Natural Vortex Research Articles

Control of the von Kármán vortex street with focusing and vectoring of jet using synthetic jet array

In the present study, a novel flow control technique based on jet focusing and vectoring from a synthetic jet array (SJA) for controlling the wake of a bluff body is proposed and demonstrated. A numerical investigation into the flow past a square cylinder modified by the SJA has been carried out at a free stream Reynolds Number of 100. The SJA consists of four independently controlled synthetic jet actuators operating at a peak velocity of eight times the free stream and fifteen times the natural vortex shedding frequency of the square cylinder. The SJA is operated in two different regimes; a focusing regime involving phase delay (Δφ) with non-linear variation between the actuators and a vectoring regime with a linear phase delay without changing the geometric or operating parameters of the SJA. It has been found that jet focusing is able to reduce the coefficient of drag by as much as 43% for Δφ=90°. Focusing is also observed to reduce the fluctuations in the wake velocity with the maximum reduction in fluctuations also corresponding to Δφ=90°. Jet vectoring is able to deflect the von Kármán vortex street in a singular direction along with shifting of the front stagnation point with maximum deflection for Δφ=60°. Furthermore, vectoring leads to an asymmetry in the wake velocity field with the shifting of the velocity deficit region in the direction of the vectoring along with an asymmetry in the wake velocity fluctuations. This novel approach toward synthetic jet induced active flow control allows for greater manipulation of the flow field characteristics of bluff bodies than present methods with applications in areas of underwater and micro air vehicle maneuvering, automobile, and building aerodynamics among others.

Anisaldehyde-based deep eutectic solvent dispersive liquid–liquid microextraction (DES-DLLME) followed by UPLC–MS/MS for simultaneous determination of selected parabens and bisphenols in food products: Method development and assessment of the ecological implications

A rapid and environmentally friendly method based on dispersive liquid–liquid microextraction (DLLME) technique, coupled with UPLC–MS/MS analysis was employed for simultaneous determination of selected bisphenols and parabens residues in food products. In this research, anisaldehyde and decanoic acid with a molar ration of 3:1 was prepared as a natural deep eutectic extracting solvent. Various extraction parameters such as the volume of the natural deep eutectic solvent, vortex duration, centrifugation duration, sample volume and pH were systematically explored and optimized. Determination coefficients of ≥0.9990 were achieved for the analyzed compounds under the optimal conditions. The limits detection were in the range of 0.0005 to 0.02 µg/L, while extraction recoveries ranged from 97.8 % to 100.2 % with relative standard deviations (%RSD) not exceeding 6.8 %. To assess the practical applicability of the proposed method, it was employed for the determination of five parabens and three bisphenols in eighty food products including soft drinks, energy drinks, sauces and juices collected from the Saudi market. The environmental implications of the proposed method were assessed using the following evaluation tools, Eco-Scale Assessment (ESA), Green Analytical Procedure Index (GAPI) and Analytical GREEnness metric (AGREE). To the best of our knowledge, this is the first study to determine the investigated analytes using anisaldehyde based deep eutectic solvent.

Vortex synchronization-enabled heat-transfer enhancement in a channel with backward- and forward-facing steps

A channel with one backward-facing step and one forward-facing step is a typical configuration in engineering applications. In the channel, good heat transfer performance is often required, and the enhancement is usually achieved by employing different passive control methods, such as modification of geometric configuration or application of nanofluid. However, the other control method, i.e., active flow control (AFC), which is likely more effective, has been rarely applied in such a scenario. This study aims to bridge this gap by exploring how a rigid plate affects the heat transfer of the channel. The plate either is stationary or actively rotates, corresponding to passive flow control or AFC. The influences of the horizontal position of the plate (S) and its orientation angle (θ) on the heat transfer performance are studied when the plate is stationary to provide a baseline. Compared to the baseline, the effects of S, θ, and the rotation frequency (fr) are revealed when the plate undergoes a sinusoidal rotation. Such a thermo-fluid dynamic problem is numerically simulated by the immersed-boundary lattice Boltzmann method. The results show that the plate can improve the heat transfer performance no matter whether it rotates or not, compared to the case without a plate. The rotating plate outperforms the stationary one when θ and fr are properly chosen at each S. Substantial improvement can be achieved when vortex synchronization or resonance occurs in the channel, i.e., when the natural vortex shedding frequency is close or equal to fr.

Ground-induced suppression of chaos in the self-excited flow behind a plunging airfoil

We numerically investigate the forced synchronization of the self-excited flow behind a plunging airfoil in ground effect at a Reynolds number of Re = 1000. On varying the plunging amplitude and frequency, we find a rich array of nonlinear dynamics, such as a period-1 limit cycle due to natural vortex shedding as well as two-frequency quasiperiodicity on a torus attractor (T2). For certain non-resonant plunging frequencies without a ground surface, we find that low-dimensional chaos emerges via the Ruelle–Takens–Newhouse route. However, we find that the chaos can be suppressed by introducing a ground surface, inducing a direct transition from T2 quasiperiodicity to 1:1 phase locking as the plunging amplitude rises over the boundaries of the Arnold tongue. Apart from suppressing chaos, the ground surface also causes the lift and drag coefficients to become less sensitive to the plunging motion itself. Knowledge of the critical plunging conditions required for forced synchronization and chaos could be useful in various engineering applications, such as the design of pico air vehicles.

Extraction of 5 benzotriazole ultraviolet filters from soil samples using natural deep eutectic solvent vortex assisted liquid–liquid microextraction combined with GC–MS

Benzotriazole (BTRs) ultraviolet filters are a class of substances found in the environment that pose potential hazards to human health and environment. Therefore, it is essential to develop techniques for determining BTRs in the environment. In this paper, a simple, green, and effective vortex assisted liquid–liquid microextraction (VALLME) was developed to determine trace BTRs in the environment, combining natural deep eutectic solvents (NADES) with Gas chromatography-mass spectrometer (GC–MS). Result parameters were optimized by single factor analysis, Factorial Multilevel Categoric Design and Central Composite Design, and optimal extraction solve (NADES) was obtained by mixing choline chloride (ChCl) and lactic acid (LA) with the ratio 1:1. After optimization, the linearity (r2 ≥ 0.9929), LODs (0.010–0.083 μg/ml), LOQs (0.033–0.276 μg/ml), and RSD (2.96–4.21 %) were verified. For the first time, a method based on the new type of NADES for the determination of BTRs ultraviolet filters in soil was propose, which could replace traditional extractants for BTRs and serve as a sustainable and environmentally friendly extraction medium for other matrices.

소용돌이 속에서 만난 엘리엇과 포우

This paper delves into the works of two influential literary figures, Edgar Allan Poe and T. S. Eliot, to explore their notion of vortex. While Poe’s “A Descent into the Maelström” presents a harrowing tale of a man’s encounter with a natural vortex, Eliot’s The Waste Land explores the destructive power of natural elements and their symbolic implications. Through a comparative analysis of these works, this paper aims to uncover the thematic and symbolic connections between Poe and Eliot’s vortex, shedding light on the psychological and existential aspects of human experience. While these works belong to different literary traditions and styles, they share certain thematic resonances in their treatment of the vortex as a metaphor for the turbulent forces that shape human existence.

Significant influence of fluid viscoelasticity on flow dynamics past an oscillating cylinder

This study focuses on numerically investigating the impact of fluid viscoelasticity on the flow dynamics around a transversely forced oscillating cylinder operating in the laminar vortex shedding regime at a fixed Reynolds number of $Re = 100$ . Specifically, we explore how fluid viscoelasticity affects the boundary between the lock-in and no lock-in regions and the corresponding wake characteristics compared with a simple Newtonian fluid. Our findings reveal that fluid viscoelasticity enables the synchronization of the vortex street with the cylinder motion at lower oscillation frequencies than those required for a Newtonian fluid. Consequently, the lock-in region boundary for a viscoelastic fluid differs from that of a Newtonian fluid and expands in the non-dimensional cylinder oscillation amplitude and frequency parameter space. In the primary synchronization region, the wake of a Newtonian fluid exhibits ‘2S’ (two single vortices) and ‘P+S’ (a pair of vortices and a single vortex) shedding modes. In contrast, a ‘2P’ (two pairs of vortices) vortex mode is observed for a viscoelastic fluid within the same region. To gain a deeper understanding of the differences in the coherent flow structures and their associated frequencies between the two fluids, we employ the data-driven reduced-order modelling technique, known as the dynamic mode decomposition (DMD) technique. Utilizing this technique, we successfully extract and visualize the two competing fundamental frequencies (cylinder oscillation and natural vortex shedding frequencies) and their associated flow structures in the case of the no lock-in state, whereas only the dominant cylinder oscillation frequency and associated flow structure in the case of the lock-in state. Furthermore, we propose that the presence of excess strain resulting from the stretching of polymer molecules in viscoelastic fluids leads to a distinct difference in the wake structure compared with Newtonian fluids. This observation aligns with the findings obtained from the $Q$ -criterion and vorticity transport analysis of the wake.

Self-excited vortex-acoustic lock-in in a bluff body combustor

We investigate self-excited vortex-acoustic lock-in in a bluff body combustor. The bluff body not only anchors the flame but also sheds vortices. Mutual interaction between vortex shedding and the combustor acoustic field leads to lock-in. A lower-order model for vortex shedding is coupled to the acoustic equations to obtain a set of discrete dynamical maps, which are then solved numerically. Lock-in is identified when a definite phase relationship between vortex shedding and acoustic field remains unaltered with time. The common frequency during (phase) lock-in is either close to the natural acoustic or vortex shedding frequencies, accordingly termed A- or V-lock-in, respectively. Instability and amplitude suppression occur with most parts of the A- and V-lock-in regions, respectively. Furthermore, we relate the lock-in and pre-lock-in regimes observed in our previous experiments (Singh & Mariappan, Combust. Sci. Technol., 2019, pp. 1–29) to A- and V-lock-in phenomena, respectively. Among the two lock-in phenomena, combustion instability is favoured by $1:1$ A-lock-in, whose boundaries in the parameter space can be obtained from a forced response of the vortex shedding process. Finally, we discuss the bifurcations leading to lock-in.

Forced-motion simulations of vortex-induced vibrations of wind turbine blades – a study of sensitivities

Abstract. Vortex-induced vibrations on wind turbine blades are a complex phenomenon not predictable by standard engineering models. For this reason, higher-fidelity computational fluid dynamics (CFD) methods are needed. However, the term CFD covers a broad range of fidelities, and this study investigates which choices have to be made when wanting to capture the vortex-induced vibration (VIV) phenomenon to a satisfying degree. The method studied is the so-called forced-motion (FM) approach, where the structural motion is imposed on the CFD blade surface through mode shape assumptions rather than fully coupled two-way fluid–structure interaction. In the study, two independent CFD solvers, EllipSys3D and Ansys CFX, are used and five different turbulence models of varying fidelities are tested. Varying flow scenarios are studied with low to high inclination angles, which determine the component of the flow in the spanwise direction. In all scenarios, the cross-sectional component of the flow is close to perpendicular to the chord of the blade. It is found that the low-inclination-angle and high-inclination-angle scenarios, despite having a difference equivalent to up to only a 30∘ azimuth, have quite different requirements of both grid resolution and turbulence models. For high inclination angles, where the flow has a large spanwise component from the tip towards the root, satisfying results are found from quite affordable grid sizes, and even with unsteady Reynolds-averaged Navier–Stokes (URANS) k–ω turbulence, the result is quite consistent with models resolving more of the turbulent scales. For low inclination, which has a high degree of natural vortex shedding, the picture is the opposite. Here, even for scale-resolving turbulence models, a much finer grid resolution is needed. This allows us to capture the many incoherent vortices, which have a large impact on the coherent vortices, which in turn inject power into the blade or extract power. It is found that a good consistency is seen using different variations of the higher-fidelity hybrid RANS–large eddy simulation (LES) turbulence models, like improved delayed detached eddy simulation (IDDES), stress-blended eddy simulation (SBES) and k–ω scale-adaptive simulation (SAS) models, which agree well for various flow conditions and imposed amplitudes. This study shows that extensive care and consideration are needed when modeling 3D VIVs using CFD, as the flow phenomena, and thereby solver requirements, rapidly change for different scenarios.

Modification of the wake of a wall-mounted bathymetry obstacle submitted to waves opposing a tidal current

In this paper, the effects of regular waves propagating against the current on the wake of a wide bathymetric obstacle are experimentally investigated. For that purpose, a square cylinder of height representing 1/8th of the water column, mounted perpendicular to the flow, is used. Both Reynolds and Froude numbers are close to the ones encountered at sea and swell properties (amplitude, frequency and wavelength) which are typical conditions in the English Channel. To study this complex hydrodynamic interaction, PIV measurements are used to capture the velocity field around and in the wake of the cylinder. The wake of this wide cylinder has been extensively studied and is characterised by its direction towards the water surface and by energetic and wide vortices arising from the sheared layer at a Strouhal number of approximatively 0.06, after a merging of smaller eddies. In this work, the focus is on how surface gravity waves, propagating against the current, modify the generation of these turbulent structures. The results show that the cylinder wake is strongly modified in the presence of waves, even if, on average, the main wake structure is globally conserved. The waves act both on the vortex generation and the wake development with modifications in terms of turbulent energy distribution and level, wake recovery and ascent rate. The vortex shedding becomes highly energetic and well-organised from the cylinder position. Its return period is extremely regular and corresponds to half of the wave frequency which is really close to the natural vortex shedding frequency. That results in a doubling of the statistical length scale of the vortices.

A review on complex turbulent dynamic phenomenon of natural vortex length in cyclone separator

Abstract The natural vortex length is a complex turbulent dynamic phenomenon of cyclone separator, which can provide reference for the height design. It is calculated by the axial distance between the vortex end and the bottom of vortex finder. At present, scholars mainly attribute the influencing factors of natural vortex length to cylinder diameter, inlet area and vortex finder diameter, ignoring the influence of other structural parameters and operating parameters, so the accuracy and applicability of empirical formula are poor. This study described the mechanism of the vortex end and analyzed the PVC phenomenon. Then, an example was provided to illustrate the limitations and shortcomings of empirical formula. In addition, the influences of some geometric parameters and operating parameters on natural vortex length were summarized. Therefore, this work could provide an important reference for design optimization of cyclone separator height.

Coexistence of natural and forced vortex dislocations in step cylinder flow

The wake behind a step cylinder [consisting of a small diameter cylinder (d) and a large diameter cylinder (D)] with diameter ratio D/d=2 at Reynolds number ReD = 200 (the mode A* regime) is simulated by direct numerical simulations. New detailed information of the interaction between natural vortex dislocations and forced vortex dislocations is described. In the large cylinder wake, the forced and natural vortex dislocations coexist. The regular formation of forced vortex dislocation is found to be delayed under the effect of natural vortex dislocations. The occurrence of natural vortex dislocations is suppressed in the large cylinder wake close to the small cylinder. Moreover, the effect of vortex dislocations on structural loads is described. The results of this paper provide a more thorough understanding of the formation and interaction between the natural and forced vortex dislocations.

Wind energy generation by forced vortex shedding

Oscillating wind energy conversion systems that rely on vortex-induced vibrations (VIV) suffer from low energetic efficiency, but active flow control can produce significant improvements. This research investigates wind energy generation resulting from alternating slot blowing (ASB) on a circular cylinder, experimentally and theoretically. On the basis of measured peak lift coefficients, a low momentum coefficient (<0.04) excitation regime and a high momentum coefficient (>0.04) forcing regime were identified. In the excitation regime, a clear amplitude peak was observed close to the nominal natural vortex shedding frequency. In the forcing regime, separation or circulation control time-scales resulted in mild peaks at approximately half of the natural shedding frequency. In all regimes, the natural vortex shedding amplitudes were exceeded; in particular, by up to a factor of three in the forcing regime. Using a mathematical simulation model, it was shown that an ASB system produces 3.8 times higher net peak power coeffcients − comparable to small wind turbines − with a 7.3 times greater bandwidth than a conventional VIV energy harvester. Economic benefits can potentially be realized by significantly upscaling the system and adding a second degree-of-freedom. Future research will focus on improved slot design, supercritical flow excitation and forcing, and non-linear mathematical modelling of the dynamical system.

Investigations on the effects of structural damping on vortex-induced vibration response of an airfoil at a high angle of attack via the aero-damping map

Large-scale modern wind turbines at standstill are prone to vortex-induced vibrations. In this study, we propose the use of the aero-damping map to investigate the complex vibration responses of the wind turbine airfoil at 90° of attack angle with different levels of structural dampings. The vibration amplitude and response frequency in the lock-in condition and soft lock-in conditions agree well with the contour line on which the sum of aerodynamic damping and structural damping is equal to zero. The mechanism of frequency soft lock-in is explored from the aspect of energy transfer that when the equilibrium state cannot be maintained at the natural frequency due to high structural damping, the system locks to a frequency between the natural frequency and vortex shedding frequency of the stationary airfoil to achieve lower aerodynamic damping and more energy absorption from the air. The transient response of the beat vibration is also investigated with the aero-damping map combined with the dynamic mode decomposition method. It is found that the lock-in mode and von Kármán mode coexist in the unsteady flow field during beat vibration. The competition between the two modes causes the system to be in an intermittent state of alternating frequency lock-in stage with lower aerodynamic damping and unlock-in stage with higher aerodynamic damping, hence resulting in the amplitude amplification and attenuation alternately.

Interaction between coherent and turbulent oscillations in non-reacting and reacting wake flows

The presence of large-scale coherent structures can significantly impact the dynamics of a turbulent flow field and the behaviour of a flame stabilized in that flow. The goal of this study is to analyse how increasing free-stream turbulence can change the response of the flow to longitudinal acoustic excitation of varying amplitudes. We study the flow in the wake of a cylindrical bluff body at both non-reacting and reacting conditions, as the presence of a flame can significantly alter the global stability of the flow. The frequency of longitudinal acoustic excitation is set to match the natural frequency of anti-symmetric vortex shedding for this configuration and we vary the free-stream turbulence using perforated plates upstream of the bluff body. The results show that varying the level of free-stream turbulence can influence not only the amplitude of the coherent flow response, but also the symmetry of vortex shedding in the presence of longitudinal acoustic excitation. Increasing the turbulence intensity can fundamentally change the structure of the time-averaged flow and can directly impact the coherent flow response in two ways. First, increasing turbulence intensity can enhance the amplitude of the natural anti-symmetric vortex shedding mode in the wake. Second, increasing turbulence intensity weakens the symmetric response of the flow to the longitudinal acoustic excitation. In the non-reacting and reacting conditions, both symmetric and anti-symmetric modes are present and are characterized using a spectral proper orthogonal decomposition. We see evidence of interaction between the symmetric and anti-symmetric modes, which leads to an interference pattern in the coherent vorticity response in the shear layers. We conclude by presenting a conceptual model for the influence that turbulence has on these flows.

Nonlinear dynamical features of vortex-acoustic lock-on in a backward-facing step combustor

Unstable shear layers characteristic of step combustors display strong vortex shedding and play a dominant role in combustion instability. Past non-premixed flame experiments with Reynolds number (Re) as the bifurcation parameter showed that during instability, the frequency of acoustic oscillations locks-on to the natural vortex shedding mode for a range of Re. In the present work, we study the dynamical features of this type of lock-on. We employ a vortex model to bring out the nonlinearity in the flame response to vortical perturbations. This is coupled with a Galerkin model for the acoustic field. Regimes of aperiodic oscillations, low-amplitude lock-on and high-amplitude lock-on are predicted in agreement with experimental trends. Phase portraits show a transition to instability during lock-on via a supercritical Hopf bifurcation with an increase in limit cycle amplitudes. Synchronisation between the acoustic pressure and vortex-driven heat release perturbation is studied using recurrence analysis. The system transitions from asynchronous to phase synchronisation in the low-amplitude lock-on regime, characterised by an increasing degree of phase correlation. In the high-amplitude lock-on regime, a state of generalised synchronisation exists, where in addition to the phase, the amplitudes also show strong correlation.

Improving advantages and reducing risks in increasing cyclone height via an apex cone to grasp vortex end

• Introduction of a cone leads to maintain the cyclone efficiency with an excessive height. • It is found that the vortex turning is forced to occur at the location of apex cone. • The added apex cone can stretch the vortex length to protect the efficiency. • The stagnant upward airflow in the centre is helpful to protect the efficiency. • The cone enhances the tangential velocity of inner vortex rather than outer vortex. For a cyclone, it is possible to improve separation efficiency and reduce pressure drop by increasing the cyclone height. However, an exceeded height increase could result in a dramatical drop in separation efficiency. In this study, experimental and computational fluid dynamics simulation results exhibit that the introduction of an apex cone at the dust outlet could avoid the risk of separation efficiency drop but lead to a continuous reducing of the pressure drop. Generally, the optimal cyclone height should be closely related to the natural vortex length. While, when the vortex end contracts into the separation space in the cyclone with an exceeded height, severe back-mixing of particles always occurs, which will result in the decrease of separation efficiency. Herein, it is found that when an apex cone is installed at the dust outlet, the vortex end can be grasped by the cone so as to weaken the back-mixing of particles. Meanwhile, the introduction of this apex cone can enhance the secondary separation to capture the back-mixed particles again so as to protect the efficiency. In addition, it is found that the enhanced secondary separation could come from either the stagnant current of axial velocity in the center or the improved tangential velocity of inner vortex whereas the forcibly extending the length of vortex to exceed its natural length will not significantly increase efficiency.

Ventricular Flow Dynamics With an Intra-Ventricular Balloon Pump: An In Vitro Analysis.

Due to the high treatment costs associated with durable ventricular assist devices, an intra-ventricular balloon pump (IVBP) was developed to provide low-cost, short-term support for patients suffering from severe heart failure. It is imperative that intraventricular flow dynamics are evaluated with an IVBP to ensure stagnation points, and potential regions for thrombus formation, are avoided. This study used particle image velocimetry to evaluate flow patterns within the left ventricle of a simulated severe heart failure patient with IVBP support to assess left ventricle pulsatility as an indicator of the likelihood of flow stasis. Two inflation timings were evaluated against the baseline severe heart failure condition: IVBP co-pulsation and IVBP counter-pulsation with respect to ventricular systole. IVBP co-pulsation was found to have a reduced velocity range compared to the severe heart failure condition (0.44 m/s compared to 0.54 m/s). IVBP co-pulsation demonstrated an increase in peak velocities (0.25 m/s directed toward the aortic valve during systole, as opposed to 0.2 m/s in severe heart failure), indicating constructive energy in systole and cardiac output (1.7 L/min increase with respect to severe heart failure baseline - 3.5 L/min) throughout the cardiac cycle. IVBP counter-pulsation, while exhibiting the greatest peak systolic velocity directed to the aortic valve (0.4 m/s) was found to counterasct the natural vortex flow pattern during ventricular filling, as well as inducing a secondary ventricular pulse during diastole and a 23% increase in left ventricle end-diastolic volume (indicative of dilation). Ideal IVBP actuation timing did not result in reduced intraventricular pulsatility, indicating promising blood washout.

On the wake response of a square cylinder subjected to an inline nonharmonic forcing

In this work, we study the effect of two spectrally simple nonharmonic inline forcing waveforms on the wake response of a square cylinder. The characteristics of wake response under nonharmonic forcing were studied and compared to wake response under harmonic forcing for a constant Reynolds number 100. By varying the relative strength of the spectral components and the secondary frequency of the nonharmonic forcing of the inflow, an asymmetric modulated wake and an asymmetric 2P + 2S wake were observed for a two-tone nonharmonic forcing. These modes combine the features of the wake response of individual spectral components. In some regions of the parameter space, the wake response did not correlate well with the spectral components of harmonic forcing. An amplitude-modulated forcing was also studied. For amplitude-modulated forcing, the additional frequency component did not affect the wake structure. This observation indicates that the wake may act as a low pass filter for inline flow frequency components above the natural vortex shedding frequency.

Influence of Roughness on the Asymmetric Flow Field of a Slender Body

Low speed and high angle of attack are problems that must be faced in vertical launching missiles. A natural asymmetric vortex phenomenon occurs at a low speed and high angle of attack of a slender body. In this paper, the Detached Eddy Simulation (DES) method is adopted to simulate the asymmetric flow of a slender body at a high angle of attack. The influence of roughness is analysed from the flow field and pressure distribution. And the DES method is verified by comparing it with the wind tunnel test results. The flow fields of the four models with the surface roughness of 0, 0.8, 5, and 100 are compared. The downstream flow still appears asymmetric when the surface is smooth, indicating that the stability of the flow field is not enough to maintain the symmetry of the flow field. The simulation results show that the adverse pressure gradient increases in the region where the boundary layer separates with the roughness greatly increasing, but the structure of the flow field at the head is slightly different. On the whole, the surface pressure and lateral force per unit length ( C f z p m ) transform alternately along the axial direction, and the period of alternating reverses increases with the increase of roughness. Finally, the pressure tends to be in equilibrium, and C f z p m approaches zero. It should be noted that the distribution of C f z p m is slightly different on the head, indicating that the asymmetry of pressure on the cylinder section is an important factor controlling the magnitude and the direction of lateral force. The influence of roughness on the flow around a slender body is acquired in this paper, and it has reference significance to the roughness problem of the actual missile.