Dynamics of a Taylor bubble in steady and pulsatile co-current flow of Newtonian and shear-thinning liquids in a vertical tube

A computational analysis is carried out to ascertain the effects of steady and pulsatile co-current flow, on the dynamics of an air bubble rising in a vertical tube containing water or a solution of Carboxymethylcellulose (CMC) in water. The mass fraction (m_f) of CMC in the solution is varied in the range 0.1% ⩽ m_f ⩽ 1% to accommodate zero-shear dynamic viscosities in the range 0.009–2.99 Pa-s. It was found that the transient and time-averaged velocities of Taylor bubbles are independent of the bubble size under both steady as well as pulsatile co-current flows. The lengths of the Taylor bubbles under the Newtonian conditions are found to be consistently greater than the corresponding shear-thinning non-Newtonian conditions for any given zero-shear dynamic viscosity of the liquid. In contrast to observations in stagnant liquid columns, an increase in the dynamic viscosity of the liquid (under Newtonian conditions) results in a concomitant increase in the bubble velocity, for any given co-current liquid velocity. In shear-thinning liquids, the change in the bubble velocity with an increase in m_f is found to be relatively greater at higher co-current liquid velocities. During pulsatile shear-thinning flows, distinct ripples are observed to occur on the bubble surface at higher values of m_f, the locations of which remain stationary with reference to the tube for any given pulsatile flow frequency, while the bubble propagated upwards. In such a pulsatile shear-thinning flow, a localised increase in dynamic viscosity is accompanied near each ripple, which results in a localised re-circulation region inside the bubble, unlike a single re-circulation region that occurs in Newtonian liquids, or shear-thinning liquids with low values of m_f. It is also seen that as compared to frequency, the amplitude of pulsatile flow has a greater influence on the oscillating characteristics of the rising Taylor bubble. The amplitude of oscillation in the bubble velocity increases with an increase in the CMC mass fraction, for any given value of pulsatile flow amplitude.     

Experimental investigation of certain aspects of upward vertical bubble and slug flows

The paper describes an installation, and measurements performed with its aid, in which it was possible to observe bubble flows as well as slug flows. Measurements and observations were carried out in vertical upward flow of water, with air injected into it, flowing through a plexiglass tube of 20 mm i.d. and 1500 mm long. The purpose of the investigation was to identify the parameters and influences which determine the observed flow pattern. The results show that there exists a range of values of the superficial velocity U _LS and U _GS in which it is possible to observe both flow patterns depending on the method of air injection employed. The transition zone bubble-slug shows reasonable agreement with the data of Taitel et al., whereas that for the slug-froth transition is close to the data of Oshinowa and Charles, and Griffith and Wallis. The distributions of bubble diameters and plug and Taylor-bubble dimensions are acceptably Gaussian. It is surmised that considerable discrepancies in the delineation of flow-regime boundaries which exist between different investigators are due to hitherto unidentified influences and parameters.List of symbols a distance between aligned bubbles - C ₀ distribution parameter - D inner tube diameter - d _S bubble diamter - L _b length of a Taylor bubble - L _E entrance length - L _S length of liquid plug - U _G actual gas velocity - U _GS superficial gas velocity: - U _L actual liquid velocity - U _LS superficial liquid velocity: - U _S superficial velocity - t time - average void fraction     

Terminal velocities of clean and fully-contaminated drops in vertical pipes

Terminal velocities and shapes of drops rising through vertical pipes in clean and fully-contaminated systems are measured by using a high-speed video camera and an image processing method. Silicon oils and glycerol water solutions are used for the dispersed and continuous phases, respectively. Triton X-100 is used for surfactant. Clean and contaminated drops take either spherical, spheroidal or deformed spheroidal shapes when the diameter ratio λ is less than a critical value, λ_C, whereas they take bullet shapes for λ > λ_C (Taylor drops). The applicability of available drag and Froude number correlations is examined through comparisons with the measured data. Effects of surfactant on the shape and terminal velocity of a Taylor drop are also discussed based on the experimental data and interface tracking simulations. The conclusions obtained are as follows: (1) drag and Froude number correlations proposed so far give reasonable estimations of the terminal velocities of clean drops at any λ, (2) the terminal velocities of contaminated drops are well evaluated by making the viscosity ratio μ^* infinity in the drag correlation for clean drops in the viscous force dominant regime, (3) the effects of surfactant on the shape and terminal velocity of a Taylor drop become significant as the Eötvös number, Eo_D, decreases and μ^* increases, and (4) the reduction in surface tension due to the addition of surfactant would be the cause of the increase in the terminal velocity and elongation of a contaminated Taylor drop.     

Unsteady separated and reattaching turbulent flow over a two-dimensional square rib

The spatio-temporal characteristics of the separated and reattaching turbulent flow over a two-dimensional square rib were studied experimentally. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. Profiles of time-averaged streamwise velocity and wall-pressure fluctuations showed that the shear layer separated from the leading edge of the rib sweeps past the rib and directly reattaches on the bottom wall (x/H=9.75) downstream of the rib. A thin region of reverse flow was formed above the rib. The shedding large-scale vortical structures (fH/U₀=0.03) and the flapping separation bubble (fH/U₀=0.0075) could be discerned in the wall-pressure spectra. A multi-resolution analysis based on the maximum overlap discrete wavelet transform (MODWT) was performed to extract the intermittent events associated with the shedding large-scale vortical structures and the flapping separation bubble. The convective dynamics of the large-scale vortical structures were analyzed in terms of the autocorrelation of the continuous wavelet-transformed wall pressure, cross-correlation of the wall-pressure fluctuations, and the cross-correlation between the wall pressure at the time-averaged reattachment point and the streamwise velocity field. The convection speeds of the large-scale vortical structures before and after the reattachment point were U_c=0.35U₀ and 0.45U₀, respectively. The flapping motion of the separation bubble was analyzed in terms of the conditionally averaged reverse-flow intermittency near the wall region. The instantaneous reattachment point in response to the flapping motion was obtained; these findings established that the reattachment zone was a 1.2H-long region centered at x/H=9.75. The reverse-flow intermittency in one period of the flapping motion demonstrated that the thin reverse flow above the rib is influenced by the flapping motion of the separation bubble behind the rib.     

On the interaction of Taylor bubbles rising in two-phase co-current slug flow in vertical columns: turbulent wakes

An experimental study on the interaction between Taylor bubbles rising through a co-current flowing liquid in a vertical tube with 32 mm of internal diameter is reported. The flow pattern in the bubble's wake was turbulent and the flow regime in the liquid slug was either turbulent or laminar. When the flow regime in the liquid slug is turbulent (i) the minimum distance between bubbles above which there is no interaction is 5D-6D; (ii) the bubble's rising velocity is in excellent agreement with the Nicklin relation; (iii) the experimental values of the bubble length compare well with theoretical predictions (Barnea 1990); (iv) the distance between consecutive bubbles varied from 13D to 16D and is insensitive to the liquid Reynolds number. When the flow regime in the liquid slug is laminar (i) the wake length is about 5D-6D; (ii) the minimum distance between bubbles above which there is no interaction is higher than 25D; (iii) the bubble's rising velocity is significantly smaller than theoretical predictions. These results were explained in the light of the findings of Pinto et al. (1998) on coalescence of two Taylor bubbles rising through a co-current liquid. Received: 2 February 2000 / Accepted: 15 March 2001     

Upward and downward inclination oil–water flows

The effect of upward (+5°, +10°) and downward (−5°) pipe inclinations on the flow patterns, hold up and pressure gradient during two-liquid phase flows was investigated experimentally for mixture velocities between 0.7 and 2.5 m/s and phase fractions between 10% and 90%. The investigations were performed in a 38 mm ID stainless steel test pipe with water and oil as test fluids. High-speed video recording and local impedance and conductivity probes were used to precisely identify the different flow patterns. In both positive and negative inclinations the dispersed oil-in-water regime extended to lower mixture velocities and higher oil fractions compared to horizontal flow. A new flow pattern, oil plug flow, appeared at both +5° and +10° inclination while the stratified wavy pattern disappeared at −5° inclination. The oil to water velocity ratio was higher for the upward than for the downward flows but in the majority of cases and all inclinations oil was flowing faster than water. At low mixture velocities the velocity ratio increased with oil fraction while it decreased at high velocities. The increase became more significant as the degree of inclination increased. The frictional pressure gradient in both upward and downward flows was in general lower than in horizontal flows while a minimum occurred at all inclinations at high mixture velocities during the transition from dispersed water-in-oil to dual continuous flow.     

Interaction between Taylor bubbles rising in stagnant non-Newtonian fluids

The interaction between Taylor bubbles rising in stagnant non-Newtonian solutions was studied. Aqueous solutions of carboxymethylcellulose (CMC) and polyacrylamide (PAA) polymers were used to study the effect of different rheological properties: shear viscosity and viscoelasticity. The solutions studied covered a range of Reynolds numbers between 10 and 714, and Deborah numbers up to 14. The study was performed with pairs of Taylor bubbles rising in a vertical column (0.032 m internal diameter) filled with stagnant liquid. The velocities of the leading and trailing bubbles were measured by sets of laser diodes/photocells placed along the column. The velocity of the trailing bubble was analysed together with the liquid velocity profile in the wake of a single rising bubble (Particle Image Velocimetry data obtained from the literature). For the less concentrated CMC solutions, with moderate shear viscosity and low viscoelasticity, the interaction between Taylor bubbles was similar to that found in Newtonian fluids. For the most concentrated CMC solution, which has high shear viscosity and moderate viscoelasticity, a negative wake forms behind the Taylor bubbles, inhibiting coalescence since the bubbles maintain a minimum distance of about 1D between them. For the PAA solutions, with moderate shear viscosity but higher viscoelasticity than the CMC solutions, longer wake lengths are seen, which are responsible for trailing bubble acceleration at greater distances from the leading bubble. Also in the PAA solutions, the long time needed for the fluid to recover its initial shear viscosity after the passage of the first bubble makes the fluid less resistant to the trailing bubble flow. Hence, the trailing bubble can travel at a higher velocity than the leading bubble, even at distances above 90D.     

Bubbly jets in stagnant water

Air–water bubbly jets are studied experimentally in a relatively large water tank with a gas volume fraction, C_o, of up to 80% and nozzle Reynolds number, Re, ranging from 3500 to 17,700. Measurements of bubble properties and mean axial water velocity are obtained and two groups of experiments are identified, one with relatively uniform bubble sizes and another with large and irregular bubbles. For the first group, dimensionless relationships are obtained to describe bubble properties and mean liquid flow structure as functions of C_o and Re. Measurements of bubble slip velocity and estimates of the drag coefficient are also provided and compared to those for isolated bubbles from the literature. The study confirms the importance of bubble interactions to the dynamics of bubbly flows. Bubble breakup processes are also investigated for bubbly jets. It was found that a nozzle Reynolds number larger than 8000 is needed to cause breakup of larger bubbles into smaller bubbles and to produce a more uniform bubble size distribution. Moreover, the Weber number based on the mean water velocity appears to be a better criteria than the Weber number based on the bubble slip velocity to describe the onset of bubble breakup away from the nozzle, which occurs at a Weber number larger than 25.     

Lift force acting on single bubbles in linear shear flows

Lift coefficients, C_L, of single bubbles in linear shear flows are measured to investigate effects of the bubble shape, the liquid velocity gradient and the fluid property on C_L. The range of the Morton number, M, tested is from logM = − 6.6 to − 3.2. The shapes of bubbles are spherical and ellipsoidal. A correlation of bubble aspect ratio for single bubbles in infinite stagnant liquids proposed in our previous study can give good evaluations for bubbles in the linear shear flows. The C_L of spherical bubbles at low bubble Reynolds numbers, Re, depend on the dimensionless shear rate Sr and Re and decrease with increasing Re. These characteristics agree with the Legendre-Magnaudet correlation. The use of a single dimensionless group such as Re, the Eötvös number, the Weber number and the Capillary number cannot correlate C_L of non-spherical bubbles. The trend of the critical Re for the reversal of the sign of C_L is the same as that for the onset of oscillation of bubble motion, which supports the mechanism proposed by Adoua et al., at least within the range of −6.6 ≤ logM ≤ −3.2. An experimental database of C_L is provided for validation of available C_L models and CFD.     

Reynolds Number Dependence of Mixed Structure Functions of Temperature and Longitudinal Velocity

Reynolds number dependence of mixed structure functions of longitudinal velocity u and temperature Θ is examined over a R _λ (Taylor microscale Reynolds number) range of 180-5950 for four flows. It is found that the mixed structure functions exhibit some behaviours similar to those of individual ones of the velocity and temperature. The prediction of the bivariate lognormal model for the R _λ dependence of the mixed structure functions is approached by the present measurements only at very high R _λ. At values of the longitudinal separation r close to the integral length scale as well as Taylor microscale, the velocity and temperature increments are not statistically independent. Several methods have been used to estimate the intermittency exponents μ and μ_Θ of the velocity and temperature in the lognormal model. Each method yields a different value of μ and μ_Θ, which also depend on R _λ and the type of flows. The present measurements suggest that the best estimates for μ and μ_Θ are 0.25 ± 0.05 and 0.30 ± 0.05, respectively.     

Numerical simulation of a bubble rising in shear-thinning fluids

The motion of a single bubble rising freely in quiescent non-Newtonian viscous fluids was investigated experimentally and computationally. The non-Newtonian effects in the flow of viscous inelastic fluids are modeled by the Carreau rheological model. An improved level set approach for computing the incompressible two-phase flow with deformable free interface is used. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The simulation results demonstrate that the algorithm is robust for shear-thinning liquids with large density (ρ₁/ρ_g up to 10³) and high viscosity (η₁/η_g up to 10⁴). The comparison of the experimental measurements of terminal bubble shape and velocity with the computational results is satisfactory. It is shown that the local change in viscosity around a bubble greatly depends on the bubble shape and the zero-shear viscosity of non-Newtonian shear-thinning liquids. The shear-rate distribution and velocity fields are used to elucidate the formation of a region of large viscosity at the rear of a bubble as a result of the rather stagnant flow behind the bubble. The numerical results provide the basis for further investigations, such as the numerical simulation of viscoelastic fluids.     

An experimental study of gas-liquid slug flow

Experimental measurements were carried out for upward gas-liquid slug flow in a 50.8 mm diameter pipe. Parallel conductance wires were used to distinguish the Taylor bubbles and liquid slugs and to determine translation velocities and lengths, an electrochemical probe provided the magnitude and direction of the wall shear stress and a radio-frequency local probe was used for the axial and radial distribution of voidage in the liquid slugs. Data are reported over wide range of flow conditions covering slug flow and into the churn flow pattern. Comparison with the Fernandes model predictions are presented. Numerical simulation of slug flow provided information on the structure of flow in a liquid slug and, in particular, on the process of mixing behind a Taylor bubble.List of symbols D pipe diameter - f Taylor bubble frequency - F _Gi (x) gas existence function for i-th liquid slug - g gravitational acceleration - l _A distance for the wall shear stress reversal in a liquid slug - l _B distance for the wall shear stress reversal in a Taylor bubble region - l _LS length of a liquid slug - l _TB length of a Taylor bubble - n number of samples in an ensemble - u axial velocity - U _M superficial mixture velocity (U _SG + U_SL) - U _N translation velocity of the leading Taylor bubble - U _NLS average translation velocity of liquid slugs - U _NTB average translation velocity of Taylor bubbles - U _OT overtaking velocity of the trailing Taylor bubble - U _SG superficial gas velocity - U _SL superficial liquid velocity - v radial velocity - w (y) velocity profile at the inlet to a liquid slug - x axial coordinate - y radial coordinate - void fraction - _LS void fraction in a liquid slug - =l _TB /(l_TB + l_LS) - density - surface tension - shear stress - saturation ratio, = _w / g h - ensemble average     

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining a transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval (U _c , 2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. The value of U _c decreases monotonically from 2 to 1 as the bubble area increases from 0 to . However, for a bubble of an arbitrarily given size, as T 0, a solution exists on any given branch with the relative bubble velocity U satisfying the relation 2–U=cT ^2/3, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U>2. These results are in agreement with earlier analytical results for a finger.In Part II an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.This research has been supported by National Science Foundation Grant DMS-8713246. Partial support was also provided by the NASA Langley Research Center (NAS1-18605) while the author was in residence at the Institute of Computer Applications in Science and Engineering.     

FLOW PAST A 2-D BACKWARD-FACING STEP WITH AN OSCILLATING WALL

The spatial-temporal movements of the reattachment (x_r) and separation (x_s) points in a 2-D backward-facing step flow with a bottom wall oscillated sinusoidally at selected frequencies and amplitudes were characterized using multiple hot-film sensor arrays and smoke flow visualization methods. The results also show that both x_rand x_smoved toward (away from) the step during upward (downward) motion of the wall, and that their rate of variation or the covered distance is a strong function of the wall oscillation. The present measurements would provide a practical means for the study of unsteady separated flows, as well as for the validation of CFD modelling.     

Experimental study of single bubble motion in a liquid metal column exposed to a DC magnetic field

The motion of single Argon bubbles rising in the eutectic alloy GaInSn under the influence of a DC longitudinal magnetic field (parallel to the direction of bubble motion) was examined. The magnetic field strength was varied up to 0.3 T corresponding to a magnetic interaction parameter N (which measures the ratio of electromagnetic forces to inertial forces) slightly greater than 1. The liquid metal was at rest in a cylindrical container. Bubble and liquid velocities were measured using ultrasound Doppler velocimetry (UDV). The measured bubble terminal velocity showed oscillations indicating a zigzag movement of ellipsoidal bubbles. For small bubbles (d_e ⩽ 4.6 mm) an increase of the drag coefficient with increasing magnetic interaction parameter N was observed, whereas for larger bubbles (d_e ⩾ 5.4 mm) the application of the magnetic field reduces the drag coefficient. The measurements revealed a distinct electromagnetic damping of the bubble induced liquid velocity leading to more rectilinear bubble trajectories when the magnetic field is applied. Moreover, significant modifications of the bubble wake structure were observed. Raising of the magnetic field strength caused an enlargement of the eddies in the wake. The Strouhal number decreases with increasing magnetic interaction parameter N.     

Direct resolution of differential pressure fluctuations to characterize multi-scale dynamics in a gas fluidized bed

A direct resolution approach was proposed to decompose differential pressure signals from a gas fluidized bed into macro- and super-imposing components, which were further subjected to structure density function analysis (SDF analysis) to study dynamics of multi-scale structures in flow. Direct resolution performed well in extracting feature information of multi-scale structures, especially macro- and meso-scale structures whose dynamic behaviors majorly affected hydrodynamics in bed, from measured differential pressure fluctuations. With the assistance of Gaussian fitting and Kolmogorov–Smirnov test, SDF analysis divided the probability distribution of multiple structures with respect to their amplitude scale r into four feature regions (Regions B-I, B-II, B-III and Region A). Parameter K_SDF derived from slope of Region B-II quantified frequency of various meso-scale structures in flow, and well followed the tendency of flow patterns transition after being normalized by bubble (slug) rising velocity U_b(sl). Frequency of macro-scale structures in slugging flow depended greatly on rising velocity of slugs, so SDF_macro increased with increased fluidization velocity. Developed turbulent flow had a high SDF_macro exceeded 0.8 Hz due to the fast passage and split/integration of large voids. Structures localized in Region A mainly represented noise from measurements, other measurable micro-scale disturbances in single phases or phase-interfaces, and had an occurring frequency increased with increase of fluidization velocity.     

A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct

For the two cavity models whose upward and downward wall heights are different from each other, laminar heat transfer is studied numerically in a finite difference method. The effects of cavity configuration, free-stream velocity and buoyancy force on flow and temperature fields as well as heat transfer at the bottom surface are discussed. The flow pattern of DOF (Downward-Facing cavity)-model is more intricated than that of UPF (Upward-Facing cavity)-model, depending on the aspect ratio of cavity or main flow velocity. The mean Nusselt numberNu _m at the bottom surface of both cavity models tends generally to increase with increasing Re_HorGr _w/Re _H ² . However, in the flow region ofRe _H & 500 for DOF-cavity, theNu _m for 0.4 ≦ D₂/D₁ ≦ 0.6 is somewhat lower than that obtained from the other cavities and does not always increase with increasingRe _H.     

Effects of hydrophilic particles on bubbly flow in slurry bubble column

To investigate the effects of hydrophilic particles on slurry bubble flows in a bubble column, distributions of the local gas holdup and the bubble frequency are measured using an electric conductivity probe. Particles are made of silica and their diameter is 100 μm. The particle volumetric concentration C_S is varied from 0 to 0.40. The measured data imply that the presence of particles promotes bubble coalescence. The film drainage time for two coalescing bubbles in a quasi two-dimensional bubble flow in a small vessel is also measured to quantitatively evaluate the particle effect on coalescence. A particle-effect multiplier is introduced into a coalescence efficiency model by taking into account the data of film drainage time and is implemented into a multi-fluid model. The main conclusions obtained are as follows: (1) the local gas holdup and bubble frequency in slurry bubble flows decrease with increasing the particle concentration, (2) the hydrophilic particles enhance bubble coalescence and the enhancement saturates at C_S ≃ 0.45, (3) the particle effect on coalescence is well accounted for by introducing the particle-effect multiplier to the film drainage time, and (4) the multi-fluid model can give good predictions for the distribution of the local gas holdup in the slurry bubble column.     

Particle convective heat transfer near the wall in a supercritical water fluidized bed by single particle model coupled with CFD-DEM

Supercritical water fluidized bed (SCWFB) is a promising reactor to gasify biomass or coal. Its optimization design is closely related to wall-to-bed heat transfer, where particle convective heat transfer plays an important role. This paper evaluates the particle convective heat transfer coefficient (h_pc) at the wall in SCWFB using the single particle model. The critical parameters in the single particle model which is difficult to get experimentally are obtained by the computational fluid dynamics-discrete element method (CFD-DEM). The contact statistics related to particle-to-wall heat transfer, such as contact number and contact distance, are also presented. The results show that particle residence time (τ), as the key parameter to evaluate h_pc, is found to decrease with rising velocity, while increase with larger thermal boundary layer thickness. τ follows a gamma function initially adopted in the gas–solid fluidized bed, making it possible to evaluate h_pc in SCWFB by a simplified single particle model. The theoretical predicted h_pc tends to increase with rising thermal gradient thickness at a lower velocity (1.5 U_mf), while first decreases and then increases at higher velocity (1.75 and 2 U_mf). h_pc occupies 30%–57% of the overall wall-to-bed heat transfer coefficient for a particle diameter of 0.25 mm. The results are helpful to predict the overall wall-to-bed heat transfer coefficient in SCWFB combined with a reasonable fluid convective heat transfer model from a theoretical perspective.     

Turbulent flow over a rough backward-facing step

This work characterizes the impacts of the realistic roughness due to deposition of foreign materials on the turbulent flows at surface transition from elevated rough-wall to smooth-wall. High resolution PIV measurements were performed in the streamwise-wall-normal (x–y) planes at two different spanwise positions in both smooth and rough backward-facing step flows. The experiment conditions were set at a Reynolds number of 3450 based on the free stream velocity U_∞ and the mean step height h, expansion ratio of 1.01, and the ratio of incoming boundary layer thickness to the step height, δ/h, of 8. The mean flow structures are observed to be modified by the roughness and they illustrate three-dimensional features in rough backward-facing step flows. The mean reattachment length X_r is significantly reduced by the roughness at one PIV measurement position while is slightly increased by the different roughness topography at the other measurement position. The mean velocity profiles at the reattachment point indicate that the studied roughness weakens the perturbation of the step to the incoming turbulent flow. Comparisons of Reynolds normal and shear stresses, productions of normal stresses, quadrant analysis of the instantaneous shear-stress contributing events, and mean spanwise vorticity reveal that the turbulence in the separated shear layer is reduced by the studied roughness. The results also indicate an earlier separation of the turbulent boundary layer over the current rough step, probably due to the adverse pressure gradient produced by the roughness topography even before the step.