streamwise velocity deficit definition of the wake, the streamwise oriented dynamically evolving vortices are detected. For the detailed dynamics examination, the Oscillation Pattern Decomposition method was used. Waves of various structures travelling along the cylinder axis as well as some pulsations were identified. The wake dynamics is characterised by the streamwise velocity component deficit and the streamwise vorticity concentration. Both structures are moving periodically in transversal direction with the same frequency, the velocity deficit is shifted by a quarter of period behind the vorticity concentration in the shedding process.

Enhanced outer peaks in turbulent boundary layer using uniform blowing at moderate Reynolds number

Uniform blowing through a permeable surface acts as an active flow control method in wall bounded flows. Such control technique was investigated in a zero pressure gradient turbulent boundary layer over a flat plate. Measurement data were obtained with the help of Laser Doppler Anemometry technique. Besides the drag reduction characteristics of such flow control method, time averaged measurement of stream-wise and wall-normal velocity components was taken at Reynolds number based on momentum thickness () of 1100–3670. Due to the difference in surface condition with and without blowing, mean properties of the boundary condition at wall influence the flow properties when scaled with outer scaling properties. Enhanced turbulence is observed in Reynolds stresses using statistical analysis including the thickening of the boundary layer.

Three-dimensional flow field reconstruction in the wake of a confined square cylinder using planar PIV data

A method is presented to perform the three-dimensional reconstruction of the velocity field in laminar flows using planar PIV data. The developed method relies on a convenient, repeated application of two data processing tools developed by two of the authors and called the higher order dynamic mode decomposition and the spatio-temporal Koopman decomposition. The present reconstruction method is an extension of a general method recently presented by three of the authors (Pérez et al., 2020), in which synthetic PIV data (obtained via numerical simulation) along three mutually orthogonal families of planes were used. In this article, instead, actual experimental data are considered, which requires additional data processing tools, developed in the article, to both cope with experimental noise and synchronize the various PIV datasets obtained in different timespans. The method is applied to analyze the wake of a square cylinder confined in a channel, at moderate Reynolds number. Due to limitations of the experimental setup used to obtain data for this configuration, only two families of planar PIV measurements are available that are contained in planes parallel to the sides of the channel. Because of this limitation, only the streamwise velocity component is three-dimensionally reconstructed. The performance of the method is tested in the wake of the confined square cylinder, comparing the reconstructed data with experimental PIV data measured on additional test planes (not used in the reconstruction). The obtained reconstructions of the streamwise velocity are reasonably accurate.

Growth of vortical disturbances entrained in the entrance region of a circular pipe

The development and growth of unsteady three-dimensional vortical disturbances entrained in the entry region of a circular pipe is investigated by asymptotic and numerical methods for Reynolds numbers between $1000$ and $10\,000$ , based on the pipe radius and the bulk velocity. Near the pipe mouth, composite asymptotic solutions describe the dynamics of the oncoming disturbances, revealing how these disturbances are altered by the viscous layer attached to the pipe wall. The perturbation velocity profiles near the pipe mouth are employed as rigorous initial conditions for the boundary-region equations, which describe the flow in the limit of low frequency and large Reynolds number. The disturbance flow is initially primarily present within the base-flow boundary layer in the form of streamwise-elongated vortical structures, i.e. the streamwise velocity component displays an intense algebraic growth, while the cross-flow velocity components decay. Farther downstream the disturbance flow occupies the whole pipe, although the base flow is mostly inviscid in the core. The transient growth and subsequent viscous decay are confined in the entrance region, i.e. where the base flow has not reached the fully developed Poiseuille profile. Increasing the Reynolds number and decreasing the frequency causes more intense perturbations, whereas small azimuthal wavelengths and radial characteristic length scales intensify the viscous dissipation of the disturbance. The azimuthal wavelength that causes the maximum growth is found. The velocity profiles are compared successfully with available experimental data and the theoretical results are helpful to interpret the only direct numerical dataset of a disturbed pipe-entry flow.

Mode classification for vortex shedding from an oscillating wind turbine using machine learning

This study presents an effective strategy that applies machine learning methods to classify vortex shedding modes produced by the oscillating cylinder of a bladeless wind turbine. A 2-dimensional computational fluid dynamic (CFD) simulation using OpenFOAMv2006 was developed to simulate a bladeless wind turbines vortex shedding behavior. The simulations were conducted at two wake modes (2S, 2P) and a transition mode (2PO). The local flow measurements were recorded using four sensors: vorticity, flow speed, stream-wise and transverse stream-wise velocity components. The time-series data was transformed into the frequency domain to generate a reduced feature vector. A variety of supervised machine learning models were quantitatively compared based on classification accuracy. The best performing models were then reevaluated based on the effects of artificial noisy experimental data on the models’ performance. The velocity sensors orientated transverse to the pre-dominant flow (u y ) achieved improved testing accuracy of 15% compared to the next best sensor. The random forest and k-nearest neighbor models, using u y , achieved 99.3% and 99.8% classification accuracy, respectively. The feature noise analysis conducted reduced classification accuracy by 11.7% and 21.2% at the highest noise level for the respective models. The random forest algorithm trained using the transverse stream-wise component of the velocity vector provided the best balance of testing accuracy and robustness to data corruption. The results highlight the proposed methods’ ability to accurately identify vortex structures in the wake of an oscillating cylinder using feature extraction.

Classification of flame prehistory and quenching topology in a side-wall quenching burner at low-intensity turbulence by correlating transport effects with CO[formula omitted], CO and temperature

Thermochemical states of a turbulent, lean premixed dimethyl ether/air flame were assessed for the first time using simultaneous measurements of gas temperature T, CO2 and CO mole fractions with locations as close as 120 μm above the quenching wall. This is realized by combined dual-pump coherent anti-Stokes Raman spectroscopy (DP-CARS) and two-photon laser-induced fluorescence (LIF) of CO. In addition to thermochemical states, the flow and flame dynamics were measured separately using a combined two component particle image velocimetry (PIV) and planar LIF of the OH radical at high (4 kHz) and low (50 Hz) repetition rates. The data from the independent measurements was linked by the instantaneous flame front topologies, determined by the qualitative OH-LIF in both experiments. The grid-generated turbulence intensity was found to be relatively low in the bulk flow (∼4.5%, streamwise velocity component) with the turbulent flame classified within the regime of wrinkled flamelets (w′/sL between 0.3 and 0.75, for streamwise velocity component). The flame-wall interaction could be assigned to either a side-wall quenching (SWQ)-like (∼50%) or a head-on quenching (HOQ)-like scenario (∼50%), with a transition between these scenarios taking place within a few milliseconds. The thermochemical states depend significantly on whether a SWQ-like or a HOQ-like scenario is present. Here, the thermochemistry of the SWQ-scenario is studied in detail, and three zones, A, B, C, could be distinguished in the state space on the basis of the (CO2,T) correlations. Zone A is characterized by strong wall heat losses and mixing influences, while zone B features less pronounced wall heat losses and mixing processes. In zone C the impacts of turbulence almost completely disappear and conditions comparable to a laminar near-wall flow are observed. The distinguishability of the three zones in the (CO,T) or (CO,CO2) correlations is less clear, which underlines the importance of the additional CO2 measurement in the DP-CARS methodology.

예인수조 LDV를 이용한 평판 경계층과 와이어 타입 난류촉진장치의 상호작용에 관한 연구

The present study aims to investigate the interaction of a wire-type turbulence stimulator and the laminar boundary layer on a flat plate by flow field measurement. For the towing tank tests, a one-dimensional Laser Doppler Velocimetry (LDV) attached on a two-axis traverse was used to measure the streamwise velocity component of the boundary layer flow in zero pressure gradient, disturbed by a turbulence stimulator. The wire diameter was 0.5 and 1.0 mm according to the recommended procedures and guidelines suggested by the International Towing Tank Conference. Turbulence development by the stimulator was identified by the skin friction coefficient, mean and Root Mean Square (RMS) of the streamwise velocity. The laminar boundary layer with the absence of the wire-type stimulator was similar to the Blasius solution and previous experimental results. By the stimulator, the mean and RMS of the streamwise velocity were increased near the wall, showing typical features of the fully developed turbulent boundary layer. The critical Reynolds number was reduced from 2.7×10<SUP>5</SUP> to 1.0×10<SUP>5</SUP> by the disturbances caused by the wire. As the wire diameter and the roughness Reynolds number (Rek) increased, the disturbances by the stimulator increased RMS of the streamwise velocity than turbulent boundary layer.

Wind farm wake modeling based on deep convolutional conditional generative adversarial network

Modeling of wind farm wakes is of great importance for the optimal design and operation of wind farms. In this work a surrogate modeling method for parametrized fluid flows is proposed for wind farm wake modeling, based on the state-of-the-art deep learning framework i.e. deep convolutional conditional generative adversarial network. Based on the proposed method and the data generated by high-fidelity large eddy simulations, a novel wind farm wake model is developed. The developed model is first validated against high-fidelity data and the results show that it achieves accurate, efficient, and robust prediction of wind turbine wake flow, at all the streamwise locations including both near wake and far wake, for both streamwise and spanwise velocity components, and at the cases with different inflow wind profiles. Then an extensive parametric study is carried out and the results show that the model generalizes well to unknown flow scenarios. Furthermore, a case study for a wind farm is investigated by the developed model. The prediction results are then compared with high-fidelity simulations, showing that the model can predict the wind farm wake flow (including both the streamwise and spanwise velocity fields) very well.

A Standard Criterion for Measuring Turbulence Quantities Using the Four-Receiver Acoustic Doppler Velocimetry

Acoustic Doppler velocimetry (ADV) enables three-dimensional turbulent flow fields to be obtained with high spatial and temporal resolutions in the laboratory, rivers, and oceans. Although such advantages have led ADV to become a typical approach for analyzing various fluid dynamics mechanisms, the vagueness of ADV system operation methods has reduced its accuracy and efficiency. Accordingly, the present work suggests a proper measurement strategy for a four-receiver ADV system to obtain reliable turbulence quantities by performing laboratory experiments under two flow conditions. Firstly, in still water, the magnitude of noises was evaluated and a proper operation method was developed to obtain the Reynolds stress with lower noises. Secondly, in channel flows, an optimal sampling period was determined based on the integral time scale by applying the bootstrap sampling method and reverse arrangement test. The results reveal that the noises of the streamwise and transverse velocity components are an order of magnitude larger than those of the vertical velocity components. The orthogonally paired receivers enable the estimation of almost-error-free Reynolds stresses and the optimal sampling period is 150–200 times the integral time scale, regardless of the measurement conditions.

Wake Width: Discussion of Several Methods How to Estimate It by Using Measured Experimental Data

Several methods of defining and estimating the width of a turbulent wake are presented and tested on the experimental data obtained in the wake past an asymmetric prismatic airfoil NACA 64(3)-618, which is often used as tip profile of the wind turbines. Instantaneous velocities are measured by using the Particle Image Velocimetry (PIV) technique. All suggested methods of wake width estimation are based on the statistics of a stream-wise velocity component. First, the expansion of boundary layer (BL) thickness is tested, showing that both displacement BL thickness and momentum BL thickness do not represent the width of the wake. The equivalent of 99% BL thickness is used in the literature, but with different threshold value. It is shown that a lower threshold of 50% gives more stable results. The ensemble average velocity profile is fitted by Gauss function and its σ-parameter is used as another definition of wake width. The profiles of stream-wise velocity standard deviation display a two-peak shape; the distance of those peaks serves as wake width for Norberg, while another tested option is to include the widths of such peaks. Skewness (the third statistical moment) of stream-wise velocity displays a pair of sharp peaks in the wake boundary, but their position is heavily affected by the statistical quality of the data. Flatness (the fourth statistical moment) of the stream-wise velocity refers to the occurrence of rare events, and therefore the distance, where turbulent events ejected from the wake become rare and can be considered as another definition of wake width. The repeatability of the mentioned methods and their sensitivity to Reynolds’ number and model quality are discussed as well.

A numerical modelling investigation of the development of a human cough jet

PurposeThis study aims (1) to numerically investigate the characteristics of a human cough jet in a quiescent environment, such as the variation with time of the velocity field, streamwise jet penetration and maximum jet width. Two different turbulence modelling approaches, the unsteady Reynolds-averaged Navier–Stokes (URANS) and large eddy simulation (LES), are used for comparison purposes. (2) To validate the numerical results with the experimental data.Design/methodology/approachTwo different approaches, the URANS and LES, are used to simulate a human cough jet flow. The numerical results for the velocity magnitude contours and the spatial average of the two-dimensional velocity magnitude over the corresponding particle image velocimetry (PIV) field of view are compared with the relevant PIV measurements. Similarly, the numerical results for the streamwise velocity component at the hot-wire probe location are compared with the hot-wire anemometry (HWA) measurements. Furthermore, the numerical results for the streamwise jet penetration are compared with the data from the previous experimental work.FindingsBased on the comparison with the URANS approach and the experimental data, the LES approach can predict the temporal development of a human cough jet reasonably well. In addition, the maximum width of the cough jet is found to grow practically linearly with time in the far-field, interrupted-jet stage, while the corresponding axial distance from the mouth of the jet front increases with time in an approximately quadratic manner.Originality/valueCurrently, no numerical study of human cough flow has been conducted using the LES approach due to the following challenges: (1) the computational cost is much higher than that of the URANS approach; (2) it is difficult to specify the turbulent fluctuations at the mouth for the cough jet properly; (3) it is necessary to define the appropriate conditions for the droplets to obtain statistically valid results. Therefore, this work fills this research gap.

Velocity uncertainty quantification based on Riparian vegetation indices in open channels colonized by Phragmites australis

One of the main purposes of Ecohydraulics is to predict the effects of riparian vegetation on aquatic ecosystems within real water channels. The interaction between water flow and riparian plants significantly affects flow dynamics, hydraulic conveyance, and water quality of vegetated water bodies. This study aimed at quantifying analytically the uncertainty in flow average velocity estimations associated with the uncertainty of Leaf Area Index (LAI) of Phragmites australis (Cav.) Trin. ex Steudel covering a vegetated channel. The impacts of this species on the hydrodynamics of vegetated streams are far to be completely understood. The uncertainty in flow average velocity was assessed through the first-order second-moment statistical method, by comparing direct and indirect LAI measurements of mature Phragmites australis plants. Indirect LAI values were obtained using the LICOR® LAI-2000 Plant Canopy Analyzer device. The results of this study suggest that the uncertainties in flow average velocity estimations are comparable to those associated with experimental measurements of streamwise velocity components retrieved in real vegetated flows fully covered by mature Phragmites australis plants.

DNS Of entropy generation rates for turbulent flows subjected to high temperature gradients

Direct Numerical Simulations are performed to analyze the influence of key boundary conditions and flow characteristics on entropy generation rate statistics in a highly anisothermal forced convective turbulent channel flow of a thermo-dependent fluid submitted to asymmetrical heating. Each parameter is varied separately to quantify its influence compared to a reference simulation, the hot to cold wall temperature ratio from 1.5 to 3, the mean friction Reynolds number from 150 to 210, the mean thermodynamic pressure from 1bar to 3bar. Two thermal boundary condition types are also compared (fixed temperatures vs. fixed heat flux density at the walls). For each parameter that is varied, the evolution of the entropy generation rate mean, root-mean-square and correlations with the temperature and the streamwise or wall-normal velocity components are presented and discussed. All simulations have in common the thermal asymmetry and the highly non-isothermal nature of the flow: beyond the changes induced by the variation of each parameter, the common characteristics of the statistical quantity profiles are also analyzed. This work establishes how the spatial distribution of the local entropy generation rate is modified by the parameters studied, in which direction and with which sensitivity. It demonstrates the significant influence of the thermal boundary condition type on the entropy generation rate fluctuations near the walls.

Numerical Analysis of Wind Wake Superposition and Boundary Layer Interaction

Understanding the wake impacts to a wind farm is critical for layout planning and turbine design. Wind Wake Models estimates wake development through a single turbine which is then aggregated with a wake variety of methods to calculate the combined wake profile for a wind farm. This study considered downstream wake interactions, and the energy content in the wake profile as the wake developed for three rows and five downstream turbines. This study also looks at the influence of different atmospheric stratifications to wind farm wake superposition. Our findings for the wake and boundary superimposition model determine that the streamwise velocity component range from 8.8 to 9.0 m s-1 (98 to 100 %) for the stable ABL ranges and 8.92 to 9.0 m s-1 (99 to 100 %) for the unstable ABL ranges. This study further determines that the minimum streamwise velocity for the stable and unstable ABL are 8.97 and 8.96 m s-1, and the mean normalized velocity deficit for the stable and unstable ABL are 0.972 and 0.975. The wake deficit for the superimposition of a coupled wake boundary model in the stable case surpasses that of the unstable case due to lower turbulence.