An investigation of channel flow with a smooth air water interface

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1 Exp Fluids (5) 56:8 DOI.7/s RESEARCH ARTICLE An investigation of channel flow with a smooth air water interface Reza Madad John Elsnab Cheng Chin Joseph Klewicki, Ivan Marusic Received: December 4 / Revised: March 5 / Accepted: 9 March 5 / Published online: 9 June 5 Springer-Verlag Berlin Heidelberg 5 Abstract Experiments and numerical simulation are used to investigate full developed laminar and turbulent channel flow with an air water interface as the lower boundar condition. Laser Doppler velocimetr measurements of streamwise and wall-normal velocit components are made over a range of Renolds number based upon channel height and bulk velocit from to 4, which encompasses the laminar, transitional and low Renolds numbers turbulent regimes. The results show that the airflow statistics near the stationar wall are not significantl altered b the air water moving interface and reflect those found in channel flows. The mean statistics on the water interface side largel exhibit results similar to simulated Poiseuille Couette flow (PCF) with a solid moving wall. For secondorder statistics, however, the simulation and experimental results show some discrepancies near the moving water surface, suggesting that a full two-phase simulation is required. A momentum and energ transport tubes analsis is investigated for laminar and turbulent PCFs. This analsis builds upon the classical notion of a streamtube and indicates that part of the energ from the pressure gradient is transported towards the stationar wall and is dissipated as heat inside the energ tubes, while the remainder is transmitted to the moving wall. For the experiments, the This article belongs to a Topical Collection of articles entitled Extreme Flow Workshop 4. Guest Editors: I. Marusic and B. J. McKeon. * John Elsnab john.elsnab@unimelb.edu.au Department of Mechanical Engineering, Universit of Melbourne, Parkville, VIC, Australia Department of Mechanical Engineering, Universit of New Hampshire, Durham, NH 84, USA airflow energ is transmitted towards the water to overcome the drag force and drive the water forward; therefore, the amount of energ transferred to the water is higher than the energ transferred to a solid moving wall. Introduction Numerous engineering applications involve an interaction between a gas flowing adjacent to a moving liquid. This interaction has been investigated extensivel due to its application in the petroleum, chemical and nuclear industries as well as in geophsical and environmental sciences (Banerjee 7). Despite the efforts in this area of research, there remains an incomplete understanding of turbulent gas motion near a liquid interface. This arises from difficulties in experimentall measuring or numericall simulating velocit fields in the vicinit of moving surfaces and is further complicated b the turbulent nature of the flow in most applications of practical interest. The investigation of this flow (concurrent gas liquid flow) is considerabl complicated b the two-phase boundar condition. In this stud, we test how well a simplified Poiseuille Couette flow can be used to act as a prox for the real two-phase flow, and in doing so, clarif aspects of the underling phsics. A number of experimental studies have looked at the interaction between a turbulent airflow and a water film flowing parallel to it. Onl a few, however, have looked at the present configuration, which is an air water channel. Hanratt and Engen (957) conducted experiments in such a channel to examine the interaction between a turbulent air stream above a moving water film. Their results indicated no distortion in the airflow velocit profile for a smooth water surface and for a water surface with ripples. Hanratt and Engen (957) and Dkhno et al. (994)

2 8 Page of measured the air velocit profiles and found that the maximal velocit shifts % towards the stationar wall. These trends displa a significantl different behaviour with those observed b later researchers. For example, both Paras et al. (998) and Wongwises and Kalinitchenko () measured the air velocit profiles and found that the maximal velocit shifts towards the interface. The inconclusive results of this basic statistical quantit suggest that further stud is warranted. The objective of this research is to determine the effects of an air water interaction on the airflow statistics near the interface and stationar wall in a (nominall) full developed channel flow. The streamwise and wall-normal velocit components are obtained using two-component laser Doppler velocimetr (LDV). A surrogate direct numerical simulation (DNS) of a Poiseuille Couette flow is also performed using the experimentall obtained interface velocit as the boundar condition at δ + = 5, where δ + = δu τ /ν, δ is the half channel height, U τ is the friction velocit, and ν is the kinematic viscosit. This allows one to comment on the accurac of a reduced simulation, which is a substantiall cheaper computation to perform in comparison with a two-phase simulation. These comparisons also provide insights into the underling flow phsics. The flow phsics of the two-phase flow and PCF is further clarified using a momentum and energ transport tube analsis. Meers and Meneveau () describe the properties of momentum and energ transport tubes, which are analogous to a streamtube. Experimental details. Experimental facilit The experiments were conducted in the facilit schematicall shown in Fig.. The air height, H, is 4.9 mm with an aspect ratio of. The depth of the water beneath the air flow was 5 mm. The aspect ratio is sufficient to ensure a nominall two-dimensional flow (Dean 978). Air is drawn through the diffuser using a suction fan. Water circulation Exp Fluids (5) 56:8 was nominall promoted b a fixed speed pump in the direction of airflow. The pump alone produces a surface velocit of approximatel. m/s. The concurrent flow in combination with a weir generates a stable moving air water interface that was primaril driven b the airflow itself. Water enters the tank from a -mm-diameter PVC pipe that is split using two 8-mm-diameter pipes. The water then passes through two mesh screens and a honecomb section to ensure water flow uniformit at the channel inlet. The surface velocit of the water flow was quantified using a video camera to track insoluble Polethlene particles floating on the surface (specific gravit of.95.96). Also, it was observed that the pump (without running the fan) produces a water surface oscillation of less than ±.5 mm (.5 %H) and equates to.5.5 viscous units.. LDV measurements The LDV sstem was calibrated using two methods: a spinning disc (Park et al. ) and a spinning wire (Bean and Hall 999; Kurihara et al. ). The preferred method of calibration for a two-component LDV sstem is a spinning disc. The measurement volume is focused onto the surface of a roughened disc that is driven b a servomotor. The horizontal (U) and vertical (V) components of velocit were calibrated b positioning the measurement volume at 9 and, respectivel. The total uncertaint in both components was approximatel.5 %. A spinning wire was used to ensure that the LDV sstem sampling rate of each channel is correct. A significant difference between the spinning wire and disc methods is that onl a single particle (e.g. wire tip) passes through the probe volume per revolution in comparison with multiple particles. The nominal standard deviation in the sampling rate over a range in angular velocit from to 6 RPM for the U and V components is.6 and.9 /s, respectivel. The LDV measurement volume had dimensions of.85 mm in height,.85 mm in width and. mm in length for the blue beam (488. nm), and.89 mm in height,.89 mm in width and. mm in length for the green beam (54.5 nm) (Kurihara et al. ). The Y X Inlet Contraction Working Section Measurement Section Vertical Diffuser Horizontal Diffuser Fan Water 4.88 m m Weir AirBarrier Fig. Schematic of the experimental setup

3 Exp Fluids (5) 56:8 measurement volume in terms of viscous units was + z 7, +.5, and + x.5 at δ+ =. Further details regarding the LDV measurement volume, calibration methods, and results can be found in Madad ().. Inner normalization and scaling Scaling analsis of turbulence quantities requires an estimate of the wall shear stress, τ w. The friction velocit is derived from the wall shear stress, U τ = τ w /ρ, where ρ is the fluid densit. For full developed, two-dimensional Poiseuille Couette flow, use of the mean statement of momentum conservation ields, τ mw τ sw = H dp dx where τ mw = µ du d mw and τ sw = µ du d sw are the wall shear stress at the moving wall and stationar wall, respectivel, µ is the dnamic viscosit, p is the mean pressure, and x is the streamwise axis. The contribution from the vertical sidewalls contributes to the overall pressure drop in Eq., but is negligible since the aspect ratio is greater than. The friction velocit for the stationar wall, U τsw, and moving wall, U τmw, are determined using a four-point linear curve-fit of U within the linear sublaer. The uncertaint in the balance between the left-hand side and right-hand side of Eq. is less than 7 %. Telban and Renolds (98) suggested the moving wall velocit scaling is likel to be proportional to (/H).5 and γ, where γ, is the ratio of the Couette (HU mw /ν) to Poiseuille (HU b /ν) flow Renolds number, U b is the bulk velocit, and is the distance from the moving wall. In this stud, the following relationship proposed b Thurlow and Klewicki () is applied to obtain the local friction velocit of the moving wall U τmw = U τmw 5γ /H Using U τmw improves the collapse of the data in comparison with U τmw. Note that for the present analsis, this onl changes U τmw on average b 4.6 %..4 Experimental parameters The experimental data were measured at a fixed downstream distance of 7H from the inlet. This distance exceeds that required for full developed flow (H) (Lien et al. 4; Mont 4) for the case of solid wall channels. In the present case, the airflow can be considered streamwise homogeneous to a ver good approximation. Since the LDV settings are the same for all the measurements, the spatial resolution degrades slightl () () Page of 8 Table Parameters and smbol definition used in the data presentation Re δ + sw δ + mw U τ sw (m/s) U τ mw (m/s) Smbol Note that the subscript sw and mw denote stationar and moving wall, respectivel with increasing δ +. For parameter range and smbol definition, see Table. The lowest Renolds number, Re = HU b /ν = 7 (δ + = 4.4), is in the laminar regime and the remainder are in the transitionall turbulent regime with a smooth moving water surface. The highest Renolds number, Re = 467 (δ + = 4), corresponds to the first appearance of ripples on the water surface..5 Poiseuille Couette flow simulation The direct numerical simulation of Poiseuille Couette flow is based upon a spectral element/ Fourier spatial discretization with a second-order velocit-correction projection scheme for the temporal discretization as described b Blackburn and Sherwin (4). The Fourier coordinate requires geometric homogeneit in the spanwise direction, while the remaining planar geometr is discretized using nodal spectral elements with a Gauss Lobatto Legendre local mesh in each element. A tenth order Legendre polnomial is emploed within each spectral element. The computational domain length in the streamwise is L x = πδ, the spanwise width is L z = πδ, and the domain height is δ. This volumetric domain consists of 8 56 collocation points in the streamwise, spanwise and wall-normal directions, respectivel. There are at least 4 grid points within the buffer region, + = U τ /ν, with grid points within The chosen domain length is sufficient for the convergence of the statistics considered in this work according to Chin et al. (). For this simulation, the time-step is =. (dimensionless) and the collection of statistics is initiated after sufficient time (a minimum of five wash-through times based on the bulk flow speed and domain length) has elapsed to allow the flow to reach a statisticall stead state. The

4 8 Page 4 of Exp Fluids (5) 56:8 turbulence statistics are then averaged over wash-through times to achieve convergence. The simulation parameters are: x + = 9.94, + wall =.75, + centre =.5, and z + = The full developed turbulent PCF simulation is conducted at a Renolds number of δ + = 5. The fixed velocit of the moving water surface obtained from the experimental results is used as the boundar condition. At δ + = 5, the velocit at the air water interface is U mw =. m/s. C f.4.. Results.8 4 Re. Mean velocit profiles The mean velocit profiles normalized b the maximum velocit, U m, over the Renolds number range of 4 <δ + < 45 are presented in Fig. a. The analtical U U m U U m (a) H.4.6 Fig. Normalized mean velocit profiles for 4 <δ + < 45 (a). The smbol definition is presented in Table and the solid line corresponds to laminar PCF theor where the stationar wall is at /H =. A comparison between the mean velocit profile from the experiment and simulated PCF (dashed-line) at δ + = 5 is shown in.8.8 Fig. Skin friction coefficient values for < Re < 4 from the experiment. Description: filled diamond, stationar wall C f ; filled circle, moving water wall C f ; and solid line, Eq. (Dean 978) solution for laminar Poiseuille Couette flow is in agreement with the measured data at δ + = 4. As expected, the experimental data show that the mean velocit profiles flatten in the non-laminar regime. A comparison of the experimental mean velocit profile at δ + = 5 and simulated PCF is shown in Fig. b. The simulation data match the experimental data near the stationar wall ( < /H <.) and reasonabl well over the remainder of the channel height.. Skin friction The coefficient of friction, C f, for pure Poiseuille flows is obtained using Dean s equation (Dean 978) and is given as C f =.7 Re.5 The C f values obtained from Eq. and the experimental data for the stationar wall/moving water surface are shown in Fig.. Ver good agreement is seen between the stationar wall friction coefficients and the results of Dean s empirical equation. As expected from PCF with a forward moving wall, e.g. (Thurlow and Klewicki ), the values of C f for the moving side are lower than the stationar side; here, C f mw is on average about 5 % lower C f sw.. Inner normalized mean velocit profiles The inner-normalized mean velocit profiles for the stationar side and the moving side (using U τsw and U τmw, respectivel) are shown in Fig. 4a, b, respectivel. For the moving side, the water surface velocit is subtracted from the mean velocities. These profiles merge onto a single curve for + and collapse well on ()

5 Exp Fluids (5) 56:8 Page 5 of 8 (a) Stationar wall 5 (a) Stationar wall 5 U U Moving wall 5-5 Moving Wall U U U MW U U U MW Fig. 4 Inner-normalized mean velocit profiles for the stationar wall (a) and for the moving water surface. Description: smbols, see Table, dashed-line, U + = +, and the solid line, U + = /.4ln( + ) the U + = + curve within the viscous sublaer (Fig. 4). Beond + =, the higher Renolds number profiles approach a logarithmic-like dependence. These trends are similar to the results of Elsnab et al. () for postlaminar channel flows over a range of low Renolds numbers. Comparisons between the inner-normalized velocit profiles from the experiment and simulated PCF for the stationar and moving side are shown in Fig. 5a, b, respectivel, as well as DNS channel flow at matched δ +. The mean velocit profile obtained from the experiments and DNS nominall adhere to inner-scaling in the near-wall region and core flow. Also, the water motion does not have an appreciable effect on the stationar wall velocit profile. This observation is consistent with previous PCF studies [e.g. Telban and Renolds (98) and Thurlow and Klewicki ()]. For a fixed δ +, both the stationar wall and moving wall sides inner-normalized velocit profiles are in good agreement with DNS channel flow data b Laadhari () provided that the wall velocit is subtracted from the moving wall data. Fig. 5 Velocit profile of the stationar side (a) and the moving side. Description: smbols, see Table, solid line, simulation at δ + = 5 and channel flow DNS b Laadhari () where the dashdot line is at δ + = 9 and the dashed-line is at δ + =. Note that the profiles are shifted.5 viscous units for clarit.4 Turbulent velocit fluctuations The root-mean-square (rms) streamwise velocit fluctuations, u rms, for the stationar side is presented in Fig. 6a. The peak position in u rms for all experimental results is located at + 5, and the maximum value is on average about 5 % lower than DNS profiles of Tsukahara et al. (5) at δ + = 8 and. The u rms for the moving side is shown in Fig. 6b. The position of the peak u rms for the water side is + 7, and the maximum value is about 4 % lower than for the present stationar wall data (see Fig. 8a). These results are in good agreement with the observations of Thurlow and Klewicki () and Spencer et al. (9). The rms wall-normal velocit fluctuations, v rms, for the stationar wall along with channel flow DNS results b Tsukahara et al. (5) at δ + = 8 and are shown in Fig. 7a, and for the moving side in Fig. 7b. The variation in v rms from the stationar wall (/H = ) towards the moving water surface is shown in Fig. 8b. The peak wallnormal turbulence intensit near the air water interface

6 8 Page 6 of Exp Fluids (5) 56:8.5 (a) Stationar wall.8 (a) Stationar wall.6 u rms.5 rms Moving wall Moving wall.5.6 u rms U MW.5 rms U MW Fig. 6 RMS velocit fluctuations of the streamwise velocit. Description: dashed-line, δ + = 8, solid line, δ + = are from DNS channel flow data b Tsukahara et al. (5); and smbol definition, see Table (/H = ) at higher Renolds numbers, 4 δ + 44, is higher than near the stationar wall (/H = ). However, this is not the case for lower Renolds numbers, 76 δ + 8. For 76 δ + 8, the maximum value of v rms remains the same near the stationar and moving surfaces and shows similar behaviour to Poiseuille flow. For 4 δ + 44, the maximum value near the stationar wall is lower than the interface value. The effect of the moving water on v rms + does not agree with PCF studies and becomes more significant with increasing Renolds number. A possible explanation for this observation is the phsical difference between a solid moving wall and an air water interface (presence of water surface oscillation). Because the air water interface is compliant and not shearfree, the parallel surface fluctuations are not zero due to the slip boundar condition, as the are for a solid surface. Additionall, because the interface is compliant and onl kept flat b surface tension, the normal fluctuations can be larger near the interface. This, of course, depends on the relative strength of the interface stresses as compared to the turbulent pressure fluctuations. Fig. 7 Root-mean-square velocit fluctuations of wall-normal velocit. Description: dashed-line, δ + = 8, solid line, δ + = are from DNS channel flow data b Tsukahara et al. (5); and smbol definition, see Table The streamwise rms velocit fluctuation profiles of the simulated PCF and current experiment at δ + = 5 are essentiall identical for the stationar side, with the peak near the stationar wall located at + = 4 and 6 for the simulation and experiment, respectivel. Close to the moving water surface, however, the peak appears farther from the moving wall for the experiment ( + = ) than for the simulation ( + = 5). The peak of v + rms near the stationar wall is higher than the peak near the moving wall for the simulation, while the opposite occurs for the experiment at δ + = 5. The overall features of the experimentall derived rms profiles and their differences with the simulation are clarified in Fig. 8a, b..5 Renolds stress The inner-normalized Renolds stress profiles for both stationar wall and moving water side are shown in Fig. 9. The Renolds stress increases in peak value and the shifts outward in viscous units with increasing Renolds number for both the stationar and moving water side of the channel. The Renolds stress varies linearl from the peak towards

7 Exp Fluids (5) 56:8 Page 7 of 8 (a).8 (a) Stationar wall.5.6 u rms rms Moving wall Fig. 8 Root-mean-square velocit fluctuations of streamwise velocit (a) and root-mean-square velocit fluctuations of wall-normal velocit where /H = is the stationar wall. Description: solid line corresponds to the simulation at δ + = 5, and the smbol definition is presented in Table Fig. 9 Inner-normalized Renolds stress profiles for the stationar wall (a) and for the moving water surface. Smbol definition is presented in Table, and the solid line corresponds to the simulation at δ + = 5 the centreline for the stationar side and is nearl linear for the moving water side. This linear variation is consistent with channel flow results, which can be derived from classical analsis of the once-integrated mean momentum equation. For the moving side, the experimental data at δ + = 5 show much higher Renolds stress from the core region to the buffer laer (corresponding to.5 < /H <.9) compared to simulated PCF. Water level oscillations ma at least partl underlie this rather dramatic difference..6 Turbulence kinetic energ production The turbulent kinetic energ production, E + p () = < uv > + U + / +, is a dominant term in the kinetic energ budget. Profiles of E p + normalized b the stationar wall friction velocit for the experiment and simulation are shown in Fig.. Both profiles exhibit consistent results with diminishing energ production close to the channel centreline and peaks near both walls with amplification of E p + near the stationar wall and attenuation near E p Fig. Inner-normalized turbulent kinetic energ production profiles from the experiment and simulation. The solid line corresponds to the simulation at δ + = 5, and /H = is the stationar wall the moving wall. Spencer et al. (9) also observed a similar trend, as the energ production is lower close to the co-moving wall.

8 8 Page 8 of It is also of interest to consider the difference between the energ production profiles of experimental and simulated results for half of the channel towards the moving wall (.5 < /H < ). Although the peak near the moving wall (DNS) is higher than the peak near the moving water surface (experiment), the area under both profiles is approximatel the same, and the net energ production of the DNS is about 5 % larger than the experiment, which is attributed to the difference in <uv> + velocities since the mean velocit gradient is essentiall smmetric across the channel..7 Transport of momentum and energ Momentum and energ transport can be graphicall depicted using transport tube analses, which builds upon the classical notion of a streamtube. Meers and Meneveau () used these concepts to visualize turbulent flow processes associated with wind turbine arras. There is no exchange of momentum or energ through the corresponding tube mantle. Momentum and energ transport tubes, like streamtubes, are not Galilean invariant. The similarit between classical streamtubes and the momentum/energ transport tubes is that the flux is constant across sections except for integral effects of sinks and sources due to viscous dissipation and turbulent kinetic energ production. For stead, inviscid flow, streamtubes, momentum and energ transport tubes all coincide since the viscous and Renolds stress are zero. However, for turbulent flows, momentum tubes can be significantl different from the energ transport tubes due to the Renolds stresses. The combination of laminar Couette and Poiseuille flows is of interest because its structure provides a basis for better understanding of momentum and energ transport in the presence of a no-slip and a moving wall. The velocit profile for laminar PCF is U = (dp/dx)( H)/(µ) + U mw /H. Using the velocit profile, the two components of momentum flux are F =U = ( ) dp ( ) + U mw dx µ F = ν U ( = ν µ ) dp dx ( ) + U mw where it is assumed H =. Integration of d/dx = F /F and rearrangement allows the momentum lines, x = (x), to be written as x = C 8ν 4 + C U mw 4ν (C U mw) 6Cν (4) (5) (C U mw) 6C (C U mw) 4 ν C ln(u mw C + C) ν (6) Exp Fluids (5) 56:8 where C = (dp/dx)/(µ). The momentum transfer lines for different moving wall velocities are constructed using Eq. 6. The velocit profiles and corresponding momentum lines for different PCFs normalized with the moving wall velocit for a constant pressure gradient are shown in Fig.. The evolution of the momentum transport lines from Poiseuille-tpe flow (a) to Couette-tpe flow (d) is shown in these figures. The momentum added in the bulk flow through the pressure gradient is transported towards the sidewalls because the pressure gradient dominates. However, the location of the zero momentum transport line, Y ZCM=, continuall moves towards the moving wall with increasing wall velocit. At the zero momentum transport line, the total advection of momentum occurs horizontall. B increasing the moving wall velocit, the effect of Couette flow dominates over the pressure gradient and the momentum lines eventuall form a profile similar to pure Couette flow. The energ transport lines for laminar flow have similar shape as the momentum lines, but twice the slope. The interpretation for energ tubes for Poiseuille- and Couettetpe flows is as follows: for Poiseuille-tpe flow (Fig. a), the kinetic energ of the pressure gradient is dissipated as heat inside the tubes towards the stationar wall (top wall) and transferred to the moving wall (bottom wall). B increasing the moving wall speed, a larger part of the energ from the pressure gradient is transferred to the moving wall and converted to the work done b the moving wall. The rest of the energ is dissipated as heat inside the mantle and is directed towards the stationar wall (see Fig. b, c). For the Couette-tpe flow (Fig. d), the work done b the moving wall dominates over the pressure gradient, and the energ of moving wall is transferred entirel towards the stationar wall. This energ is dissipated as heat inside the energ tubes before reaching the stationar wall. The momentum lines for the laminar airflow PCF solution and the laminar experimental data are shown in Fig.. The momentum lines for the analtical and experimental results are similar, although the location of the zero momentum transport line from the experimental data moves slightl towards the moving water (.47H), in comparison with the analtical solution (.5H). As indicated with arrows in Fig., the momentum added to the bulk flow through the pressure gradient is transferred towards the stationar top wall and the moving water surface (bottom wall). The effect of the pressure gradient dominates over the effect of the moving wall (Couette effect), and the momentum lines of the current experiment are similar to the laminar pure Poiseuille flow. However, the location of the zero momentum transport line for the experimental results moves slightl towards the moving water surface. The momentum added b the pressure

9 Exp Fluids (5) 56:8 Page 9 of 8 (a).5.5 U U m U U m 4 8 (c).5.5 U U m 4 8 (d).5.5 U U m 4 8 Fig. Velocit profiles and momentum lines of laminar PCF with different moving wall velocit (a through d corresponds to the different velocit profiles shown at the left). The dashed-line is the zero momentum transport line. = is the stationar wall. Note that it is assumed H =

10 8 Page of Exp Fluids (5) 56:8 (a) (a) Fig. The momentum lines of the laminar airflow. Analtical solution for laminar PCF (a) and experimental data of the airflow with a moving water surface, where /H = is the stationar wall Fig. Energ lines of airflow for simulated data (a) and experimental data where /H = is the stationar wall gradient to the airflow is transmitted to the water, which in turn drives the water forward. The momentum from the moving water surface is then transported towards the stationar bottom wall of the water tank over a large streamwise distance (H)..7. Turbulent flow Using the results presented in Meers and Meneveau (), the two components of the energ flux for the turbulent airflow are formed as follows: F = U + U < uu > ( F =U < uv > ν U ) Hence, the slopes of the tangent lines of this vector field are given b: d dx = F F = U < uv > ν U + < uu > (7) (8) (9) Numerical integration ields an energ line for turbulent airflow with one stationar wall and a moving water surface. The energ lines of the experiment and simulation are shown in Fig.. The data in this figure reveal that the energ line of the simulated Poiseuille Couette flow with a moving solid wall for this Renolds number is similar to pure Poiseuille flow since the ratio of Couette to Poiseuille Renolds number is low (γ =.7). In addition, the location of the zero energ transport line (no vertical transport) is at the channel s centreline. However, the energ line of the current experiment shows its location moves significantl towards the moving wall (/H.). Near both the stationar and the moving wall, the transport lines become vertical as more of the energ transport occurs through viscous diffusion. Close to the stationar wall, this vertical energ line is about.5h from the wall. Both the DNS and experimental data show the same trend. The simulated PCF data show that near the moving wall the vertical line extends the same distance into the flow. In contrast, the experimental data show that this line extends much farther (.H) from the moving water surface.

11 Exp Fluids (5) 56:8 Page of 8 4 Concluding remarks The results show that over the range of Renolds numbers investigated, the airflow statistics near the stationar wall are not effected b the air water moving interface and are comparable with pure Poiseuille flows. Also, a number of the statistics on the moving side show results similar to the simulated PCF with a solid moving wall. It can be concluded that, in order to simulate airflow within a fixed wall and a moving water with a smooth surface (no waves), there is minimal need to simulate water flow underneath the interface to obtain nominall accurate mean airflow statistics at a fixed streamwise distance, i.e. a moving water surface can be simulated as a solid moving wall. However, for second-order statistics, a two-phase simulation (from bottom wall of the water tank to top wall of the air channel) is required, as simulation and experimental results have discrepancies near the moving water surface. Here, momentum and energ tube analsis reveals that these discrepancies are due to a greater consumption of the airflow energ to overcome the water drag and drive the water forward, as compared to the PCF configuration with a moving solid wall. Despite these differences in momentum and energ at the surface, an interesting question remains as to wh the mean statistics for the two-phase flow still agree reasonabl well with the PCF case. Here we speculate that surface tension ma spatiall localize the effect of the boundar condition. Essentiall, the water surface behaves like an elastic sheet due to force from surface tension. The ratio of the viscous to surface tension forces is the capillar number (Ca). At δ + = 5, it is estimated that Ca <. (characteristic length is the full developed length of the flow -.44 m), therefore, surface tension forces are greater than viscous forces acting on the water surface. When surface tension dominates, a good approximation for the mean flow is obtained b modelling the two-phase flow as PCF. As δ + increases, ripples form on the water surface indicating the gravit effects become important, i.e. U/U b = f (Re, Ca, Fr), where Fr is the Froude number. Clearl this becomes an increasingl complicated flow that requires further investigation. Acknowledgments The authors gratefull acknowledge the support of the Australian Research Council. We would also like to thank Dr Laadhari and Dr Tsukahara for making their DNS data available. We are also grateful to make this contribution in celebration of Lex Smits illustrious career. References Banerjee S (7) Transport at the air sea interface. Springer, Berlin Bean VE, Hall JM (999) New primar standards for air speed measurement at NIST. 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