Rectangular Cylinder Research Articles

Resonant triad interactions of gravity waves in cylindrical basins

We present the results of a theoretical investigation into the existence, evolution and excitation of resonant triads of nonlinear free-surface gravity waves confined to a cylinder of finite depth. It is well known that resonant triads are impossible for gravity waves in laterally unbounded domains; we demonstrate, however, that horizontal confinement of the fluid may induce resonant triads for particular fluid depths. For any three correlated wave modes arising in a cylinder of arbitrary cross-section, we prove necessary and sufficient conditions for the existence of a depth at which nonlinear resonance may arise, and show that the resultant critical depth is unique. We enumerate the low-frequency triads for circular cylinders, including a new class of resonances between standing and counter-propagating waves, and also briefly discuss annular and rectangular cylinders. Upon deriving the triad amplitude equations for a finite-depth cylinder of arbitrary cross-section, we deduce that the triad evolution is always periodic, and determine parameters controlling the efficiency of energy exchange. In order to excite a particular triad, we explore the influence of external forcing; in this case, the triad evolution may be periodic, quasi-periodic or chaotic. Finally, our results have potential implications on resonant water waves in man-made and natural basins, such as industrial-scale fluid tanks, harbours and bays.

Investigation of nonlinear and transitional characteristics of flutter varying with wind angles of attack for some typical sections with different side ratios

This study conducted a comprehensive investigation into the flutter responses of three closed sections, namely two streamlined box girders and a 5:1 rectangular cylinder, which possess different side ratios. Different types of flutter were measured during the tests. The nonlinear and transitional characteristics of the flutter were thoroughly discussed. The effects of the wind angle of attack and side ratio on the reduced critical wind speed, limit cycle oscillation amplitude and the transition behaviors of the flutter were investigated. The complex modal motion information of the three systems was discussed. The main factors contributing to the transition of flutter, and the dynamic mechanisms of the occurrence of different flutter manifestations, were investigated. This was achieved by examining the evolution of their modal damping ratios with the vibration amplitude and wind speed. Finally, an examination was conducted to evaluate the impact of the mechanical damping ratio on the transition behavior of flutter as well as its effectiveness in mitigating flutter responses for the considered sections. Results showed that the various manifestations of the flutter are mainly ascribed to the gradually evolved modal damping ratio, where aerodynamic damping plays the most important role in producing different types of limit cycle oscillations and transitional behaviors of flutter. Moreover, the modal damping ratio slowly transitions with the wind angle of attack, wind speed, or the side ratio of a section, instead of experiencing any mutation, despite the observation of some distinct types of flutter during the tests.

Linear global and asymptotic stability analysis of the flow past rectangular cylinders moving along a wall

The primary instability of the steady two-dimensional flow past rectangular cylinders moving parallel to a solid wall is studied, as a function of the cylinder length-to-thickness aspect ratio ${A{\kern-4pt}R} =L/D$ and the dimensionless distance from the wall $g=G/D$ . For all ${A{\kern-4pt}R}$ , two kinds of primary instability are found: a Hopf bifurcation leading to an unsteady two-dimensional flow for $g \ge 0.5$ , and a regular bifurcation leading to a steady three-dimensional flow for $g < 0.5$ . The critical Reynolds number $Re_{c,2\text{-}D}$ of the Hopf bifurcation ( $Re=U_\infty D/\nu$ , where $U_\infty$ is the free stream velocity, $D$ the cylinder thickness and $\nu$ the kinematic viscosity) changes with the gap height and the aspect ratio. For ${A{\kern-4pt}R} \le 1$ , $Re_{c,2\text{-}D}$ increases monotonically when the gap height is reduced. For ${A{\kern-4pt}R} >1$ , $Re_{c,2\text{-}D}$ decreases when the gap is reduced until $g \approx 1.5$ , and then it increases. The critical Reynolds number $Re_{c,3\text{-}D}$ of the three-dimensional regular bifurcation decreases monotonically for all ${A{\kern-4pt}R}$ , when the gap height is reduced below $g < 0.5$ . For small gaps, $g < 0.5$ , the hyperbolic/elliptic/centrifugal character of the regular instability is investigated by means of a short-wavelength approximation considering pressureless inviscid modes. For elongated cylinders, ${A{\kern-4pt}R} > 3$ , the closed streamline related to the maximum growth rate is located within the top recirculating region of the wake, and includes the flow region with maximum structural sensitivity; the asymptotic analysis is in very good agreement with the global stability analysis, assessing the inviscid character of the instability. For cylinders with $AR \leq 3$ , however, the local analysis fails to predict the three-dimensional regular bifurcation.

Flow transition and fluid forces reduction for flow around two tandem cylinders

The numerical study of two-dimensional flow in a channel past two tandem rectangular cylinders is performed using the lattice Boltzmann method (LBM). Investigations are performed for different aspect ratios (AR) and gap spacings (g) values at Reynolds number (Re = 100). We selected four aspect ratios and ten gap spacing values. These parameters attribute five different flow behaviors. The flow transitions and sensitivity of the fluid forces are analyzed with the help of vorticity contours visualization, streamlines visualization, time trace analysis of forces, power spectra of lift forces, and integral parameters. The outcomes of these investigations yield that both parameters are very effective for the transition of the flow regime. It is examined that drag force is a decreasing function of AR, and a 65% reduction is found on the upstream cylinder in a square case. The g = 4 is the critical gap spacing for AR = 1. The mean values of forces exhibit nearly constant behavior for large gap spacing for any fixed AR. Secondary vortex shading frequency is also seen when the flow is interactive.

Investigation into the effect of vortex distribution on the flow field around a semi-submerged rectangular cylinder with different aspect ratios

ABSTRACT Vortex distribution affects the flow field variation of offshore structures at different aspect ratios (ARs; length-to-draft). This paper investigates the relationship between the vortex distribution and flow field around a semi-submerged rectangular cylinder (SRC) at a low Reynolds number (Re = 36300) using the OpenFOAM platform. First, vortex generation is explored, and then the influence of vortex distributions on the flow field around the SRC is analyzed. The numerical results show that when the SRC pierces the free surface, the wake region is different from the Kármán vortex street due to the free surface. AR mainly affects the range of the wake region and the SRC bottom vortex. In terms of vortex generation and differences in vortex structure, the variations of the flow field around the SRC are significantly affected by the vortex at the bottom of the SRC.

Turbulent flow around a short rectangular cylinder in uniform flow at moderate Reynolds numbers

The influence of Reynolds number (Re) on the wake characteristics, Kelvin-Helmholtz instabilities and von-Kármán vortex shedding process around a short rectangular cylinder with length to height ratio of 0.5 was studied using particle image velocimetry. The Reynolds numbers based on cylinder height and free-stream velocity ranged from 3000 to 21000. The flow characteristics were analyzed using the instantaneous and mean velocity fields, as well as the Reynolds stresses, while the unsteady dynamics were elucidated using frequency spectra, proper orthogonal decomposition (POD) and reverse flow area. The results demonstrate that the size of the wake vortex reduced but the magnitudes of the Reynolds stresses increased with increasing Re, until Reynolds number independence is reached at Re = 10000. Regardless of Reynolds number, spectral analyses of the velocity fluctuations, POD mode coefficients and fluctuating reverse flow area showed dominant peaks at the same fundamental vortex shedding frequency. Meanwhile, instantaneous flow visualization showed that the structural coherency of the large-scale vortices increased with increasing Reynolds number. Cross-correlation analysis also revealed that the odd and even POD mode coefficients of the first two mode pairs, respectively, acted to contract and expand the instantaneous reverse flow area at the higher Reynolds numbers.

The galloping of a 4:1 rectangular cylinder at Re = 300

The flow-induced vibration (FIV) of a rectangular cylinder with a side ratio of 4 at Re = 300 is numerically investigated by a two-dimensional spectral-element method. The cylinder is constrained to vibrate only in the cross-flow direction. The effects of mass ratio and damping ratio are studied. Boss typical FIV, vortex-induced vibration (VIV), and galloping were found. Although the quasi-steady theory predicts that galloping will not occur for a 4:1 rectangular cylinder, we still find galloping in the mass ratio range of 6 < m* < 28. VIV is dominant at low, reduced velocities; however, galloping is found after a certain value. Galloping may be caused by the trailing edge vortex. In the case of low mass ratios, VIV will suppress galloping. It was found that, within a certain range of reduced velocity and mass ratio, the increase in damping will weaken vortex induced vibration, thus causing galloping to reappear.

Distribution and spanwise correlation of aerodynamic forces on a 5:1 rectangular cylinder in the vortex-induced vibration stage

Vortex-induced vibration (VIV) is a type of fluid–solid coupling vibration with a complex flow-field structure. Herein, the wall pressures around a 5:1 rectangular cylinder in the stationary and vibration states are studied via wind tunnel tests. By conducting the spectrum analysis, a novel method is proposed to divide the flow-field of the side surface into recirculation, main vortex, and reattachment regions. The method proposed can be used as a reference for partitioning the flow-field. Based on the partition results, the effects of the maximum amplitudes and development VIV stages on the spanwise correlations of the aerodynamic forces in different subregions are investigated. The results show that the correlation coefficients of the aerodynamic forces in all three subregions increase with the value of maximum amplitude, while the correlation coefficients in the stationary state are all the smallest. Additionally, the spanwise correlations are most affected by the maximum amplitude in the recirculation region and least affected in the main vortex region. Moreover, the maximum spanwise correlation coefficients in the three subregions do not appear at the maximum amplitude, but in the VIV rising stage, owing to the interaction between the self-excited force and vortex shedding force.

A proper orthogonal decomposition analysis upon aerodynamic structures under clean and rough conditions

A transitional flow regime is known to induce complex flow structures upon aerodynamic geometries such as airfoils, and the dynamics of laminar separation bubbles (LSBs) pose a relevant research field. In addition to being affected by the Reynolds value itself, LSBs are shown to be equally sensitive to the surface roughness of the airfoils. The study analyses wind tunnel-derived surface-pressure distribution datasets obtained for a particular airfoil of the standard family developed by the National Advisory Committee for Aeronautics (NACA), namely, the NACA0021, subjected to the range 0.8×104<Re<1.6×104 at different angles of attack under two flow configurations that correspond to a clean and roughened surface. The analysis is undertaken via the proper orthogonal decomposition (POD) technique. The results show that the decomposition of the temporal series of surface-pressure data and the processing of the most energetic POD modes recovers the position of the LSBs, properly capturing the closure point of the separation bubbles and, hence, the turbulence transition location. Some of the most energetic POD modes observed are closely related, in terms of shape, to the POD modes present at the reattachment point on a 5:1 rectangular cylinder. This could indicate there is a recognizable pattern in coherent structures of pressure fluctuations when it comes to a reattached flow. Therefore, a principal component analysis such as the POD presented in this study can be used to determine the reattachment position of the flow or the transition point in the presence of a LSB.

Development of Three-Dimensional (3D) Biodegradable Polyglycolic Acid Fiber (PGA) Preforms for Scaffold Applications: Experimental Patterning and Fiber Volume Fraction-Porosity Modeling Study.

Three-dimensional (3D) biodegradable polyglycolic acid fiber (PGA) preforms were developed as temporary scaffolds for three-dimensional tissue regeneration applications. Three-dimensional biodegradable polyglycolic acid fiber (PGA) preforms including various degrees of interlaced structures called 3D plain, semi-interlaced, and orthogonal woven preforms were designed. Analytical relations and finite element model-based software (TexGen) on fiber volume fraction and porosity fraction were proposed to predict scaffolds' stiffness and strength properties considering micromechanics relations. It was revealed that yarn-to-yarn space, density, and angles of all 3D PGA fiber preforms were heterogeneous and demonstrated direction-dependent features (anisotropy). Total fiber volume fractions (Vfp) and porosity fraction (Vtpr) predicted by analytic and numerical modelling of all 3D scaffolds showed some deviations compared to the measured values. This was because yarn cross-sections in the scaffolds were changed from ideal circular yarn (fiber TOW) geometry to high-order ellipse (lenticular) due to inter-fiber pressure generated under a tensile-based macrostress environment during preform formation. Z-yarn modulus (Ez-yarn) and strength (σz-yarn) were probably critical values due to strong stiffness and strength in the through-the-thickness direction where hydrogel modulus and strengths were negligibly small. Morphology of the scaffold showed that PGA fiber sets in the preform were locally distorted, and they appeared as inconsistent and inhomogeneous continuous fiber forms. Additionally, various porosity shapes in the preform based on the virtual model featured complex shapes from nearly trapezoidal beams to partial or concave rectangular beams and ellipsoid rectangular cylinders. It was concluded that 3D polyglycolic acid fiber preforms could be a temporary supportive substrate for 3D tissue regeneration because cells in the scaffold's thickness can grow via through-the-thickness fiber (z-yarn), including various possible mechanobiology mechanisms.

Research on flow around two tandem rectangular cylinders

Uniform flow around two identical rectangular cylinders arranged in tandem has been investigated via the lattice Boltzmann method. With a fixed Reynolds number of 100, the effects of side ratio (γ = 1/2, 1/4, 1/8 and 1/16) and spacing ratio (S* = 0.25–12) on the fluid dynamics are investigated. Results indicate that both side ratio and spacing ratio have significant influences on the flow structure, vortex shedding frequency and hydrodynamic force. Several distinct vortex wake modes including the single bluff-body (SBB), shear-layer reattachment (SLR) and secondary vortex formation (SVF) modes are observed. The variations of Strouhal number, drag and lift coefficients versus spacing ratio are similar between all the current side ratios. In the branches of small and large spacing ratios, the fluid dynamics are obviously different and there is a critical spacing ratio, beyond which the relevant mechanical parameters jump suddenly as a result of the flow mode transition. A phenomenon of two-stage drag frequency separation between two cylinders occurs in the region of low side ratio and large spacing ratio, and its formation mechanism has also been analysed on the basis of flow characteristics and frequency spectra of force coefficients.

Semi-analytical study of linear waves interaction with a vertical permeable cylinder of arbitrary cross-section based on perturbation theory

ABSTRACT This paper studies linear waves incident to a vertical permeable cylinder with arbitrary cross-section based on the boundary element method and perturbation theory. Considering a near-zero thickness for the permeable media, and using Darcy's law, the governing equation for the wave incident to a porous circular cylinder is derived based on the boundary element method. Then using perturbation theory and considering a small parameter ε denoting the variation of cylinder radius from circular ones, the corresponding equations were expanded for non-circular cylinders. The developed method was applied to ellipse-shaped and rectangular cylinders. The wave forces and the wave strength inside the cylinder under a variety of parameters such as wavenumber, and porosity parameter were studied. One application of these research results is a better understanding of the behaviour of non-circular aquaculture cages in sea waves. According to the results, near-trapped modes can occur inside rectangular cages with small porosity parameters.

Comparison of the Flow around Circular and Rectangular Emergent Cylinders with Subcritical and Supercritical Conditions

There are multiple initiatives aimed at strengthening coastal communities against tsunami disaster risks, such as growing vegetation belts, construction of embankments, moats, and different hybrid alternatives. To find a solution for strengthening the coastal buildings themselves, we firstly reviewed the flow phenomena around a single emergent (circular and rectangular) cylinder (case C1), which was considered as a piloti-type column under different Froude conditions, and evaluated the formation of surface bow-waves, hydraulic jump detachment, and wall-jet-like bow-waves. Secondly, the flow characteristics were investigated under the same Froude conditions with side-by-side two-cylinder (case C2) and four-cylinder (case C4) arrays in an open channel. Surface bow-wave length (LBw) increased by 7–12% over the rectangular cylinders (RCs) compared to the circular cylinders (CCs) with a subcritical flow. For the supercritical flow with a 1/200 bed slope, hydraulic jump detachment was observed in relation to the Froude number. The observed length of the hydraulic jump detachment (Ljump) varied between 3.1–8.5% and 4.2–12.9% for the CCs and RCs in the supercritical flow with a 1/200 bed slope. In addition, the wall-jet-like bow-wave height (hjet) over the CCs was increased by 37% and 29% compared to the RCs with a supercritical flow and zero bed slope (orifice-type flow). For case C4, a hydraulic jump was observed for the supercritical flow over the horizontal channel bed. Finally, empirical equations were defined concerning the geometrical shape and arrangement based on the experiment data for the single and side-by-side configurations of the cylinders to validate the height of the wall-jet-like bow-wave as the most critical flow property.

Experimental investigations of wave interaction with semi-submerged horizontal rectangular cylinder of elastic bottom

Laboratory experiments were conducted to investigate the interaction of gravity waves with a semi-submerged rectangular cylinder of elastic bottom. Laboratory investigations were conducted for a wide range of wave parameters and a structure of different drafts. The analysis of results focuses on wave transmission at the structure, wave-induced pressures excreted on the plate, plate deflections, etc. The results shows that the nonlinear pressure and plate deflection components arising from the interaction of incoming waves with the structure are often significant. The results show that the nonlinear components often exceed their linear counterparts even for waves of low steepness. This is an original and surprising outcome of significant practical importance as the large nonlinear pressure and plate deflection components may spark a resonance. The problem is serious because plate natural vibration frequencies are often lower than the frequency of fundamental waves or their nonlinear components and the vibration of a plate may be amplified by incoming waves or their nonlinear products. The occurrence of a resonance amplified by incoming waves may lead to the failure of a structure. This outcome is of significant practical importance because it may occur for a wide range of wave parameters.

EKSPLORASI ETNOMATEMATIKA PADA BANGUNAN BERSEJARAH BILIK PADI DAN JIROK KERINCI

Culture and mathematics are very closely related, one of which is jirok and pondok padi. In the jirok and pondok padi there are many mathematical elements. Apart from having elements of mathematics, this also has something to do with history so that not only mathematics but history is also found in jirok and pondok padi. This study aims to explore relics that have been almost forgotten among young people and also introduce mathematical elements such as geometry which can be seen in the jirok and rice chamber buildings. The research method used in this study uses descriptive descriptive research. Sources of data in this study using data from interviews, observations, documentation and literature review. In interviews involving village heads for the 2013-2019 period and traditional leaders who took place in the village of Koto Bento, the number of research subjects was 2 people. The results of the study describe that in the jirok and pondok padi there are mathematical elements that have never been exported and are known by the public, including the concept of rectangular flat shapes, isosceles triangles, triangles, long squares, squares, and cylinders.

Experimental Study of Turbulent Wake Flow Around Trapezoidal Cylinders With Varying Streamwise Aspect Ratios

AbstractThe effects of streamwise aspect ratio (AR) on the asymmetric wake flow over and behind right-angled trapezoidal cylinders with AR (= upper cylinder length to height ratio) = 1, 2, 3, 4, and 5 were investigated using particle image velocimetry. The Reynolds number based on the freestream velocity and cylinder height was 14700. The flow characteristics are examined in terms of the mean velocity flow, Reynolds stresses, probability density function (PDF), and two-point correlations. The results show that the primary vortex in the AR1 and AR2 trapezoidal cases extends into the wake region but is confined to the surface of the longer cases and two asymmetrical wake vortexes are only observed in the longer cases. Dual peaks of elevated streamwise Reynolds stresses are observed in the wake region, regardless of the aspect ratios. The magnitudes of the Reynolds stresses and turbulent kinetic energy are higher in the shorter cases (AR1, AR2, and AR3 cases) compared to the longer cases. The PDF distributions show a bimodal asymmetrical shape in the shorter cases but a nearly Gaussian distribution in the AR5 case. Two-point autocorrelations of the streamwise and vertical velocity fluctuations revealed that the spatial coherency of the turbulent structures is highly sensitive to the streamwise aspect ratio and reference locations. Systematic comparison between the present asymmetric results and symmetric wakes generated by rectangular cylinders with similar aspect ratios and Reynolds number shows significant differences between the asymmetric and symmetric wakes, especially at smaller aspect ratios.

Effects of streamwise aspect ratio on the spatio-temporal characteristics of flow around rectangular cylinders

Turbulent flows over rectangular cylinders with streamwise aspect ratios (AR) of 1, 2 and 4 were experimentally studied using time-resolved particle image velocimetry at a Reynolds number based on free-stream velocity and cylinder height of 16200. These aspect ratios represent cylinders for which the mean separated shear layers from the leading edges are shed directly into the wake region (AR1), reattach over the cylinder (AR4), and an intermediate case (AR2). The effects of aspect ratio on the transport phenomena, turbulence production and its budget are investigated. The spatio-temporal characteristics and the interactions between the small-scale Kelvin-Helmholtz (KH) vortices and the energetic large-scale von-Kármán (VK) vortices are examined using frequency spectra, while the dynamics of the coherent structures are elucidated using proper orthogonal decomposition (POD). The mean flow topology reveals a massive recirculation bubble in the wake of the AR2 cylinder, compared to AR1 and AR4. While a single dominant vortex shedding frequency is observed for AR1 and AR4, a dual vortex shedding instability is manifested for the AR2 cylinder, which is intimately connected with the intermittent reattachment and detachment of flow over the AR2 cylinder. The interactions between the KH and VK vortices are shown to vary non-linearly with aspect ratio, as the flow transitions from the fully detached case (AR1) to fully reattached case (AR4). The differences in the vortex shedding process are revealed in the dynamics of the first POD mode pair. For AR1 and AR4, the fundamental shedding frequency is dominant and the first POD mode pair contain similar energy content, suggesting regular vortex shedding patterns. For AR2, dual shedding frequencies are observed with significant cycle-to-cycle variation, suggesting irregular vortex shedding patterns.

Flow-induced vibration modeling of bluff bodies with data assimilation

Vortex-induced vibration (VIV) and galloping are two typical flow-induced vibration (FIV) problems of bluff bodies, which often cause fatigue damage or destruction of structures. Therefore, the accurate and effective FIV prediction has become a requirement of the industry in order to prevent structural damage and guide design. Although the semi-empirical model (such as the wake oscillator model) is an efficient FIV prediction tool, the precision ability of existing models is constrained due to empirical parameters and unideal mathematical equations. Generally, the numerical simulation and wind tunnel experiments are relatively accurate methods, but for complex fluid–structure interaction problems, their cost is too high. As a result, a data-driven FIV prediction model is proposed to accomplish effective and high-precision prediction in this study. The Ensemble Kalman filter (ENKF) data assimilation (DA) technique is used to combine the experimental data with a semi-empirical model. First, the sensitivity of empirical parameters is analyzed, and the most sensitive ones are selected as the target parameters for data assimilation. The mean deviation of ensemble (MDE) is proposed to represent the sensitivity of parameters. Then DA-based model is used to predict the galloping and VIV of a rectangular cylinder. The results indicate that the accuracy of the DA-based model is up to 10 times greater than that of the initial semi-empirical model. With the data-driven technology, the typical ‘quasi-steady’ theory of galloping has been improved for low Scruton number values. For the wake oscillator model, assimilating the parameters of the acceleration and velocity coupled terms can improve the prediction accuracy of VIV. Also, this modeling procedure can be regarded as a new parameter identification method from forced and free vibration.

Numerical investigation of mixed convection from rectangular cylinders subjected to upper cross flow

Unsteady combined natural and forced convection heat transfer from a rectangular cylinder subjected to upward cross flow is investigated numerically. The working fluids are air (Pr = 0.7) and water (Pr = 7), and the flow is laminar. The governing flow and energy equations are solved using a fractional step finite-difference scheme. The effects of the cylinder aspect ratio (a = L/D), Reynolds and Richardson numbers on the flow and heat transfer characteristics are investigated. Numerical simulations were carried out for the cylinders with aspect ratios of a = 0.5, 1, and 2, while the Richardson and Reynolds numbers varied between 0 to 10, and 100 to 200, respectively. The mean drag, mean rms lift coefficients, as well as the Strouhal number and the mean Nusselt number were computed for each simulation to determine the quantitative effects on flow and heat transfer. Steady flow is observed for Pr = 0.7, Ri = 0.5, and a = 0.5 or for Re ≥ 150 and Ri ≥ 1. For Ri = 10 and Re = 200, the flow becomes unsteady in the downstream region and trigger vortex street formation for a = 0.5, 1, and 2. Decreasing the aspect ratio, as well as increasing Reynolds number, increases the heat transfer from the cylinder. The rms lift coefficient decreases sharply at Ri < 1 for Pr = 0.7, Ri < 2 for Pr = 7 due to vortex breakdown. Further increase in the Richardson leads to a slight increase in rms lift coefficient except for Re = 200 where the sharp increase is observed due to triggered vortex formation again. For air, the increase in the mean Nusselt number in Ri = 10 case with respect to the forced convection case (Ri = 0) was 54–65% and 80–98%, respectively, for a = 0.5 and 2, while these values for water were realized as 50–68% and 53–63%, respectively. Using the computed data and nonlinear regression, the mean Nusselt number and the drag coefficients were developed.

Three-dimensional aerodynamic lift on a rectangular cylinder in turbulent flow at an angle of attack

The aim of the present work is to derive the closed-form solution for the three-dimensional aerodynamic admittance (3D AAF) of the lift on a 5:1 rectangular cylinder in turbulent flow at an angle of attack (AoA), which can be used to study the unsteady effects of AoA. The separated one- and two-wavenumber aerodynamic admittances are introduced to assess the contributions of u and w components of turbulence to the lift force at an AoA. These admittances are divided into two parts: the two-dimensional aerodynamic admittance (2D AAF) for fully coherent gusts and the gust-related spanwise correction factors. The closed-form expressions for the one- and two-wavenumber spanwise correction factors of the 3D AAF are derived provided that the floating parameters in the coherence models of the lift force and turbulence are determined experimentally. Although the proposed 3D AAF model is a semi-analytical solution, it still provides explicit insight into the unsteady effects of u and w components of turbulence and the distortion of the free-stream turbulence. Based on theoretical and experimental investigations, it is shown that the unsteady effects of AoA on the coherence and spectra of the lift become more prominent with the increase of AoA, and reach their maximum as the AoA reaches 10°. This phenomenon can be attributed to the contribution of the u component, which plays a dominant role in determining the aerodynamic behaviour of the lift as the AoA approaches 10°. Notably, the spanwise correction factors of the 3D AAF will amplify the results based on the strip theory at low frequencies as the AoA is within 7°, and vice versa. In addition, it should be noted that the proposed approach allows us to quantitatively study the unsteady behaviour of the lift force on bluff bodies with complicated cross-sectional shapes, such as a streamlined bridge deck.