Unsteady Motion Research Articles

Study on the mechanism of the buzz flow in a supersonic intake

The flow field in a supersonic intake has been investigated computationally to understand the unsteady shock motions at an incoming Mach number of 1.95. The exit area variation is achieved by moving the flap downstream of the inlet model. Inviscid, unsteady simulations of the shock movement are compared with simulations of the viscous flow. The purpose is to understand the possibility of an inviscid mechanism as the underlying process of shock swallowing. It is observed for inviscid simulations that during the shock movement process, the system breaks the steady flow and a transient flow is initiated followed by a new steady state condition. On the contrary, this is not observed in viscous flow simulations which suggest the possibility of an unsteady mechanism that can propagate upstream of supersonic flow to make changes in the flow field. The analysis suggests that shock swallowing is related to the inviscid phenomenon and it may be associated with an unsteady chocking wave.

Preliminary Study on Mixing Mechanism of Three-Dimensional Vortices in the Wake of Lobe-Type Rear Variable Area Bypass Injector

In this work, an innovative lobe-type rear variable area bypass injector is proposed, which can take into account both mixing exhaust performance to increase thrust at a high Bypass Ratio (BR), and bypass throttling at low BR. In order to explore the aerodynamic characteristics of the variable injector, the unsteady motion characteristics and the congenerous thermal transport effect of three-dimensional wake vortices within the BR range of 0.18 to 0.68 are numerically analyzed. The results demonstrate that the injector can adjust the sidewall of the collapsible lobe based on the injection of bypass flow, and significantly strengthen streamwise vortices induced by lobe peak (SV-LP), which can effectively drive the migration of the heterogeneous fluid element, so as to compensate for the inefficient mixing ability of Kelvin-Helmholtz (K-H) vortices. When the BR is raised to 0.36, the increasing SV-LP will gradually replace the low-disturbance K-H vortices in the dominant position of the quasi-ordered flow field by virtue of a strong entrainment effect. Therefore, the injector can maintain a relatively high thrust augmentation in a wide working envelope.

Investigation of the secondary flow by convergent–divergent riblets in a supersonic turbulent boundary layer over a compression ramp

In this paper, the effect of the secondary flow induced by convergent–divergent riblets in supersonic turbulent boundary layers over a 24° compression ramp at Mach number 2.9 is studied via direct numerical simulation. Two riblet cases with the wavelength Λ being 1.1δ and 1.65δ (δ is the boundary layer thickness) are conducted to examine their impact on the secondary rolling motion, momentum transfer, turbulent fluctuations, flow separation, and unsteady shock motion. As the flow develops over the riblet section, both the size and intensity of the secondary rolling motion tend to increase. For the riblet case with Λ/δ=1.1, a single rolling mode is observed within a half wavelength, while a pair of co-rotating vortical structures is obtained for Λ/δ=1.65. Both rolling patterns lead to an apparent spanwise variation of the flow field. The results reveal that the secondary flow contributes to the increase of both the mean momentum flux and turbulent fluctuations. By using the spanwise averaging, the mean momentum flux contributed from the dispersive stress and compressible effect caused by the secondary flow is identified. Both components appear to enhance the near-wall momentum mixing, and a larger enhancement is observed for Λ/δ=1.1, where the intensity of the secondary flow is stronger. Compared to the baseline case, the area of the separation zone at Λ/δ=1.1 and Λ/δ=1.65 is decreased by 56% and 38%, respectively. For all the cases, the low-frequency motion near the foot of the shock is observed. In comparison, the frequency of the low-frequency motion for the riblet case is two times higher than that in the baseline case, owing to the reduction of the separation area and length.

Exact solutions of time-dependent oscillations in multipolar spherical vortices

Exact solutions of the time-dependent three-dimensional nonlinear vorticity equation for Euler flows with spherical geometry are provided. The velocity solution is the sum of a multipolar oscillatory function and a rigid cylindrical motion with swirl. The multipolar oscillation is a velocity mode whose radial and angular dependencies are given by the spherical Bessel functions and vector spherical harmonics, respectively. The local frequency of the velocity oscillations equals the angular speed of the rigid flow times the angular azimuthal wavenumber of the oscillating flow. The unsteady motion corresponds to inertial oscillations in multipolar flows with spatial azimuthal waves (non-vanishing azimuthal wavenumber) in the presence of a background flow with constant axial vorticity. In these nonlinear solutions, the curl of the Lamb vector has a linear dependence with the oscillation velocity, a property that makes it possible for the oscillating motion to satisfy different linear wave equations. Based on these inviscid time-dependent velocity modes, new exact solutions to the time-dependent Navier–Stokes equation are also provided.

Unsteady simulation of AUVs approaching seafloor by self-propulsion using multi-block hybrid dynamic grid method

Autonomous underwater vehicles (AUVs) have been widely applied in the vicinity of the seafloor for various purposes, including pipeline, cable, and structure inspection; bottom detection and following; and bottom-mounted docking systems. Squatting is a crucial problem that occurs when cruising in the vicinity of the seafloor, which affects the maneuverability and safety of an AUV. Therefore, it is necessary to have a high-accuracy prediction of the AUV hydrodynamic performance to obtain an automatic guidance controller for safety. In this study, the hydrodynamic performance was investigated by a physics-based unsteady simulation of a self-propelled AUV approaching seafloor using multi-block hybrid dynamic grid method, combined with six degrees of freedom (6DOF), user-defined functions (UDFs), and Arbitrary Lagrangian–Eulerian (ALE) approach. This simulation was used to explore the principle of the complex unsteady motions experienced by an AUV operating at the vertical plane in the vicinity of the seafloor. The results indicated that, for an AUV speed higher than the critical speed (0.5 m/s at H/D= 1.832, where Re=5.49 × 105), the AUV experienced a speed loss and increased resistance, thrust, and suck force. The speed loss was due to the larger increment in resistance than that in thrust. The magnitude and direction of the trim moment were highly sensitive to variations in AUV speed, resulting from the two low-pressure regions. One region was at the AUV bow neck induced by the bow vortex and the other was at the AUV stern neck induced by the rotating propeller. The unsteady interaction between the AUV and seafloor during AUV self-propulsion was elucidated by flow analysis.

Time-resolved PIV measurements inside and downstream of a 180° bend

The flow in a 180° bend with a radius of curvature 1.5 time the pipe diameter (Rc/D of 1.5) was studied for a Reynolds number of 34,800 to characterize the development of the mean velocity and Reynolds stresses and the unsteady motions that may affect the heat or mass transfer in the latter part of the bend. Two-component, time-resolved measurements were performed on the axial symmetry plane and on cross sectional planes in the bend and up to 1D downstream of the bend using refractive index matched Particle Image Velocimetry. The unsteady flow structures were examined using the Snapshot Proper Orthogonal Decomposition (POD) technique. Frequency spectra of the POD coefficients, transients of the coefficients and low-order reconstructions were used to characterize the time scales and dynamics of the motions. The results showed that the initial development of the flow was similar to that in a 90° bend but the development of the mean secondary flow, and the low-speed region associated with this feature, appeared delayed relative to the 90° bend in the middle section of the 180° bend. The results in the second half of the 180° bend showed that the mean longitudinal velocity near the inner wall was larger than that near the outer wall in the latter part of the bend. Changes in the unsteady interaction of the flow with the outer wall in the middle of the 180° bend also appeared to cause significant unsteadiness in the flow near the inner wall in the latter part of the bend. The mean secondary flow towards the end of the 180° bend was significantly diminished relative to the flow in the middle of the bend and largely suppressed by 1D downstream of the bend. Reconstructions of the instantaneous secondary flow showed occurrences of large secondary velocities along the sidewalls up to 170°, but these were substantively reduced even at 0.25D into the downstream bend.

Added mass and damping of structures with periodic angular shape

Symmetry relations are derived for the added mass and damping of structures where the shape is unchanged by rotation about the vertical axis through an angle $\theta = 2 {\rm \pi}/N$ with the integer $N\ge 3$ . For this type of structure, the added mass and damping for horizontal translation are the same for all directions, as in the case of axisymmetric structures. The same symmetry applies to rotations about horizontal axes. The principal application is to offshore structures and other bodies floating on the free surface or submerged, but the same symmetry relations apply more generally to unsteady body motions in an ideal fluid.

Low-Order Modeling of Dynamic Stall on Airfoils in Incompressible Flow

Airfoil dynamic stall in incompressible flow is characterized by two interacting viscous flow phenomena: time-varying trailing-edge separation and the shedding of intermittent leading-edge-vortex structures. In the current work, a physics based low-order method capable of modeling the interactions between the two flow phenomena is developed with the aim of predicting dynamic stall with only a few empirical tuning parameters. Large computational datasets are used to understand the flow physics of unsteady airfoils so as to augment an inviscid, unsteady airfoil theory to model the time-dependent viscous effects. The resulting model requires only three empirical coefficients for a given airfoil and Reynolds number, which could be obtained from a single moderate-pitch-rate unsteady motion for that airfoil/Reynolds number combination. Results from the low-order model are shown to compare excellently with computational and experimental solutions, in terms of both aerodynamic loads and flow-pattern predictions. In addition to formulating a method with limited empirical dependencies, the current research provides valuable insights into the flow physics of unsteady airfoils and their connection to rapidly predictable theoretical parameters.

Unsteady motions in the turbulent separation bubble of a two-dimensional wing

The unsteadiness of a turbulent separation bubble (TSB) formed close to the trailing edge of a two-dimensional wing was investigated using time-resolved particle image velocimetry. The angle of attack was set to 9.7° and the chord-based Reynolds number was 720 000. The TSB consisted of two shear layers and formed a triangular shape in the streamwise–wall-normal plane. The vertices of this triangle consisted of an intermittent detachment point, a fixed corner close to the airfoil trailing edge and an intermittent endpoint in the wake region. The velocity field had three energetic regions each with different Strouhal numbers (Stl): (a) an upstream turbulent boundary layer (TBL) with Stl = 0.1 to 4, (b) a TSB with Stl = 0.03 to 0.08 and (c) two shear layers with Stl = 0.4 to 0.8. The low-frequency motions in the TSB consisted of large zones of positive and negative streamwise velocity fluctuation that were several times wider than the large-scale structures of the upstream TBL. These zones forced an undulation of the separation line and were attributed to Görtler structures. They were also correlated with the velocity fluctuations between the two shear layers. The breathing motion of the TSB occurred at Stl = 0.05. This breathing correlated with the location of the TSB endpoint and the flapping of the upper shear layer. The detachment point of the TSB featured broad fluctuations and did not demonstrate a strong correlation with the breathing motion.

Characterizing interface topology in multiphase flows using skeletons

The unsteady motion of a gas–liquid interface, such as during splashing or atomization, often results in complex liquid structures embedded in the ambient fluid. Here, we explore the use of skeletonization to identify the minimum amount of information needed to describe their geometry. We skeletonize a periodic liquid jet by a modification of a recently introduced approach to coarsen multiphase flows while retaining a sharp interface. The process consists of diffusing an index function and at the same time moving the interfaces with it, until they “collapse” into each other and form skeletons. The skeleton represents the basic topology of the jet and we also keep track of how much the interface is moved (or how much volume is “accumulated”) during the process, which can be used to approximately reconstruct the jet. We explore various quantitative measures to characterize and distinguish the skeletons. These include standard morphometrics such as branch length distribution, after segmenting the skeletons into branches, and a more sophisticated representation of the skeleton structures called topology morphology descriptor, to obtain an “equivalent” description of the skeletons by retaining information about the topology in a compact way.

Effects of Surface Roughness on Shock-Wave/Turbulent Boundary-Layer Interaction at Mach 4 over a Hollow Cylinder Flare Model

Although it is understood that surface roughness can impact boundary layer physics in high-speed flows, there has been little research aimed at understanding the potential impact of surface roughness on high-speed shock-wave/boundary-layer interactions. Here, a hollow cylinder flare model was used to study the potential impact of distributed surface roughness on shock-wave/boundary-layer interaction unsteadiness. Two surface conditions were tested—a smooth steel finish with an average roughness of 0.85 μm and a rough surface (3K carbon fiber) with an average roughness value of 9.22 μm. The separation shock foot from the shock-wave/boundary-layer interaction on the hollow cylinder flare was tracked by analyzing schlieren images with a shock tracking algorithm. The rough surface increased boundary layer thickness by approximately a factor of 10 compared to the smooth case, significantly altering the interaction scaling. Despite normalizing results, based on this boundary layer scaling, the rough surface case still exhibited mean shock foot positions further upstream more than the smooth surface case. Power spectra of the unsteady shock foot location data demonstrated that the rough surface case exhibited unsteady motion with attenuated energy relative to the smooth-wall case.

Solving the Moment Amplification Factor of a Lateral Jet by the Unsteady Motion Experimental Method

In this paper, unsteady motion tests of a lateral jet adjusting an air vehicle’s attitude are carried out. Curves of pitch moment amplification factors (KM) for a lateral jet versus angle of attack (α) are obtained using a wind tunnel free-flight test technique with a jet and data processing method. This new method overcomes the disadvantage of previous experiments that can study only one unsteady characteristic. The free-flight test technique in the proposed method ensures that the test model can be coupled in real-time with multiple parameters (unsteady flow caused by the jet, unsteady air vehicle aerodynamic force, and unsteady air vehicle motion). This approach simulates an actual air vehicle’s complete jet test process and ensures more authentic and reliable test results. In the new data processing method, continuous data curves are fitted to discrete data points, making it easier to convert the angular displacement versus time curve into the pitch moment versus α curve to obtain KM. The results show that when the pressure of the micro high-pressure gas cylinder is 2.0 MPa, KM is below 1, indicating that the lateral jet does not significantly promote the pitching moment. When the gas cylinder pressure is 4.0 MPa and the angle of attack is 5° < |α| < 16°, KM is greater than 1, and the lateral jet promotes the pitching moment. When 16° < |α| < 20°, KM is less than 1, and the lateral jet does not significantly contribute to the pitching moment. It was further found that KM decreases slowly with increasing α. When |α| > 30°, the influence of the jet on the pitching moment nearly disappears.

Response of a turbulent separation bubble to zero-net-mass-flux jet perturbations

Separating turbulent boundary layers exhibit unsteady motions at various frequencies. Using numerical and analytical techniques we identified the distinct strong responses of the flow to actuations at its natural unsteady frequencies. The low-frequency motion of the separating shear layer can be modulated by small streamwise perturbations thus leading to a smaller mean separation region. The key control mechanisms are the strong structural changes dominated by two-dimensional roller vortices. The stress/load unsteadiness on the wall is a possibly harmful outcome of flow control.

Computational study of compressible flow through choke valve

Failure of choke valves due to vortex shedding and flow-induced vibration (FIV) is common problem in industry. Mechanisms of head-on collision of fluid jets within a choke valve is investigated computationally in this manuscript. The benchmarked simulations are conducted at fixed flow rate and two different choke positions. The vorticity contours overlaid by velocity field are presented across various planes within the valve, shedding light on dynamics of the flow. The formation of a time-averaged four-lobed vortical structure is evident within the valve chamber. There is strong vortex shedding taking place along the tails of head-on colliding jets exhibiting unsteady flipping motion. Mach contours reveal choked flow condition upon constricted region of the valve ports. Pressure contours, accompanied by density graphs, uncover stagnation zone forming within the valve. Temperature profiles, on the other hand, detail significant gas cooling upon throttling due to Joule–Thomson effect. In order to extract dominant frequencies of vibration and corresponding Strouhal numbers, signal processing of transient pressure data at various probes inside the valve chamber has been performed through Fast-Fourier Transform (FFT), autocorrelation analysis, and continuous wavelet transform. At higher valve opening, spread-out dominant frequencies lie in the range <5000 Hz. However, at lower opening (or valve flow coefficient) two distinct peaks approximately at 5000 Hz and 10,000 Hz are visible from processed signals.

Numerical Study on Hydrodynamic Coefficient Estimation of an Underactuated Underwater Vehicle

Hydrodynamic coefficient estimation is crucial to the shape design, dynamic modeling, and control of underwater vehicles. In this paper, we conduct a numerical study on the hydrodynamic coefficient estimation of an underactuated underwater vehicle (actuated only in the surge, heave, and yaw degrees of freedom) by adopting the computational fluid dynamics (CFD) approach. Firstly, the mechanical structure of an underactuated underwater vehicle is briefly introduced, and the dynamic model of the underwater vehicle with hydrodynamic effects is established. Then, steady and unsteady Reynolds Averaged Navier–Stokes (RANS) simulations are carried out to numerically simulate the towing test, rotating arm test, and Planar Motion Mechanism (PMM) test of the underwater vehicle numerically. To simulate unsteady motions of the underactuated underwater vehicle, a sliding mesh model is adopted to simulate flows in the computational fluid domain that contain multiple moving zones and capture the unsteady interactions between the underwater vehicle and the flow field. Finally, the estimated hydrodynamic coefficients of the underwater vehicle are validated in a physical experiment platform, and the results show that the numerical estimates are in good agreement with the experimental data.

Significance of Darcy-Brinkman porous drag forces and Cattaneo-Christov thermal transportation on the features of second-grade fluid flows conveying copper nanomaterials past an unsteady stretching permeable sheet heated convectively

The main thermo-hydro-rheological behaviors featuring the unsteady convective laminar motion of copper-methanol second-grade nanofluid over a linearly stretching permeable sheet is explored numerically in the framework of Cattaneo-Christov theory to provide a better understanding of the heat transfer mechanism within a Darcy-Brinkman porous medium. By adopting the single-phase nanofluid model along with the boundary layer approximations, the leading partial differential equations (PDEs) are derived properly and then converted mathematically into a differential structure of ordinary differential equations (ODEs) via appropriate similarity alterations. Accordingly, the resulting dimensionless boundary layer equations are tacked numerically for convective and suction boundary conditions by utilizing the generalized differential quadrature method (GDQM). To reveal the effect of such a pertinent flow parameter, extensive GDQM numerical data are outputted graphically for the velocity and temperature fields as well as tabularly for skin friction coefficient and the Nusselt number. As the main findings, it is noted that both the velocity profile and the wall temperature lessen with the suction parameter and the nanoparticle’s loading. However, an enhancement is depicted for the wall heat transfer rate with the reinforcement in those influences. In addition, it is witnessed that the effect of the surface drag forces is strengthened with the nanoparticle’s loading and weakened with a higher estimation of the suction effect.

Dynamic and kinematic characteristics of unsteady motion of a water-in-oil emulsion droplet in collision with a solid heated wall under conditions of convective heat transfer

The paper presents the experimental results of spreading, fingering and corona-like splashing of water-in-oil emulsion droplets based on n-decane, isoparaffin oil and distilled water in the range of Weber numbers We = 100–900, wall temperatures Tw = 20–80 °C and in collision with a smooth solid surface. The spreading features and separate convective rolling structures in emulsion droplets are examined at the late stages of wetting. The effect of Tw on the viscous dissipation energy and the maximum spreading coefficient is established. The validity of the assumptions explaining the contradictory behavior of the maximum spreading diameter of emulsion droplets with increasing temperature is studied. The assumption of unstable behavior of the emulsion droplet rim during spreading is proposed. The maximum emulsion corona diameter and height decrease linearly with the Tw growth due to the longer corona lifetime. The maximum corona diameter increases following the power law with increasing the Brinkman number due to an increase in the liquid viscosity and a decrease in Tw. The results help to predict the corona's behavior by determining the relationship between the viscous dissipation of the spreading liquid and the energy transferred to the liquid from the wall due to molecular (thermal) conduction.

Effect of micelle breaking rate and wall slip on unsteady motion past a sphere translating steadily in wormlike micellar solutions

Many prior experimental studies have found the existence of an unsteady or fluctuating flow field around a solid sphere when falling in wormlike micellar solutions. Based on the two-species Vasquez–Cook–McKinley constitutive model for micelles, a recent numerical study shows that the breakage of long micelles downstream of the translating sphere causes this unsteady motion [C. Sasmal, “Unsteady motion past a sphere translating steadily in wormlike micellar solutions: A numerical analysis,” J. Fluid Mech. 912, A52, (2021)]. This numerical study further shows that the micelle breakage rate and wall slip can strongly influence this phenomenon. In particular, we find that the onset of this unsteady motion is delayed to higher values of the Weissenberg number as the micelle breakage rate decreases, or in other words, micelles become hard to break. Additionally, we observe that at some values of the micelle breakage rate, again, a transition in the flow field from unsteady to steady occurs at high Weissenberg numbers. Therefore, there is a window of the Weissenberg number present to observe this unsteady motion past the translating sphere. On the other hand, we show that the presence of wall slip on the sphere surface suppresses this unsteady motion past the translating sphere, and a probable explanation is also provided for the same.

Dynamics of three-dimensional vortical structures behind a barchan dune based on tomographic particle image velocimetry

In this study, tomographic particle image velocimetry (PIV) was used to measure three-dimensional (3D) flow structures behind a fixed-bed barchan dune model at a Reynolds number of 2528 in a circulation water tunnel. The topological evolution of the 3D instantaneous vortex structures and their dynamic characteristics in the dune wake were analyzed. 3D instantaneous arch-shaped vortex “chains” shedding from the barchan and typical quasi-streamwise vortex structures induced by the development of an internal boundary layer were found to be located both before and after the reattachment region, which differs a little from the results of previous studies. Nevertheless, both conditionally averaged and typical instantaneous 3D flow fields revealed that the arch-shaped vortex system dominates the barchan dune wake, and the inclination angle of these spanwise-oriented structures was found to change as it propagates downstream. Additionally, the dynamic characteristics of the dune wake were found to be similar to a flapping phenomenon such as oscillation of the recirculation in a backward-facing step flow. To provide complementary insight into this phenomenon, the separated and reattached shear flow were also examined using two-dimensional time-resolved planar PIV. It was found that the basic unsteady flapping motion, vortex roll-up, and complex vortex interactions can all be analyzed with ease in a Lagrangian framework.

Numerical modeling of unsteady subsonic flow over the conical shape body

The article presents the results of a numerical study of the unsteady vortex motion of gas arising over the conical body with a segmental bottom surface for various angles of attack in a subsonic flow regime. The simulation is based on the viscous compressible gas model (Navier–Stokes model). For various attack angles, the patterns of vortex flow around the conical surface of the body, in the area of its conjugation with the segmental bottom surface and in the near wake are presented. Data on non-stationary behavior and the magnitude of pressure in the conjugation area are given. For numerical simulation the method of finite volumes is used. Taking into account phenomena of the flow separation, the computational grids used have condensation to the surface of the body. Numerical calculations were carried out on the basis of parallel algorithms of the method and were realized on multiprocessor computing complexes.