Two-dimensional Roughness Elements Research Articles

Investigation of the Formation and Further Development of Longitudinal Disturbances and Their Secondary Instability on the Flying Wing Model

Detailed investigation of two-dimensional roughness element influence on the flow behind three-dimensional roughness element was carried out. For the first time studies were conducted on the windward side of the flying wing in the range of free-stream 7,2 – 20 m/s in the favourable gradient region behind roughness elements. Secondary instability mechanisms of disturbances leading to turbulence stage were investigated. It was shown that longitudinal structure forming behind three-dimensional roughness element grows downstream and has its trajectory slightly bend. The longitudinal structure consists of two stationary disturbances different in size. This can be explained by presence of cross flow and secondary disturbances leading to the transition. On the straight wing model, influence of the distributed suction on the stationary disturbance development was investigated and quantitatively determined. It was shown that suction is able to relaminarize the flow and eliminate the separation of the boundary layer.

Flow organization in the near wake of isolated and sheltered two-dimensional bar roughness elements

The flow past isolated and sheltered two-dimensional (2D) bar roughness elements is investigated via 2D and 3D flow measurements for a wide range of configurations. The presented results highlight the effects of sheltering by an upstream 2D bar on the wake of a downstream 2D bar, including flow reattachment, turbulence, vortical structures, and other flow quantities.

Two-scale solution for tripped turbulent boundary layer

Recent findings on the Reynolds-number-dependent behaviour of near-wall turbulence in terms of the ‘foot-printing’ of outer large-scale structures call for a new modelling development. A two-scale framework was proposed to couple a local fine-mesh solution with a global coarse-mesh solution by He (Intl J. Numer. Meth. Fluids, vol. 86, 2018, pp. 655–677). The methodology was implemented and demonstrated by Chen & He (J. Fluid Mech, vol. 933, 2022, p. A47) for a canonical turbulent channel flow, where the mesh-count scaling with Reynolds number is potentially reduced from $O(R{e^2})$ for a conventional wall-resolved large-eddy simulation (WRLES) to $O(R{e^1})$ . The present work extends the two-scale method to turbulent boundary layers. A two-dimensional roughness element is used to trip a turbulent boundary layer. It is observed that large-scale disturbances originating at the trip have a much shorter lifetime and weaker foot-printing signatures on near-wall flow compared to those long streaky coherent structures in well-developed wall-bounded turbulent flows. Modal analyses show that the impact of trip-induced large scales can be adequately captured by a locally embedded fine-mesh block. For the tripped turbulent boundary layer, a Chebyshev block-spectral mapping is adopted to propagate source terms from the local fine-mesh blocks to the global coarse-mesh domain, driving to a target solution for the upscaled equations. The computed mean statistics and energy spectra are in good agreement with corresponding experimental data, WRLES and direct numerical simulation (DNS) results. The overall mesh count– $Re$ scaling is estimated to reduce from $O(R{e^{1.8}})$ for the full wall-resolved LES to $O(R{e^{0.9}})$ for the present two-scale solution.

A new equivalent sand grain roughness relation for two-dimensional rough wall turbulent boundary layers

The effects of different geometries of two-dimensional (2-D) roughness elements in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) on turbulence statistics and drag coefficient are assessed using single hot-wire anemometry. Three kinds of 2-D roughness are used: (i) circular rods with two different heights, $k= 1.6$ and 2.4 mm, and five different streamwise spacing of $s_{x}= 6k$ to $24k$ , (ii) three-dimensional (3-D) printed triangular ribs with heights of $k= 1.6$ mm and spacing of $s_{x}= 8k$ and (iii) computerized numerical control (CNC) machined sinewave surfaces with two different heights, $k= 1.6$ and 2.4 mm, and spacing of $s_{x}= 8k$ . These roughnesses cover a wide range of ratios of the boundary layer thickness to the roughness height ( $23 < \delta /k < 41$ ), where $\delta$ is the boundary layer thickness. All roughnesses cause a downward shift on the wall-unit normalised streamwise mean velocity profile when compared with the smooth wall profiles agreeing with the literature, with a maximum downward shift observed for $s_{x}= 8k$ . In the fully rough regime, the drag coefficient becomes independent of the Reynolds number. Changing the roughness height while maintaining the same spacing ratio $s_{x}/k$ exhibits little influence on the drag coefficient in the fully rough regime. On the other hand, the effective slope $(ES)$ and the height skewness $(k_{sk})$ appear to be major surface roughness parameters that affect the drag coefficient. These parameters are used in a new expression for $k_{s}$ , the equivalent sand grain roughness, developed for 2-D uniformly distributed roughness in the fully rough regime.

Large Eddy Simulation of Near-Bed Flow and Turbulence over Roughness Elements in the Shallow Open-Channel

Turbulent flows in rough open-channels have complex structures near the channel-bed. The near-bed flow can cause bed erosion, channel instability, and damages to fish habitats. This paper aims to improve our understanding of the structures. Transverse square bars placed at the channel-bed form two-dimensional roughness elements. Turbulent flows over the bars are predicted using large eddy simulation (LES). The predicted flow quantities compare well with experimental data. The LES model predicts mean-flow velocity profiles that resemble those in the classic turbulent boundary layer over a flat plate and profiles that change patterns in the vicinity of roughness elements, depending on the pitch-to-roughness height ratio λ/k. The relative turbulence intensity and normalized Reynolds shear stress reach maxima of 15% and 1.2%, respectively, at λ/k = 8, compared to 9% and 0.2% at λ/k = 2. The predicted bottom boundary layers constitute a large portion of the total depth, indicating roughness effect on the flow throughout the water column. Fluid exchange between the roughness cavity and outer region occurs due to turbulence fluctuations. The fluctuations increase in intensity with increasing λ/k ratio. This ratio dictates the number of eddies in the cavity as well as their locations and shapes. It also controls turbulence stress distributions. LES can be used to explore strategies for erosion control, channel restoration, and habitat protection.

Mean flow and turbulence structure over exposed roots on a forested floodplain: Insights from a controlled laboratory experiment.

The time-averaged and instantaneous flow velocity structures of flood waters are not well understood for irregular surfaces such as are created by the presence of roots and fallen branches on forested floodplains. Natural flow structures commonly depart systematically from those described for idealised roughness elements, and an important knowledge gap exists surrounding the effects of natural flow structures on vertical exchanges of fluid and momentum. An improved understanding of the flow structure is required to model flows over forested floodplains more accurately, and to distinguish their dynamics from non-vegetated floodplains or indeed floodplains with other vegetation types, such as reed or grass. Here we present a quantification of the three-dimensional structure of mean flow velocity and turbulence as measured under controlled conditions in an experimental flume using a physical reproduction of a patch of forested floodplain. The results conform in part to existing models of local flow structure over simple roughness elements in aspects such as flow separation downstream of protruding roots, flow reattachment, and the lowering of the velocity maximum further downstream. However, the irregular shape of the surface of the floodplain with exposed roots causes the three-dimensional flow structure to deviate from that anticipated based on previous studies of flows over idealised two-dimensional roughness elements. The results emphasise varied effects of inheritance of flow structures that are generated upstream—the local response of the flow to similar obstacles depends on their spatial organisation and larger-scale context. Key differences from idealised models include the absence of a fully-developed flow at any location in the test section, and various interactions of flow structures such as a reduction of flow separation due to cross-stream circulation and the diversion of the flow over and around the irregular shapes of the roots.

Influence of two-dimensional roughness element on boundary layer structure in the favourable pressure gradient region of the swept wing

In this article, the results of research about stationary and secondary disturbances development behind the localized and two-dimensional roughness elements are presented. It is shown that the two-dimensional roughness element has a destabilizing effect on the disturbances induced by the three-dimensional roughness element lying upstream. In this case, the two-dimensional roughness element causes the appearance of stationary structures, and then secondary perturbations, whose frequency range lies lower than in the case of the stationary vortices excited by a three-dimensional roughness element.

Assessment of the Impact of Two-Dimensional Wall Deformation Shape on High-Speed Boundary-Layer Disturbances

Previous experimental and numerical studies showed that two-dimensional roughness elements can stabilize disturbances inside a hypersonic boundary layer and eventually delay the transition onset. The objective of this paper is to evaluate the response of disturbances propagating inside a high-speed boundary layer to various two-dimensional surface deformations of different shapes. We perform an assessment of the impact of various two-dimensional surface nonuniformities, such as backward or forward steps, combinations of backward and forward steps, wavy surfaces, surface dips, and surface humps. Disturbances inside a Mach 5.92 flat-plate boundary layer are excited using periodic wall blowing and suction at an upstream location. The numerical tools consist of a high-accuracy numerical algorithm solving for the unsteady, compressible form of the Navier–Stokes equations in curvilinear coordinates. Results show that all types of surface nonuniformities are able to reduce the amplitude of boundary-layer disturbances to a certain degree. The amount of disturbance energy reduction is related to the type of pressure gradients that are posed by the deformation (adverse or favorable). A possible cause (among others) of the disturbance energy reduction inside the boundary layer is presumed to be the result of a partial deviation of the kinetic energy to the external flow, along the discontinuity that is generated by the wall deformation.

The impact of dynamic roughness elements on marginally separated boundary layers

It has been shown experimentally that dynamic roughness elements – small bumps embedded within a boundary layer, oscillating at a fixed frequency – are able to increase the angle of attack at which a laminar boundary layer will separate from the leading edge of an airfoil (Grager et al., in 6th AIAA Flow Control Conference, 2012, pp. 25–28). In this paper, we attempt to verify that such an increase is possible by considering a two-dimensional dynamic roughness element in the context of marginal separation theory, and suggest the mechanisms through which any increase may come about. We will show that a dynamic roughness element can increase the value of $\unicode[STIX]{x1D6E4}_{c}$ as compared to the clean airfoil case; $\unicode[STIX]{x1D6E4}_{c}$ represents, mathematically, the critical value of the parameter $\unicode[STIX]{x1D6E4}$ below which a solution exists in the governing equations and, physically, the maximum angle of attack possible below which a laminar boundary layer will remain predominantly attached to the surface. Furthermore, we find that the dynamic roughness element impacts on the perturbation pressure gradient in two possible ways: either by decreasing the magnitude of the adverse pressure peak or by increasing the streamwise extent in which favourable pressure perturbations exist. Finally, we discover that the marginal separation bubble does not necessarily have to exist at $\unicode[STIX]{x1D6E4}=\unicode[STIX]{x1D6E4}_{c}$ in the time-averaged flow and that full breakaway separation can therefore occur as a result of the bursting of transient bubbles existing within the length scale of marginal separation theory.

Phase-relationships between scales in the perturbed turbulent boundary layer

ABSTRACTThe phase-relationship between large-scale motions and small-scale fluctuations in a non-equilibrium turbulent boundary layer was investigated. A zero-pressure-gradient flat plate turbulent boundary layer was perturbed by a short array of two-dimensional roughness elements, both statically, and under dynamic actuation. Within the compound, dynamic perturbation, the forcing generated a synthetic very-large-scale motion (VLSM) within the flow. The flow was decomposed by phase-locking the flow measurements to the roughness forcing, and the phase-relationship between the synthetic VLSM and remaining fluctuating scales was explored by correlation techniques. The general relationship between large- and small-scale motions in the perturbed flow, without phase-locking, was also examined. The synthetic large scale cohered with smaller scales in the flow via a phase-relationship that is similar to that of natural large scales in an unperturbed flow, but with a much stronger organizing effect. Cospectral techniques were employed to describe the physical implications of the perturbation on the relative orientation of large- and small-scale structures in the flow. The correlation and cospectral techniques provide tools for designing more efficient control strategies that can indirectly control small-scale motions via the large scales.

乱流境界層の平均量特性に及ぼす粗さの影響

The roughness sublayer beneath a turbulent boundary layer has been investigated analytically and experimentally, and the effect has been discussed on the mean velocity profile throughout the layer. The rough surface consists of two-dimensional square roughness elements. The roughness height is proportional to streamwise distance. It is one of conditions of an equilibrium boundary layer proposed by Rotta J.C. The roughness pitch ratio is 4. The measurement within/outside the roughness sublayer was made using LDV and CTA, respectively. The Reynolds number based on the momentum thickness is 6000. The roughness Reynolds number is 149 and the roughness is in complete rough regime. The analytical solutions of streamwise mean velocity and Reynolds shear stress profiles were derived from the space averaged Reynolds equation in the cavity region between roughness elements and the mixing length model. The solutions were well consistent with the experimental results. By use of the solutions and experimental results, the center height of drag moment and the constant of the roughness function can be represented as a function of the roughness pitch ratio for the equilibrium boundary layer. Also, from the momentum integral equation, Coles's wake law, solution and experimental results, the wake parameter will be given as a function of the friction parameter and relative roughness height. Finally, the local skin friction coefficient will be formulated with a function of the roughness pitch ratio and relative roughness height.

壁面せん断乱流の対数層に対する粗さの影響

The roughness sublayer beneath a turbulent boundary layer has been investigated analytically and experimentally, and its effect has been discussed on the logarithmic velocity profile. The rough surface consists of two-dimensional square roughness elements. The roughness height is proportional to streamwise distance. It is one of conditions of an equilibrium boundary layer. The roughness pitch ratio is 4. The free stream velocity is about 9m/s. The experiments were made in zero pressure gradient. The velocity measurement within/outside the roughness sublayer was made using LDV and CTA, respectively. The momentum thickness and roughness Reynolds numbers are 6000 and 149, respectively. From the analytical solutions of streamwise mean velocity and Reynolds shear stress profiles in the cavity region between roughness elements and experimental results , the center height of drag moment and the constant of the roughness function can be represented as a function of the roughness pitch ratio. These functions are well consistent with the experimental and DNS results.

The Role of Two-Dimensional Roughness Element in the Laminar-Turbulent Process in the Favorable Pressure Gradient of the Swept Wing

In the article using a liquid crystal thermography investigated the development of stationary and secondary disturbances, which were excited by cylindrical and two-dimensional roughness elements. It was shown, that two-dimensional roughness element has a destabilizing effect on disturbances, induced by cylindrical roughness element. Also the twodimensional roughness element is able to excite the stationary structures, and then the secondary disturbances the frequency interval of which is lower than in the case of stationary vortices excitation by cylindrical roughness element

Large eddy simulation of turbulent channel flow with transverse roughness elements on one wall

This study examines the feasibility of large eddy simulation for predicting turbulent channel flows with two-dimensional roughness elements of square, circular and triangular shapes transversely placed on the bottom wall. Results are obtained for several values of the cavity width to the roughness height ratio using various subgrid-scale turbulence models. The present large eddy simulation predictions of mean streamwise velocity, root-mean-square velocity fluctuations, and skin frictional and form drags agree reasonably well with previously published results of direct numerical simulations at a low Reynolds number. All the subgrid-scale models examined here are capable of reproducing the relevant physics associated with the effect of the rough surface on the turbulent flow, exhibiting similar performances. Moreover, the use of the turbulence models leads to an improvement in the predictions of several turbulence statistics as compared with the case when no model is considered. Large eddy simulation can be combined easily with an immersed boundary method yielding satisfactory results based on a coarser grid resolution than in direct numerical simulation and, thus, it is suitable for the investigation of turbulent channel flows with riblets of various shapes.

An experimental study of the flow through and over two dimensional rectangular roughness elements: Deductions for urban boundary layer parameterizations and exchange processes

This paper investigates the flow through and over two-dimensional rectangular roughness elements, arranged in a building-street canyon geometry through a series of experiments. Geometries of different packing densities of the roughness elements (λp) were examined and the packing density values ranged from λp = 0.30 to 0.67. The purpose of the work is: (i) to investigate the flow physics observed both at the boundary layer scale as well as at the scale within the roughness elements for a range of packing densities, (ii) to deduce parameterizations of the adjusted rough boundary layer and their variation with a change in the packing density, and (iii) given a particular interest in and application to the urban atmosphere, a final aim at the roughness-element scale is to deduce the variation of the breathability with the packing density variation. Particle image velocimetery measurements of the velocity flow field as well as the turbulent kinetic energy and the Reynolds Stress (within and up to well-above the street canyons) were conducted. The results reveal qualitative flow features as well as features of the adjusted boundary layer structure—in particular the roughness and inertial sublayers, which can be associated with the surface roughness length, zero-plane displacement thickness, and the friction velocity. The lowest friction velocities are exhibited in the geometries with the highest- and lowest packing densities while the maximum friction velocities are observed in the medium-packed geometries. The exchange processes and breathability at the level of the roughness elements top were characterized and quantified by a mean exchange velocity. The results show that unlike friction velocity, the normalized exchange velocity (over the mean bulk velocity) for the most dense and sparse geometries differ by more than 80%, with the denser-packed geometries exhibiting lower exchange velocities; this is shown to be related with the thickness of the developed roughness sublayer.

Experimental study on flow and ventilation behaviours over idealised urban roughness

Flows in the urban boundary layer (UBL) are strongly affected by the inhomogeneous roughness elements at the bottom surface. In particular, in the near-ground region (roughness sublayer), the effect of the surface roughness dominates that complicates the behaviours of mean flow and turbulence and subsequently the near-wall transport processes. To safeguard the health of urban inhabitants, it is crucial to develop an in-depth understanding of the correlation among near-wall fluid motions, UBL turbulence and city ventilation. However, rather limited information is available. In this study, physical modelling in a laboratory wind tunnel is employed to measure the profiles of both stream-wise and vertical velocities over an array consisting of idealised two-dimensional (2D) roughness elements. Various arrangements are adopted in attempt to cover different flow regimes to examine city ventilation problems. The ventilation performance is measured by the air exchange rate (ACH). Consistent with our previous large-eddy simulation (LES) results, the current wind tunnel measurements suggest that city ventilation is dominated by the ACH turbulent component, i.e., air masses are mainly driven by atmospheric turbulence (at least 80% of the total ACH).

Experimental investigations of a trailing edge noise feedback mechanism on a NACA 0012 airfoil

Discrete frequency tones in the trailing edge noise spectra of NACA 0012 airfoils are investigated with the Coherent Particle Velocity method. The Reynolds number and angle of attack range, in which these discrete frequency tones are present, are consistent with published results. The discrete tones are composed of a main tone and a set of regularly spaced side peaks resulting in a ladder-type structure for the dependency on the free stream velocity. The occurrence of this discrete frequency noise could be attributed to the presence of a laminar boundary layer on the pressure side opening up into a separation bubble near the trailing edge, which was visualized using oil flow. Wall pressure measurements close to the trailing edge revealed a strong spanwise and streamwise coherence of the flow structures inside this laminar separation bubble. The laminar vortex shedding frequencies inferred from the streamwise velocity fluctuations, which were evaluated from hot-wire measurements at the trailing edge, were seen to coincide with the discrete tone frequencies observed in the trailing edge noise spectra. Previous findings on discrete frequency tones for airfoils with laminar boundary layers up to the trailing edge hint at the existence of a global feedback loop. Hence, sound waves generated at the trailing edge feed back into the laminar boundary layer upstream by receptivity and are, then, convectively amplified downstream. The most dominant amplification of these disturbance modes is observed inside the laminar separation bubble. Therefore, the frequencies of the most pronounced tones in the trailing edge noise spectra are in the frequency range of the convectively most amplified disturbance modes. Modifying the receptivity behavior of the laminar boundary layer on the pressure side by means of very thin, two-dimensional roughness elements considerably changes the discrete tone frequencies. For roughness elements placed closer to the trailing edge, the main tone frequency was seen to decrease, while the frequency spacing in-between two successive tones increased. Based on the stability characteristics of the laminar boundary layer and the characteristics of the upstream traveling sound wave, a method for predicting the discrete tone frequencies was developed showing good agreement with the measured results. Hence, with a controlled modification of the laminar boundary layer receptivity behavior, the existence of the proposed feedback loop could be confirmed. At the same time, no significant influence of a second feedback loop previously proposed for the suction side of the NACA 0012 airfoil was observed neither by influencing the boundary layer with a receptivity–roughness element nor by tripping the boundary layer at the leading edge.

New perspectives on the impulsive roughness-perturbation of a turbulent boundary layer

The zero-pressure-gradient turbulent boundary layer over a flat plate was perturbed by a short strip of two-dimensional roughness elements, and the downstream response of the flow field was interrogated by hot-wire anemometry and particle image velocimetry. Two internal layers, marking the two transitions between rough and smooth boundary conditions, are shown to represent the edges of a ‘stress bore’ in the flow field. New scalings, based on the mean velocity gradient and the third moment of the streamwise fluctuating velocity component, are used to identify this ‘stress bore’ as the region of influence of the roughness impulse. Spectral composite maps reveal the redistribution of spectral energy by the impulsive perturbation – in particular, the region of the near-wall peak was reached by use of a single hot wire in order to identify the significant changes to the near-wall cycle. In addition, analysis of the distribution of vortex cores shows a distinct structural change in the flow associated with the perturbation. A short spatially impulsive patch of roughness is shown to provide a vehicle for modifying a large portion of the downstream flow field in a controlled and persistent way.

J056014 壁面粗度のスパン方向不連続により生成された二次流れ([J05601]乱流における運動量,熱,物質の輸送現象(1))

An experimental study using two-dimensional channel flow was performed to investigate the possibility of a spanwise discontinuity of wall roughness as a device to generate secondary currents associated with longitudinal vortex. A k-type rough wall, which consists of an array of two-dimensional rectangular roughness elements, is placed on the wall and makes discontinuity of wall roughness. Mean velocity and turbulent intensity were measured with hot-wire anemometers and crossed wire probes. Velocity vector plot in cross streamwise plane clearly shows that the discontinuity of wall roughness is able to produce secondary currents. It is expected that the secondary currents are associated with longitudinal vorticity. There are certainly some evidence that the secondary currents transport fluid particles and make deformations in the mean velocity and turbulent intensity contour maps.

Disturbance evolution in a Mach 4.8 boundary layer with two-dimensional roughness-induced separation and shock

A numerical investigation of the disturbance amplification in a Mach 4.8 flat-plate boundary layer with a localized two-dimensional roughness element is presented. The height of the roughness is varied and reaches up to approximately 70% of the boundary-layer thickness. Simulations are based on a time-accurate integration of the compressible Navier–Stokes equations, with a small disturbance of fixed frequency being triggered via blowing and suction upstream of the roughness element. The roughness element considerably alters the instability of the boundary layer, leading to increased amplification or damping of a modal wave depending on the frequency range. The roughness is also the source of an additional perturbation. Even though this additional mode is stable, the interaction with the unstable mode in the form of constructive and destructive interference behind the roughness element leads to a beating and therefore transiently increased disturbance amplitude. Far downstream of the roughness, the amplification rate of a flat-plate boundary layer is recovered. Overall, the two-dimensional roughness element behaves as disturbance amplifier with a limited bandwidth capable of filtering a range of frequencies and strongly amplifying only a selected range.