Two-dimensional Roughness Elements Research Articles

Turbulent channel flow with either transverse or longitudinal roughness elements on one wall

Direct numerical simulation results are presented for turbulent channel flows with two-dimensional roughness elements of different shapes. The focus is mainly on a geometry where the separation between consecutive roughness elements is small and for which the rate of change of the roughness function with respect to the separation between consecutive elements is large. Roughness elements are placed either along the flow direction or orthogonally to it. In the latter case, the drag is increased. For the former case, the possibility of drag reduction reflects the different relative contributions from viscous and Reynolds shear stresses. The Reynolds shear stress depends on the shape of the surface more than the viscous stress and is closely related to the near-wall structures. For orthogonal elements, there is no satisfactory correlation between the roughness function and parameters describing the roughness geometry. On the other hand, a satisfactory collapse of the data is achieved when the roughness function is plotted against the root mean square wall-normal velocity averaged over the plane of the roughness crests. Relative to a smooth wall surface, the Reynolds stress tensor near the wall tends to become more isotropic when the elements are orthogonal to the flow and less isotropic when the elements are aligned with the flow. The interdependencies between the departure from isotropy in the wall region, the organization of the wall structures, and the magnitude of the drag are assessed by examining the rotational component of the turbulent kinetic energy production and the probability density function of the helicity density.

Numerical experiments on wall turbulence at low Reynolds number

A direct numerical simulation of a turbulent channel flow, with regularly spaced two-dimensional roughness elements mounted at the wall and perpendicular to the flow direction, was performed at a very low Reynolds number of Re
940 based on the centerline velocity and the full channel height. Using the lattice Boltzmann numerical algorithm, all essential scales were resolved with about 19·106 grid points (1155 x 129 x 128 in the x1, x2 and x3 directions). The computed results confirm the existence of turbulence at such a low Reynolds number. Turbulence persisted over the entire computation time, which was sufficiently long to prove its self-maintenance. By examination of statistical features of the flow across the anisotropy-in variant map, it was found that these coincide with conclusions emerging from the analysis of transition and breakdown to turbulence in a laminar boundary layer exposed to small, statistically stationary, neutrally stable axisymmetric disturbances with the stream wise intensity component ( u'1) lower than the intensities in the normal ( u'1) and span wise directions u'1< u'2 = u'3. To further support the concept and the results of
theoretical considerations of the laminar to turbulent transition process in wall-bounded flows using statistical techniques and to demonstrate its great potential for engineering, an additional simulation was performed of a plane channel flow with regularly spaced riblet elements mounted at the wall and aligned parallel with the flow direction. The supplementary simulation was done at a Reynolds number of Re = 6584 using about 250·106 grid points (4096 x 257 x 240). Analysis of the simulation results carried out across the flow region located in the mid plane between the riblet elements confirms the central result which lies in the root of the statistical dynamics of the velocity fluctuations in wall-bounded flows: when the velocity fluctuations close to the wall tend towards the one-component state, so that the stream wise intensity component is much larger than the intensities in the normal and span wise directions, u'1< u'2 = u'3, the turbulent dissipation rate vanishes at the wall, leading to a significant reduction of the wall shear stress. For the simulated flow case the local value of wall shear stress reduction was found to exceed the wall shear stress reduction SR
92% which corresponds to a fully developed laminar channel flow with smooth walls at the same Reynolds number.

Loss reduction by means of two-dimensional roughness elements on the suction surface of a linear turbine rotor cascade

This paper reports the results of experimental investigations carried out to reduce pressure losses by means of two-dimensional roughness elements (in the form of stainless steel tubes of different diameters). The roughness elements are fixed at various axial stations on the suction surface of 120° turning, 175 mm chord, impulse turbine rotor blades. Flow measurements are carried out at the exit of the cascade at five axial stations, using a five-hole probe operating in non-nulling mode. In addition, the blade surface static pressure distribution is measured. The data from the five-hole probe measurements are used to calculate pressure, velocity and flow angle distributions at the cascade exit and these results are used to calculate mass averaged values and integral parameters such as wake half-width, loss coefficient, etc. The static pressure distribution is altered very little except near the roughness element. The lift coefficient remains almost constant for all configurations and the drag coefficient is reduced for some configurations. The non-dimensional total pressure defects in the wake for all configurations followed Gaussian distribution. A two-dimensional roughness element of 0.6 mm diameter placed at 0.65 chord on the suction surface showed an appreciable reduction in pressure losses.

Boundary-Layer Receptivity to Transient Convected Disturbances

Previous work has shown that the boundary layer is receptive to acoustic and convected disturbances in regions where there is a rapid streamwise variation in the mean flow such as at the leading edge or at roughness elements or suction strips. Much of this work involved single-frequency, two-dimensional waves, and further studies are required to determine the effects of the broadband three-dimensional nature of turbulent fluctuations. An experimental investigation of the receptivity of a Blasius boundary layer to transient two-dimensional convected disturbances is presented here. A ribbon located upstream of a flat plate and aligned parallel to the plate leading edge was used to introduce disturbances into the freestream. Two-dimensional roughness elements distributed on the surface of the plate provided a receptivity site. Measurements of the boundary-layer response to single-frequency waves, pulses, and random noise disturbances are reported. Similar receptivity was measured for each of these disturbance types, showing that the broadband nature of transient disturbances does not affect the receptivity characteristics of the boundary layer and that linear superposition may be used to extend theories for single-frequency disturbances to applications involving broadband disturbances

Experimental and Computational Study of Two-Dimensional Roughness Effects on the Instability of the Flat Plate Boundary Layer.

Experimental and computational study on the linear instability region downstream of a two-dimensional roughness element(a square rod)placed in a laminar boundary layer on a flat plate is described. The numerical solutions of the two-dimensional N-S equations were obtained by the MAC(marker-and-cell)method. Hot wire measurements were conducted in the boundary layer on a flat plate in a low-turbulence wind tunnel. A sinusoidal fluctuation, which grows exponentially, is observed behind the roughness element. The characteristics of sinusoidal fluctuation(linear region)depend on κ / δ*κ, where κ is the height of the roughness element and δ*κ is the displacement thickness at the roughness element. At κ / δ*κ=1.0, the predominant frequency of naturally excited sinusoidal fluctuation lies in the unstable zone, which is predicted using the theoretical calculation based on the Orr-Sommerfeld equation applied for Lin's profile. The response characteristics of the linear instability region to artificial external excitation were investigated in detail using sound as an exciting agent. Also, flow fields with forced time-dependent disturbances are studied by the numerical method. The effects of the artificial external excitation become maximum when the frequency of disturbance coincides with the natural frequency. The numerical results for the linear instability region(frequency, phase velocity and amplification rates)agree with the experimental measurements

Grazing incidence propagation over a soft rough surface

Attenborough has recently proposed [J. Acoust. Soc. Am. 98, 1717–1722 (1995)] that the effects of surface roughness on an otherwise flat surface of finite acoustic admittance can be modeled as a smooth flat surface with an effective acoustic admittance β*. This effective admittance is determined by the normalized admittance βs and wave number ks of the original smooth surface, as well as a surface roughness parameter σν. Attenborough tested his theory by conducting excess attenuation measurements over plywood and Styrofoam surfaces with two-dimensional roughness elements. Specifically, he investigated the interference pattern between the direct and reflected signals over both smooth and rough surfaces. Experiments are conducted here with three-dimensional roughness elements at grazing incidence. Such a configuration is typical for outdoor sound propagation problems. The results presented here generally confirm Attenborough’s model and open up the analogy to a broader class of problems. It was also found that placing the effective admittance plane at the top of the roughness elements rather than at the bottom yielded slightly better results for the higher acoustic frequencies investigated.

Experimental and Computational Study of the Effect of Two-Dimensional Roughness on the Mean Velocity of a Laminar Boundary Layer.

In this report an experimental and computiational study of the flow behind a two-dimensional square roughness element placed in a laminar boundary layer on a flat plate is described Numerical solutioins of the two-dimensional N-S equations were obtained by the MAC(Marker-and-Cell)method. The experiment was carried out in a low-turbulence wind tunnel. The flow behind the roughness element consisted of a separated region and an external layer. There was no mass transfer between these regions. The computational and the experimental results for these regions were compared. The extent of the separated region depends on κ / δ*κ, where κ is the height of the roughness element and δ*κ is the displacement thickness at the roughness element. When κ / δ*κ is less than a critical value, the computational results agree with the experimental results. The boundary-layer flow separates at the roughness element and returns at 70-κ to the laminar boundary layer. In this case the length of the separated region increases with κ / δ*κ. When κ / δ*κ is larger than the critical value, the length of the separated region decreases with increasing κ / δ*κ, but the computational results do not agree with the experimental ones.

Linear and nonlinear evolution of boundary layer instabilities generated by acoustic-receptivity mechanisms

Experimental results are presented concerning the evolution of instabilities generated by the interaction between low-level broad-band acoustic waves and small two-dimensional roughness elements. Streamwise perturbation velocity spectra are measured and it is found that on the smooth plate, naturally-occurring Tollmien-Schlicting (T-S) waves grow in a manner consistent with a resonant subharmonic wave interaction. However, in the presence of small two-dimensional roughness elements, a strong primary T-S mode is forced by an interaction with the background acoustic field. This leads to a K-type of nonlinear interaction characterized by the generation of harmonics (up to six harmonics are observed) at the expense of the subharmonic. The scaling of the T-S waves and their harmonics with the number and amplitude of the wall roughness is also considered.

Application of the Spectral Multidomain Method to the Navier-Stokes Equations

An application of the spectral multidomain method to the two-dimensional, time-dependent, incompressible Navier-Stokes equations is presented. The governing equations are discretized on a non-staggered, stretched mesh with a mixed finite difference/Chebyshev method and are integrated by a time-splitting procedure. The accuracy of the multidomain method is demonstrated for two different channel flow configurations, one with a backward-facing step and the other with a rectangular step. The method is then applied to the investigation of the effects of an isolated, two-dimensional roughness element on the spatial development of instability waves in boundary layers.

FLOW ABOUND TWO-DIMENSIONAL ROUGHNESS ELEMENTS

Flow around two-dimensional roughness elements in the form of rectangular blocks has been analyzed for reynolds number 0 ≤Re≤40 and blocks of aspect ratio 0.01 ≤W/h≤∞. A very good agreement exists between numerical and experimental results. The size of the upstream separation zone weakly depends on the length of the block but decreases rapidly with an increase of the Reynolds number. In contrast, the length of the downstream separation zone increases almost linearly as Re increases. While this length depends weakly on the aspect ratio of the block, the velocity magnitude inside the separation zone considerably increases with a decrease of the length of the block. The coupling between the upstream and downstream separation zones rapidly disappears when W/h increases and both zones can be considered independent and identical to those at the upstream and downstream facing steps with W/h≥6.

Observations of near-bed velocity profiles and seabed roughness in tidal currents flowing over sandy gravels

Measurements of near-bed velocity profiles and bottom roughness in tidal currents flowing over sandy gravels in the west Solent, England, have shown that, although the seabed in the immediate vicinity of the study area was generally level and devoid of regular bed forms, the observed velocity profiles were consistently curved concave downwards. This behaviour may be attributed to the presence of an internal boundary layer which was due to form drag on irregular topography upstream of the measurement position. Loosely packed gravels of the type found in the west Solent had a geometric mean roughness length of about 0·3 cm. Comparison of the observed ratio of roughness length to mean particle size with laboratory data, suggests an equivalent two-dimensional roughness element spacing of about three particle diameters. In contrast to tidal flows over rippled sand beds, the roughness lengths for sandy gravels remained relatively constant throughout the tidal cycle. Furthermore, these measurements provided no systematic evidence of the effects of flow acceleration on profilederived estimates of the friction velocity u ∗ and the roughness length z 0.

Form drag resistance of two-dimensional stepped steep open channels

Flow in rough steep open channels is mostly found in mountain streams and in flow overtopping protected weirs. In both cases, the energy of the flowing stream may be dissipated by artificial means so that the flowing water does not result in serious damage due to scour or erosion downstream of the main slope. The best way of achieving this purpose is to lead the flow over a series of steps. In this investigation, the author tried to determine the form drag of stepped steep open channels, considering the steps as two-dimensional triangular roughness elements. Key words: open channel flow, flow resistance, channel roughness, form drag, steep channels.

Flow Formed by Spanwise Gaps Between Roughness Elements

Measurements of the three mean velocity components and the three Reynolds shear stresses were made in the region downstream of gaps between wall-mounted roughness elements of square cross section and high aspect ratio in a thick turbulent boundary layer. The effect of small and large gaps was studied in a wind tunnel at a Reynolds number of 3600, based on obstacle height and free-stream velocity. The small gap produces retardation of the gap flow as with a two-dimensional roughness element, but a definite interaction between gap and wake flows is observed. The interaction is more intense for the large gap than for the small. Both gaps generate a secondary crossflow which moves fluid away from the centerline in the wall region and toward the centerline in the outer (y &gt; 1.5H) region.

Effects caused by small discrete two-dimensional roughness elements immersed in turbulent boundary layers

Effects caused by small discrete two-dimensional roughness elements immersed in turbulent boundary layers

障壁後流に関する風洞模型実験 : 模型設置位置の境界層および模型のアスペクト比の影響について

Wind tunnel experiments concerned with the air flows behind the bluff-plates are described. The experiments with wind tunnel are to investigate the followings ; (1) The effects of the profiles of the approaching flows on the cavities of the two-dimensional bluff-plate model, (2) The effects of the aspect ratios of the bluff-plate models on the cavities of them. In the experiment (1), the wind velocity profiles of the approaching flows are changed in six degrees by the regular arrangements of two-dimensional roughness elements in up-stream region of the two-dimensional bluff-plate model. In the experiment (2), the aspect ratios of the bluff-plate models are varied from 16 to 2. Each bluff-plate is placed under the same boundary layer of the approaching flow. Mean and turbulent velocities are measured two-dimensionally by I-type hot-wire anemometer. Flow reattachment lengths, turbulent intensity profiles and the peak frequencies of power spectra are investigated in relation to H/δ, H/z_0 and W/H, in which H and W are the height and the width of bluff-plate model, δ and z_0 are boundary layer thickness and roughness parameter of approaching flow, respectively.

Turbulent flow over a periodic rough surface

In a deep, turbulent flow with negligible advection, flowing over a surface roughened by regularly spaced, two-dimensional roughness elements, measured Reynolds shear stress decreased as the surface was approached. The depth of the region of shear-stress deficit was of the order of ten element spacings. Streamwise variations in mean velocities were unable to account for the magnitude of the shear-stress deficit, and the log-law estimate of surface shear disagreed with that measured directly by a drag balance. The data are presented as further information on a puzzling phenomenon.

Mechanism by Which a Two-Dimensional Roughness Element Induces Boundary-Layer Transition

An experimental investigation of the effect of two-dimensional roughness elements on boundary-layer transition is described. Primary emphasis is given to the nature of disturbances within the recovery zone, i.e., that region in the immediate downstream of the roughness where the mean flow has been distorted by the presence of the roughness. Detailed measurements of mean velocity distributions, of disturbance spectra, and intensity, growth, and decay of disturbances at discrete frequencies were made for a range of unit Reynolds numbers. The measurements demonstrate that the behavior can best be understood by considering wave-type disturbances, and that the basic mechanism by which a two-dimensional roughness element induces earlier transition to turbulent flow is by the destabilizing influence of the flow within the recovery zone. Comparison with the behavior expected from stability theory supports this conclusion.

Predictions on momentum, heat and mass transfer in turbulent channel flow with the aid of a boundary layer growth-breakdown model

This paper deals with theoretical aspects of momentum, heat and mass transfer in turbulent channel flow and in particular with phenomena occurring close to the wall. The analysis presented involves the use of a boundary-layer growth-breakdown model. Theoretical expressions have been derived predicting heat and mass transfer at smooth surfaces in the fully developed and entrance region and at surfaces provided with “ideal” two-dimensional roughness elements. The analysis is restricted to fluids having Prandtl and Schmidt numbers larger than one. Good agreement appears to exist between theoretical predictions and experimental observations.

An experimental investigation of heat transfer from a highly cooled turbulent boundary layer.

Shocktube measurements of turbulent heat transfer in supersonic, dissociated air and in the presence of a zero pressure gradient are presented for incident shock velocities from 3 to 6 mm//zsec and initial driven tube pressures of 5, 8, 10, and 20 mm Hg. These data were obtained using platinum calorimeter gages positioned on the inside surface of a sharp leadingedge hollow cylinder with its axis aligned parallel to the frees tream flow. The range of conditions included Reynolds numbers from approximately 10 to 1.4 X 10, total enthalpies simulating flight velocities up to 8 km/sec, and walltoadiabaticwall enthalpy ratios from 0.01 to 0.04. Two-dimensional roughness elements were used to trip the boundary layer. The data obtained are compared with a number of existing techniques for the prediction of turbulent heating. Although the data was obtained at conditions outside of the range on which the method of Spalding and Chi is based, reasonable agreement with this method is shown to exist. Comparisons of existing methods of prediction are also made with other experimental data available from the literature.

Improved heat-transfer performance with boundary-layer turbulence promoters

A substantial improvement in forced-convection heat-transfer conductance is required for the development of advanced steam-cooled and gas-cooled power reactor systems. Boundary-layer turbulence promoters on the heated surfaces are of great interest for these systems because of the large increase in the heat-transfer performance which can be attained. However, much of the experimental data on turbulence promoters has been obtained in annular flow passages, and it is necessary to transform these data in order to apply them to reactor configurations. This investigation of boundary-layer turbulence promoter performance was carried out in arrays of parallel rods, the configuration of greatest interest for engineering applications. Discrete two-dimensional roughness elements, in the form of small fins transverse to the flow, were investigated experimentally to establish the effect of promoter height and promoter spacing. The results are directly applicable for optimization of heat-transfer performance, and also provide a basis for evaluating transformation techniques used for data obtained in annular passages.