Isolated Roughness Element Research Articles

Global instability in a laminar boundary layer perturbed by an isolated roughness element

Roughness-induced boundary-layer instabilities are investigated by means of hot-film anemometry in a water channel to provide experimental evidence of a global instability. It is shown that the roughness wake dynamics depends on extrinsic disturbances (amplifier) at subcritical Reynolds numbers, whereas intrinsic, self-sustained oscillations (wavemaker) are suspected at supercritical Reynolds numbers. The critical Reynolds number, therefore, separates between two different instability mechanisms. Furthermore, the critical Reynolds number from recent theoretical results is successfully confirmed in this experiment, supporting the physical relevance of 3-d global stability theory.

Flow Resistance Interactions on Hillslopes With Heterogeneous Attributes: Effects on Runoff Hydrograph Characteristics

AbstractAn improved modeling framework for capturing the effects of space and time‐variant resistance to overland flow is developed for intensively managed landscapes. The framework builds on the WEPP model but it removes the limitations of the “equivalent” plane and time‐invariant roughness assumption. The enhanced model therefore accounts for spatiotemporal changes in flow resistance along a hillslope due to changes in roughness, in profile curvature, and downslope variability. The model is used to quantify the degree of influence—from individual soil grains to aggregates, “isolated roughness elements,” and vegetation—on overland flow characteristics under different storm magnitudes, downslope gradients, and profile curvatures. It was found that the net effects of land use change from vegetation to a bare surface resulted in hydrograph peaks that were up to 133% larger. Changes in hillslope profile curvature instead resulted in peak runoff rate changes that were only up to 16%. The stream power concept is utilized to develop a taxonomy that relates the influence of grains, isolated roughness elements, and vegetation, on overland flow under different storm magnitudes and hillslope gradients. Critical storm magnitudes and hillslope gradients were found beyond which the effects of these landscape attributes on the peak stream power were negligible. The results also highlight weaknesses of the space/time‐invariant flow resistance assumption and demonstrate that assumptions on landscape terrain characteristics exert a strong control both on the shape and magnitude of hydrographs, with deviations reaching 65% in the peak runoff when space/time‐variant resistance effects are ignored in some cases.

Hypersonic transition induced by three isolated roughness elements on a flat plate

Hypersonic boundary layer transition from laminar to turbulent induced by three isolated roughness elements (ramp, diamond, and cylinder) was investigated by direct numerical simulations based on finite volume formulation with high order MDCD scheme. The effects of roughness shape on the transition mechanism, aerodynamic and aero-thermodynamic performances were quantitatively compared. The transition is dominated by three-dimensional shear layer instability and the streamwise transition locations are almost the same for all three roughness elements. The width of turbulent wake, the drag increment and the heat flux are the largest for cylinder. At the same time, the turbulent wake is the narrowest and drag and heat flux are the lowest for the ramp.

Effect of isolated roughness element height on high-speed laminar–turbulent transition

Understanding of the roughness-induced laminar–turbulent transition of supersonic and hypersonic flows is partly challenged by the intricate sensitivities presented by different correlation criteria. We investigate experimentally the effect of height for an isolated roughness element of quadrilateral planform. Heat transfer measurements document the enhancement of roughness-induced disturbances – here the associated heat flux perturbation – along a downstream axisymmetric laminar separation. With increasing element height $k$, a gradual intensification in wake disturbance levels is found for subcritical elements ($k/\unicode[STIX]{x1D6FF}_{k}<0.15$, where $\unicode[STIX]{x1D6FF}_{k}$ is the undisturbed boundary layer thickness) while elements taller than the effective condition ($k/\unicode[STIX]{x1D6FF}_{k}\geqslant 0.32$) bypass the more moderate transition mechanisms to produce a fully turbulent element wake. Results exhibit high sensitivity to flow properties at roughness height between critical and effective conditions. A reduction in wake disturbance levels with increasing height is documented within $0.23\leqslant k/\unicode[STIX]{x1D6FF}_{k}\leqslant 0.32$. This effect coincides with a decrease in kinematic viscosity at roughness height $\unicode[STIX]{x1D708}_{k}$ (as Mach number at height $M_{k}$ increases from 1.52 to 1.96) and is restricted to elements with strong local separation, whereby the influence of local shear effects is enhanced.

Geometry effect of isolated roughness on boundary layer transition investigated by tomographic PIV

Boundary layer transition over isolated roughness elements is investigated in the incompressible flow regime using tomographic PIV. Four different geometries (cylinder, square, hemisphere and micro-ramp) are considered maintaining constant height and span of the element. The main target is to compare the different flow topologies and study the effect of the element shape on accelerating boundary layer transition. The measurement domain encompasses the full transition process until the turbulent regime is established. The flow behavior is described by means of vortex topology and by statistical analysis of the velocity fluctuations. The instantaneous flow topology elucidates the mechanism of transition along its stages. A main distinction is observed between the bluff front elements that induce a horseshoe vortex due to upstream flow separation, leading to more rapid transition and the slender micro-ramp. The later geometry requires significant longer distance for transition onset. The mechanism of sideward propagation of the turbulent non-turbulent interface features a continuous convection and generation of hairpin-like vortices and remains the common denominator among all elements considered.

Roughness-Induced Transition in a Supersonic Boundary Layer

Direct numerical simulation is used to investigate the transition induced by three-dimensional isolated roughness elements in a supersonic boundary layer at a freestream Mach number of 3.5. Simulations are performed for two different configurations: one is a square planform roughness element, and the other is a diamond planform roughness element. The mean flow calculations show that the roughness element induces counter-rotating streamwise vortices downstream of the roughness element. These vortices persist for a long distance downstream, lift the low-momentum fluid from the near-wall region, and place it near the outer part of the boundary layer. This forms highly inflectional boundary-layer profiles. These observations agree with recent experimental observations. The receptivity calculations show that the amplitudes of the mass-flux fluctuations near the neutral point for the diamond-shaped roughness element are the same as the amplitude of the acoustic disturbances. They are three times smaller for the square-shaped roughness element.

A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries

In this paper, we present a method for performing uniformly high-order direct numerical simulations of high-speed flows over arbitrary geometries. The method was developed with the goal of simulating and studying the effects of complex isolated roughness elements on the stability of hypersonic boundary layers. The simulations are carried out on Cartesian grids with the geometries imposed by a third-order cut-stencil method. A fifth-order hybrid weighted essentially non-oscillatory scheme was implemented to capture any steep gradients in the flow created by the geometries and a third-order Runge–Kutta method is used for time advancement. A multi-zone refinement method was also utilized to provide extra resolution at locations with expected complex physics. The combination results in a globally fourth-order scheme in space and third order in time. Results confirming the method's high order of convergence are shown. Two-dimensional and three-dimensional test cases are presented and show good agreement with previous results. A simulation of Mach 3 flow over the logo of the Ubuntu Linux distribution is shown to demonstrate the method's capabilities for handling complex geometries. Results for Mach 6 wall-bounded flow over a three-dimensional cylindrical roughness element are also presented. The results demonstrate that the method is a promising tool for the study of hypersonic roughness-induced transition.

The behaviour of Tollmien–Schlichting waves undergoing small-scale localised distortions

This paper is concerned with the behaviour of Tollmien–Schlichting (TS) waves experiencing small localised distortions within an incompressible boundary layer developing over a flat plate. In particular, the distortion is produced by an isolated roughness element located at $\mathit{Re}_{x_{c}}=440\,000$. We considered the amplification of an incoming TS wave governed by the two-dimensional linearised Navier–Stokes equations, where the base flow is obtained from the two-dimensional nonlinear Navier–Stokes equations. We compare these solutions with asymptotic analyses which assume a linearised triple-deck theory for the base flow and determine the validity of this theory in terms of the height of the small-scale humps/indentations taken into account. The height of the humps/indentations is denoted by $h$, which is considered to be less than or equal to $x_{c}\mathit{Re}_{x_{c}}^{-5/8}$ (corresponding to $h/{\it\delta}_{99}<6\,\%$ for our choice of $\mathit{Re}_{x_{c}}$). The rescaled width $\hat{d}~(\equiv d/(x_{c}\mathit{Re}_{x_{c}}^{-3/8}))$ of the distortion is of order $\mathit{O}(1)$ and the width $d$ is shorter than the TS wavelength (${\it\lambda}_{TS}=11.3{\it\delta}_{99}$). We observe that, for distortions which are smaller than 0.1 of the inner deck height ($h/{\it\delta}_{99}<0.4\,\%$), the numerical simulations confirm the asymptotic theory in the vicinity of the distortion. For larger distortions which are still within the inner deck ($0.4\,\%<h/{\it\delta}_{99}<5.5\,\%$) and where the flow is still attached, the numerical solutions show that both humps and indentations are destabilising and deviate from the linear theory even in the vicinity of the distortion. We numerically determine the transmission coefficient which provides the relative amplification of the TS wave over the distortion as compared to the flat plate. We observe that for small distortions, $h/{\it\delta}_{99}<5.5\,\%$, where the width of the distortion is of the order of the boundary layer, a maximum amplification of only 2 % is achieved. This amplification can however be increased as the width of the distortion is increased or if multiple distortions are present. Increasing the height of the distortion so that the flow separates ($7.2\,\%<h/{\it\delta}_{99}<12.8\,\%$) leads to a substantial increase in the transmission coefficient of the hump up to 350 %.

Infrared thermography of transition due to isolated roughness elements in hypersonic flows

Boundary layer transition in high-speed flows is a phenomenon that despite extensive research over the years is still extremely hard to predict. The presence of protrusions or gaps can lead to an accelerated laminar-to-turbulent transition enhancing the thermal loads and the skin friction coefficient. In the current investigation, inverse heat transfer measurements using infrared thermography are performed on the flow past different roughness geometries in the form of cylinders and diamond at free stream Mach number equal to 7.5, h/δ ranging between 0.5 and 0.9 (where h is the roughness height and δ is the boundary layer thickness), and Reθ ranging between 1305 and 2450. The roughness elements are positioned on a 5° ramp placed at zero angle of attack. The measurements indicate that the roughness geometry influences the transitional pattern while the frontal area influences both the transition location and the maximum value of the Stanton number along the centreline. Moreover, there is a strong connection between the streamwise centreline Stanton number and the spreading of the wake width. In particular, the transition process is characterized by an approximately constant wake width. Differently, the wake width spreads at the location where the streamwise centreline Stanton number reaches the turbulent level. This point corresponds to a local maximum of the wake amplitude defined as one half of the maximum spanwise variation of the Stanton number.

Bubble-induced sheet cavitation inception on an isolated roughness element

The nucleation process on an isolated roughness element, located at the point of minimum pressure of a NACA 0015 hydrofoil was studied experimentally and computationally. The objective of this study was to investigate the working mechanism of bubble-induced sheet cavitation inception. High-speed micro-scale observations show the generation of a streak of cavitation—attached to the roughness element—in the wake of the bubble. Below its critical diameter, the bubble can detach from the streak cavity and travel on while the streak cavity remains. The solutions of a Rayleigh-Plesset equation along a streamline extracted from a RANS calculation show strong similarities with the experimental observations, but a factor 5 to 10 higher frame rate is needed to validate the calculations.

A combined experimental and numerical investigation of roughness induced supersonic boundary layer transition

The effect of surface roughness on boundary layer transition is of great importance to hypersonic vehicles. In this paper, both experimental and numerical methods are used to investigate the laminar-turbulent transition of a Mach 3 flat-plate boundary layer induced by isolated roughness element. Good agreements are achieved between experimental data and high-order numerical simulations. It is observed that, with increasing height of roughness, the transition tends to move forward. Two different types of transition mechanisms are found according to the height of the roughness elements. For the smallest roughness height of h=1mm, the shear layer instability in the wake region appears to be the leading mechanism for transition to turbulence. For two larger roughness elements of h=2mm and h=4mm, strong unsteadiness is developed from the upstream separation zone and transition is immediately accomplished, which indicates that the absolute instability in upstream separation zone dominates the transition.

Numerical Simulations of Transition due to Isolated Roughness Elements at Mach 6

An accurate prediction of transition onset behind an isolated roughness element has not yet been established. This is particularly important in hypersonic flow, where transition is accompanied by increased surface heating. In the present contribution, a number of direct numerical simulations have been performed of a Mach 6 boundary layer over a flat plate with isolated roughness elements. The effects of roughness shape, planform, ramps, and freestream disturbance levels on instability growth and transition onset are investigated. It is found that the frontal shape has a large effect on the transition onset, which is in agreement with previous studies, whereas the roughness element planform has a marginal influence. A new result is that the roughness shape in the streamwise direction (in particular, the aft section) is also an important characteristic, since an element with a ramped-down aft section allows the detached shear layer to spread out and weaken, leading to a lower instability growth rate. Above a critical value, the instability growth rate is found to be correlated with the amplitude of the low-speed streak formed by the roughness element, suggesting that a more physically based transition criterion should take account of the local liftup effect of the particular roughness shape.

Flow pattern and pollutant dispersion over three dimensional building arrays

The flow pattern and pollutant dispersion in urban canopies is investigated by large eddy simulation of flow over an array of cubes. It had been found that the pattern of flow over an isolated cubical obstacle can be characterized by an external wake of horseshoe vortex around the lower part of the windward face and an internal wake of recirculation cavity leeward. The width of the external wake Wex and the size of the internal wake Lin in the isolated roughness flow are used as key parameters to determine the wake effects on the flow and dispersion in the canopy of the same roughness height h in the isolated roughness flow. Flow patterns are categorized into five types based on the packing density as a result. The five types of urban canopy flow are introduced as (1) Isolated roughness flow when the lateral building interval WL is much greater than Wex and the streamwise building interval WS is much greater than Lin; (2) External wake interference flow when WL is less than Wex while WS is greater than Lin; (3) Internal wake interference flow when WS is in the same order of the size of Lin; (4) Skimming flow when WL is less than Wex and WS is less than Lin (5) Street network flow when WL and WS are much less than the Wex and Lin respectively. Results of time-averaging velocity field and pollutant concentration contours are demonstrated for each type of flow patterns. It is concluded that the behavior of flow pattern and pollutant dispersion is governed by the packing density from a very low packing density case, approximated as the flow around an isolated roughness element, to a high packing density case, resembled as the network flow.

Effect of a mesh on boundary layer transitions induced by free-stream turbulence and an isolated roughness element

Streamwise streaks, their lift-up and streak instability are integral to the bypass transition process. An experimental study has been carried out to find the effect of a mesh placed normal to the flow and at different wall-normal locations in the late stages of two transitional flows induced by free-stream turbulence (FST) and an isolated roughness element. The mesh causes an approximately 30 % reduction in the free-stream velocity, and mild acceleration, irrespective of its wall-normal location. Interestingly, when located near the wall, the mesh suppresses several transitional events leading to transition delay over a large downstream distance. The transition delay is found to be mainly caused by suppression of the lift-up of the high-shear layer and its distortion, along with modification of the spanwise streaky structure to an orderly one. However, with the mesh well away from the wall, the lifted-up shear layer remains largely unaffected, and the downstream boundary layer velocity profile develops an overshoot which is found to follow a plane mixing layer type profile up to the free stream. Reynolds stresses, and the size and strength of vortices increase in this mixing layer region. This high-intensity disturbance can possibly enhance transition of the accelerated flow far downstream, although a reduction in streamwise turbulence intensity occurs over a short distance downstream of the mesh. However, the shape of the large-scale streamwise structure in the wall-normal plane is found to be more or less the same as that without the mesh.

A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers

The capabilities of the triple-deck theory of receptivity for subsonic compressible boundary layers have been thoroughly investigated through comparisons with numerical simulations of the compressible Navier–Stokes equations. The analysis focused on the two Tollmien–Schlichting wave linear receptivity problems arising due to the interaction between a low-amplitude acoustic wave and a small isolated roughness element, and the low-amplitude time-periodic vibrations of a ribbon placed on the wall of a flat plate. A parametric study was carried out to look at the effects of roughness element and vibrating ribbon longitudinal dimensions, Reynolds number, Mach number and Tollmien–Schlichting wave frequency. The flat plate is considered isothermal, with a temperature equal to the laminar adiabatic-wall temperature. Numerical simulations of the full and the linearised compressible Navier–Stokes equations have been carried out using high-order finite differences to obtain, respectively, the steady basic flows and the unsteady disturbance fields for the different flow configurations analysed. The results show that the asymptotic theory and the Navier–Stokes simulations are in good agreement. The initial Tollmien–Schlichting wave amplitudes and, in particular, the trends indicated by the theory across the whole parameter space are in excellent agreement with the numerical results. An important finding of the present study is that the behaviour of the theoretical solutions obtained for$\mathit{Re}\rightarrow \infty$holds at finite Reynolds numbers and the only conditions needed for the theoretical predictions to be accurate are that the receptivity process be linear and the free-stream Mach number be subsonic.

Roughness-induced turbulent wedges in a hypersonic blunt-body boundary layer

AbstractThis paper uses measurements of surface heat transfer to study roughness-induced turbulent wedges in a hypersonic boundary layer on a blunt cylinder. A family of wedges was produced by changing the height of an isolated roughness element, providing conditions in the following range: fully effective tripping, for the largest element, with a turbulent wedge forming immediately downstream of the element; a long wake, in length several hundred times the boundary layer thickness, leading ultimately to transition; and retention of laminar flow, for the smallest element. With appropriate element size, a fully intermittent wedge formed, comprising a clear train of turbulent spots.

Direct numerical simulation of high-speed transition due to an isolated roughness element

AbstractWe study the transition of a Mach 6 laminar boundary layer due to an isolated cylindrical roughness element using large-scale direct numerical simulations (DNS). Three flow conditions, corresponding to experiments conducted at the Purdue Mach 6 quiet wind tunnel are simulated. Solutions are obtained using a high-order, low-dissipation scheme for the convection terms in the Navier–Stokes equations. The lowest Reynolds number ($Re$) case is steady, whereas the two higher $Re$ cases break down to a quasi-turbulent state. Statistics from the highest $Re$ case show the presence of a wedge of fully developed turbulent flow towards the end of the domain. The simulations do not employ forcing of any kind, apart from the roughness element itself, and the results suggest a self-sustaining mechanism that causes the flow to transition at a sufficiently large Reynolds number. Statistics, including spectra, are compared with available experimental data. Visualizations of the flow explore the dominant and dynamically significant flow structures: the upstream shock system, the horseshoe vortices formed in the upstream separated boundary layer and the shear layer that separates from the top and sides of the cylindrical roughness element. Streamwise and spanwise planes of data were used to perform a dynamic mode decomposition (DMD) (Rowley et al., J. Fluid Mech., vol. 641, 2009, pp. 115–127; Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5–28).

Parameterization of Boundary-Layer Transition Induced by Isolated Roughness Elements

The laminar-to-turbulent transition of boundary layers induced by isolated three-dimensional roughness elements is analyzed by mining a direct numerical simulation database, which covers the variation of many physical parameters, including Mach and Reynolds numbers, and obstacle shape and size. It is found that the transition process is approximately controlled by a Reynolds number based on the momentum deficit past the obstacle, which is proportional to the classical roughness Reynolds number and which approximately incorporates the effects of the roughness element shape. The analysis of the perturbation energy past the obstacle shows that the varicose mode of instability is always dominant in the close proximity of the obstacle, and it promotes transition in supercritical flow cases. On the other hand, the sinuous mode appears to dominate the evolution of marginally subcritical cases, which feature quasi-steady momentum streaks.

S1910204 高温衝撃風洞HIESTによるHTV-Rカプセル形状模型の空力加熱試験([S191-02]大気突入・減速技術(2),宇宙工学部門)

Aerodynamic heating test of a HTV-R capsule model has performed in the free-piston high-enthalpy shock tunnel JAXA-HIEST. To measure heat flux distribution, the eighty-eight and thirty-four fast-response coaxial thermocouples were instrumented on the windward surface and on the back-shell surface, respectively. Besides, Eight Piezo-resistive pressure transducers were mounted on the aft of the body to determine flow establishment around the model through millisecond order short test period. Stagnation enthalpy and stagnation pressure were varied from H_0=3.5MJ/kg to 20MJ/kg, and from P_0=14MPa to 60MPa, respectively. The unit Reynolds number was changed from 0.9 million/m to 4.5 million/m. Aeroheating characteristics was observed at model angle of attack 20 degree with fully laminar, transition and turbulent boundary layer. Turbulent heat flux was observed with 'Pizza-box' shaped isolated roughness elements on the heat-shield surface and back-shell windward surface. Measured heat flux was normalized as Stanton number for comparison with different flow condition.

Estimating aerodynamic roughness over complex surface terrain

AbstractSurface roughness plays a key role in determining aerodynamic roughness length (zo) and shear velocity, both of which are fundamental for determining wind erosion threshold and potential. While zo can be quantified from wind measurements, large proportions of wind erosion prone surfaces remain too remote for this to be a viable approach. Alternative approaches therefore seek to relate zo to morphological roughness metrics. However, dust‐emitting landscapes typically consist of complex small‐scale surface roughness patterns and few metrics exist for these surfaces which can be used to predict zo for modeling wind erosion potential. In this study terrestrial laser scanning was used to characterize the roughness of typical dust‐emitting surfaces (playa and sandar) where element protrusion heights ranged from 1 to 199 mm, over which vertical wind velocity profiles were collected to enable estimation of zo. Our data suggest that, although a reasonable relationship (R2 > 0.79) is apparent between 3‐D roughness density and zo, the spacing of morphological elements is far less powerful in explaining variations in zo than metrics based on surface roughness height (R2 > 0.92). This finding is in juxtaposition to wind erosion models that assume the spacing of larger‐scale isolated roughness elements is most important in determining zo. Rather, our data show that any metric based on element protrusion height has a higher likelihood of successfully predicting zo. This finding has important implications for the development of wind erosion and dust emission models that seek to predict the efficiency of aeolian processes in remote terrestrial and planetary environments.