Improved Prediction of the Flow in Cylindrical Critical Flow Venturi Nozzles Using a Transitional Model

A recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Örlü,J. Fluid Mech., vol. 659, 2010, pp. 116–126) showed surprisingly large differences not only in the skin friction coefficient or shape factor, but also in their predictions of mean and fluctuation profiles far into the sublayer. While such differences are expected at very low Reynolds numbers and/or the immediate vicinity of the inflow or tripping region, it remains unclear whether inflow and tripping effects explain the differences observed even at moderate Reynolds numbers. This question is systematically addressed by re-simulating the DNS of a zero-pressure-gradient turbulent boundary layer flow by Schlatteret al. (Phys. Fluids, vol. 21, 2009, art. 051702). The previous DNS serves as the baseline simulation, and the new DNS with a range of physically different inflow conditions and tripping effects are carefully compared. The downstream evolution of integral quantities as well as mean and fluctuation profiles is analysed, and the results show that different inflow conditions and tripping effects do indeed explain most of the differences observed when comparing available DNS at low Reynolds number. It is further found that, if transition is initiated inside the boundary layer at a low enough Reynolds number (based on the momentum-loss thickness)${\mathit{Re}}_{\theta } \lt 300$, all quantities agree well for both inner and outer layer for${\mathit{Re}}_{\theta } \gt 2000$. This result gives a lower limit for meaningful comparisons between numerical and/or wind tunnel experiments, assuming that the flow was not severely over- or understimulated. It is further shown that even profiles of the wall-normal velocity fluctuations and Reynolds shear stress collapse for higher${\mathit{Re}}_{\theta } $irrespective of the upstream conditions. In addition, the overshoot in the total shear stress within the sublayer observed in the DNS of Wu & Moin (Phys. Fluids, vol. 22, 2010, art. 085105) has been identified as a feature of transitional boundary layers.

Discharge coefficients of CFVN predicted for high Reynolds numbers based on low-Re-calibration

A new correlation to determine the discharge coefficient of a critical Venturi nozzle with turbulent boundary layer

The characteristics of turbulent boundary layers (TBLs) subjected to adverse pressure gradients are analysed through well-resolved large-eddy simulations. The geometries under study are the NACA0012 and NACA4412 wing sections, at and angle of attack, respectively, both of them at a Reynolds number based on inflow velocity and chord length of . The turbulence statistics show that adverse pressure gradients (APGs) have a significant effect on the mean velocity, velocity fluctuations and turbulent kinetic energy budget, and this effect is more prominent on the outer region of the boundary layer. Furthermore, the effect of flow history is assessed by means of an integrated Clauser pressure-gradient parameter (Vinuesa et al., Flow Turbul. Combust., vol. 99, 2017, pp. 565–587), through the study of cases with matching local values of and the friction Reynolds number to isolate this effect. Our results show a noticeable effect of the flow history on the outer region, however the differences in the near-wall peak of the tangential velocity fluctuations appear to be mostly produced by the local APG magnitude. The one-dimensional power-spectral density shows energetic small scales in the outer region of APG TBLs, whereas these energetic scales do not appear in zero-pressure-gradient (ZPG) TBLs, suggesting that small scales near the wall are advected towards the outer layer by the APG. Moreover, the linear coherence spectra show that the spectral outer peak of high-Reynolds-number ZPG TBLs is highly correlated with the near-wall region (Baars et al., J. Fluid Mech., vol. 823, 2017, R2), unlike APG TBLs which do not show such a correlation. This result, together with the different two-dimensional spectra of APG and high-Reynolds-number ZPG TBLs, suggests different energisation mechanisms due to APG and increase in Reynolds number. To the authors’ knowledge, this is the first in-depth analysis of the TBL characteristics over wings, including detailed single-point statistics, spectra and coherence.

The work described divides itself into three parts. The first of these describes an experimental investigation into the influence of a line sink on a turbulent boundary layer, the object of which was to ascertain the overall effect on the values of boundary layer thickness and. mean velocity profile shape factor of removing a given amount of fluid. To this end, an axisymmetrical boundary layer duct was constructed. W1 thin the limitations of the experimental investigation, which was restricted to the case of only one initial value of shape-factor, it was found possible to represent the effect of a suction strip on a boundary layer in a semi-empirical manner. It was also apparent that the transient effects as represented by the lack of universality of the mean velocity distribution only persisted for a limited extent downstream of the suction strip. The second part of this work considers the problem of the optimum . distribution of suction in order to suppress the separation of a boundary layer. A fairly comprehensive theoretical treatment of this problem is presented which can be used to define the distribution of suction for any surface over which the boundary layer flow is essentially two dimensional. The basis of this approach is that the suction distribution can be defined by specifying .an upper limit on the value of either one of the two parameters which are normally taken as defining the state at a boundary layer, i.e., momentum thickness and shape factor. The precise value lot this upper limit is defined. by the condition that the suction power required should be a minimum. A series of calculations have been Wldertaken which illustrate the general validity of this approach and. which :f'urther result in a prediction of the minimum suction quantity necessary in order to obtain a given lift coefficient. These results may be used as the basis tor a project study of an aircraft which utilises this type o£' boundary layer control, and also as a starting point for an experimental investigation which would introduce the influence of the various methods of attaining an idealised porous surface in practise. The third part of the work considers the alternative of boundary layer control by tangential blowing. Experimental measurements on a plane wall jet are compared with Glauert' s theoretical predictions and it is noted that, whereas the basic idea behind Gl.auert's approach is confirmed, some of the detailed predictions show significant discrepancies. The existence of a region of universal mean velocity distribution near the surface is confirmed. A method of caloulating the streamwise variation of the maximum velocity of a wall jet is proposed which is based on the principles of similarity of the mean velocity distribution, continuity and variation of momentum due to the action of the surface shearing force. consideration is made of the effects of . surface curvature and the superposition of a tree stream on the development of a wall jet and it is noted that the latter effect is small. In the case of :flap blowing, it is shown that the non-dimensional blowing momentum coefficient can be interpreted directly in terms of the value of the ratio of maximum jet velocity to local stream velocity where both are measured at the trailing edge.

The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using Delayed Detached Eddy Simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales and it incorporates the one-equation γ-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation γ-transition model against experimental data and a benchmark LES. The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier-Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved Large Eddy Simulations (LES). Additionally, the results of the transitional DDES model are compared to DDES without a transition model, RANS eddy viscosity model and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation γ-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation γ-transition model becomes particularly evident when predicting the separated shear layer, transition process and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation γ-transition model can be a good compromise in terms of predictive accuracy and computational costs.

Flow in the juncture of surface mounted stream-lined slabs of various aspect ratios was studied in a low speed wind tunnel for laminar as well as turbulent approach boundary layer conditions for Reynolds number of 70,000, 90,000 and 120,000. For a laminar approach boundary layer a wavy structure along the primary separation line was observed for an aspect ratio of 1 while at higher aspect ratios and in case of the turbulent boundary layer for all aspect ratios this pattern was not visible. Mean pressures measured along the plane of symmetry on the surface exhibited influence of aspect ratio as well as boundary layer condition. While the surface pressure gradient for the turbulent case continuously increased in the direction of the slab, the laminar boundary layer case had a distinct change in slope, the location of which was aspect ratio dependent. Additionally the pressure gradient for the turbulent boundary layer was lower in comparison to the laminar boundary layer. The pressure differential at the mean vortex location for the turbulent boundary layer was higher than the laminar boundary layer case and reduced with increasing aspect ratio for both cases. The mean vortex location moved away from the slab leading edge with increasing aspect ratio for the laminar case while movement in case of the turbulent boundary layer was not discernable. The mean vortex locations for the turbulent boundary layer were further upstream as compared to the laminar boundary layer cases

Energy integral equation for premixed flame-wall interaction in turbulent boundary layers and its application to turbulent burning velocity and wall flux evaluations

Direct numerical simulation of incompressible turbulent boundary layers and planar jets at high Reynolds numbers initialized with implicit large eddy simulation

Excitation of the walls of a vehicle by turbulent boundary layers constitutes a major source of interior noise in the field of transport industry. A turbulent boundary layer over a wall can provide a direct contribution to the noise and also an indirect one due to the excitation of the structure below. In the present study, simulations of turbulent boundary layers at Mach=0.5 are carried out using direct noise computation by solving the compressible NavierStokes equations. This method provides the direct contribution (despite its very low intensity) and the wall pressure fluctuations which are responsible for the indirect contribution to the aerodynamic noise. The low efficiency of the noise radiated inthe freestream can be explained by the fact that the sources are turbulence quadrupoles. In order to determine the effects of pressure gradients on both noise contributions, adverse and favorable cases are investigated. The results are compared to a reference case with zero pressure gradient computed by Gloerfelt 1,2 . Results show that an adverse pressure gradient leads to higher levels of the direct acoustic emission whereas lower levels are obtained in presence of a favorable pressure gradient in comparison to the zero gradient case. The same hierarchy of levels is visible in the wavenumber pressure spectra of wall pressure fluctuations. In the field of transport industry, boundary layer constitutes a fundamental source of aerodynamic noise (Blake 3 ). A turbulent boundary layer over a vehicle has two mechanisms of noise generation: an indirect contribution corresponding to structural excitation and a direct contribution consisting of propagation of pressure waves. Due to very low amplitudes of the direct contribution in subsonic flows compared to the overall pressure levels, it is difficult to evaluate the direct acoustic contribution experimentally and numerically. The noise radiated by a zero pressure gradient (ZPG) turbulent boundary layer has been investigated for subsonic flows (Mach 0.5, 0.7 and 0.9) by Gloerfelt 1,2,4 . In these studies, the author especially confirmed the U 8 power law dependence of the acoustic intensities and showed that the acoustic domain and the convective ridge merge at these relatively high speeds. The amplitude of the radiated pressure waves which propagate in the opposite direction of the flow is less than 1% of the aerodynamic pressure for the Mach 0.5 case. In this work, a numerical study of a Mach 0.5 turbulent boundary layer is investigated in presence of adverse and favorable pressure gradients (APG and FPG) using Large Eddy Simulation (LES). Pressure gradients are generated by means of curved geometries. An adverse pressure gradient leads to a deceleration � = − � @� + @� +

The generation of a thick fully turbulent boundary layer is investigated in a lowspeed wind tunnel at a nominal zero pressure gradient over the Reynolds number range 0.145× 10 6 · Rex · 0.58× 10 6 . The wind tunnel floor natural boundary layer is laminar with thickness ± between 5.76 mm and 8.13 mm. Different tripping devices are tested to trigger transition so to double the boundary layer thickness and provide a fully established turbulent velocity profile. Using a trip wire significantly increases ± but leads to an unsatisfactory velocity profile. Using a sandpaper strip slightly increases ± but keeps the boundary layer laminar. Using a strip of sharp-edged silicon granules doubles the boundary layer thickness that increases up to 20 mm and the mean velocity profiles are a good fit to the logarithmic law of the wall over the outer region of the boundary layer. The spectral decay of turbulent kinetic energy in this outer layer is exponential and close to i5/3, indicating turbulence equilibrium. This work is of practical interest to wind tunnel practitioners for generating equilibrium thick turbulent boundary layers at low Reynolds numbers.

In this paper, theoretical and numerical analysis of a~transonic flow field of critical flow Venturi nozzles according to the ISO~9300 standard is performed. Deviations of the flow field from an estimate based on one dimensionality are clarified. While the theoretical analysis allows prediction of these deviations, the numerical analysis allows quantification of their influence. The main studied phenomena include the local supersonic compression in transonic expansion and the Prandtl-Meyer expansion. The tendency of the flow field to spatial oscillations is shown, alongside the ability of the system to damp these oscillations.

The near-wall, subgrid-scale (SGS) model [Chung and Pullin, Large-eddy simulation and wall-modeling of turbulent channel flow, J. Fluid Mech. 631, 281--309 (2009)] is used to perform large-eddy simulations (LES) of the incompressible developing, smooth-wall, flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. This is then used to study several aspects of zero- and adverse-pressure gradient turbulent boundary layers. First, LES of the zero-pressure gradient turbulent boundary layer are performed at Reynolds numbers Reθ based on the free-stream velocity and the momentum thickness in the range Reθ = 103 - 1012. Results include the inverse skin friction coefficient, √2/Cf, velocity profiles, the shape factor H, the Karman constant, and the Coles wake factor as functions of Reθ. Comparisons with some direct numerical simulation (DNS) and experiment are made, including turbulent intensity data from atmospheric-layer measurements at Reθ = O(106. At extremely large Reθ, the empirical Coles-Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot of itself probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that the LES is suggestive of the asymptotic, infinite Reynolds-number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum Reθ of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger Reθ could be achieved with quad- or higher-precision arithmetic. Second, the time series velocity signals obtained from LES within the logarithmic region of the zero-pressure gradient turbulent boundary layer are used in combination with an empirical, predictive inner--outer wall model [Marusic et al., Predictive model for wall-bounded turbulent flow, Science 329, 193 (2010)] to calculate the statistics of the fluctuating streamwise velocity in the inner region of the zero-pressure gradient turbulent boundary layer. Results, including spectra and moments up to fourth order, are compared with equivalent predictions using experimental time series, as well as with direct experimental measurements at Reynolds numbers Reτ based on the friction velocity and the boundary layer thickness, Reτ =7,300, 13,600 and 19,000. LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers Reτ =62,000, 100,000 and 200,000 that lie within a gap in log(Reτ) space between laboratory measurements and surface-layer, atmospheric experiments. The present results support a log-like increase in the near-wall peak of the streamwise turbulence intensities with Reτ and also provide a means of extending LES results at large Reynolds numbers to the near-wall region of wall-bounded turbulent flows. Finally, we apply the wall model to LES of a turbulent boundary layer subject to an adverse pressure gradient. Computed statistics are found to be consistent with recent experiments and some Reynolds number similarity is observed over a range of two orders of magnitude.

Hydrofoil shapes are used for the marine turbine blades to capture kinetic energy from water currents effectively. Predicting transitions is a critical concern when studying the hydrofoil boundary layer. This paper analyzed the transitional behavior of the boundary layer in the National Advisory Committee of Aeronautics (NACA) hydrofoil, NACA0009, with a blunt trailing edge using the Algebraic Local-Correlation-based Transition Modeling (Algebraic LCTM) model. First, through sensitivity analysis, the effects of the maximum y+ (the dimensionless distance y to the wall), grid expansion ratio, number of normal and streamlined grids, and timescale on transition prediction were studied. The results indicate that finer y+ value and appropriate grid expansion ratios can improve the accuracy of transition prediction, while the influence of timescale on the prediction results is relatively small within the range of Courant number theory values. Second, further analysis was conducted on the transition prediction performance under different Reynolds numbers. It was found that the model predictions were consistent with experimental values at low Reynolds numbers, but the predicted transition position was advanced at high Reynolds numbers, mainly because of the significant disparity in eddy viscosity coefficients within the free flow field. In the study of leading-edge roughness bands' impact on boundary layer transition for hydrofoil, the introduction of roughness significantly expedited the transition process. The Algebraic LCTM model outperformed the gamma (γ) transition model, reducing prediction errors by 5–40% for boundary layer parameters and maintaining errors between 0.005 and 4% for wake vortex shedding frequency, as opposed to the γ model's 0–23%. The results of this study provide a theoretical basis for hydrofoil design.

An experimental investigation has been conducted to identify the effects of pressure gradient and surface roughness on turbulent boundary layers. In Part II, smooth- and rough-surface turbulent boundary layers with and without adverse pressure gradient (APG) are presented at a fixed Reynolds number (based on the length of flat plate) of 900,000. Flat-plate boundary layer measurements have been conducted using a single-sensor, hot-wire probe. For smooth surfaces, compared to the zero pressure gradient (ZPG) boundary layer, the APG boundary layer has a higher mean velocity defect throughout the boundary layer and lower friction coefficient. APG decreases the streamwise normal Reynolds stress for y less than 0.4 times the boundary layer thickness and increases it slightly in the outer region. For rough surfaces, APG reduces the roughness effects of increasing the mean velocity defect and normal Reynolds stress for y less than 23 and 28 times the average roughness height, respectively. Consistently, for the same roughness, APG decreases the integrated streamwise turbulent kinetic energy. APG also decreases the roughness effect on the friction coefficient, roughness Reynolds number, and roughness shift. Compared to the ZPG boundary layers, the roughness effects on integral boundary layer parameters—boundary layer thickness and momentum thickness—are weaker under APG. Thus, contrary to the favorable pressure gradient (FPG) in part I, APG reduces the roughness effects on turbulent boundary layers.