Flow structure and skin friction in the vicinity of a streamwise-angled injection hole fed by a short pipe

The velocity field and skin friction distribution around a row of five jets issuing into a crossflow from short (L/D ≃ 1) pipes inclined by 35° with respect to the streamwise direction, (i.e., “short holes”) are presented for two different jet supply flow directions. Velocity was measured using PIV, while the skin friction was measured with oil-film interferometry. The flow features are compared with previously published data for jets issuing through holes oriented normal to the crossflow and with numerical simulations of similar geometries. The distinguishing features of the flow field include a reduced recirculation region in comparison to the 90° case and markedly different in-hole flow physics. The jetting process caused by in-hole separations force the bulk of the jet fluid to issue from the leading half of the streamwise-angled injection hole, as previously reported by Brundage et al. (Tech Rep ASME 99-GT-35, 1999) and predicted by Walters and Leylek (ASME J Turbomach 122:101–112, 2000). The flow structure impacts the skin friction distribution around the holes, resulting in higher near-hole shear stress for a counter-flow supply plenum (jet fluid supplied by a high speed plenum flowing opposite to the free stream direction). In contrast, the counter-flow supply plenum was previously found to have the lowest near-hole wall shear stress for normal injection holes (Peterson and Plesniak in Exp Fluids 37:497–503, 2004b). Streamwise-angled injection generally reduces the near-hole skin friction due to the reduced jet trajectory resulting from the lower wall-normal jet momentum. Far downstream, the skin friction distributions are similar for the two injection angle cases.     

Roughness effects in low-<Emphasis Type="Italic"> Re</Emphasis><Subscript><Emphasis Type="Italic"> θ</Emphasis></Subscript> open-channel turbulent boundary layers

This paper reports velocity measurements obtained on a smooth and two geometrically different types of rough surfaces in an open channel. The measurements were obtained using a laser-Doppler anemometer. The recent boundary layer theory proposed by George and Castillo (1997) and conventional scaling laws are used to analyze the data. The present flow shows a strong structural similarity to a canonical turbulent boundary layer in the inner layer. The results demonstrate that surface roughness increases the wake parameter. Surface roughness also enhances the levels of turbulence intensities, Reynolds shear stress and triple correlations over most of the boundary layer, but decreases the stress anisotropy.     

Numerical Simulation of Turbulent Flow in Concentric Annuli

In this paper we consider a fully developed turbulent flow in a round pipe with a small inner annulus. The diameter of the inner annulus is less than 10% of the diameter of the outer pipe. As a consequence, the surface area of the inner pipe compared to the outer pipe is small. The friction exerted by the wall on the flow is proportional to the surface area and the wall shear stress. Due to the small surface area of the inner annulus the additional stress on the flow due to the presence of the annulus may expected to be negligible. However, it will be shown that the inner annulus drastically changes the flow patterns and gives rise to unexpected scaling properties. In previous studies (Chung et al., Int J Heat Fluid Flow 23:426–440, 2002; Churchill and Chan, AIChE J 41:2513–2521, 1995) it was argued that radial position of the point of zero shear stress does not coincide with the radial location of the point of maximum axial velocity. In our direct numerical simulations we observe a coincidence of these points within the numerical accuracy of our model. It is shown that the velocity profile close to the inner annulus is logarithmic.     

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re = 13,400 and the nominal size of the roughness was k = 0.44 mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.     

Exact formula for the spreading width of jet flow velocity under the assumption of a radial adjusting coefficient

Recently, Lee et al. (Arch Appl Mech 81:397–402, 2011) proposed a new and very interesting formula to describe the velocity profile of a submerged jet flow by introducing a radial adjusting coefficient depending on the jet flow direction. Under some simplifying assumptions (granting convergence), the authors were able to express the spreading width of the jet flow analytically in terms of infinite series. In this short note, we show that such simplifying assumptions can be relaxed and exact solutions for the spreading width of the jet flow can be obtained: Such results are computationally more efficient and are able to better demonstrate the qualitative features of the solutions.     

Re-examination of the scaling roughness function for κ-type rough walls using a servo-controlled wall drag balance

Conclusion The authors would like to underline errors in the mean velocity measurements in previous paper (Pineau et al. 1987). The direct drag measurements and Reynolds stress data were confirmed, and the new mean velocity profiles, in conjunction with the drag data resulted in exactly the same roughness scaling function as proposed by Perry and Joubert (1963) for the same k-type roughness.     

Velocity-defect scaling for turbulent boundary layers with a range of relative roughness

Velocity profile measurements in zero pressure gradient, turbulent boundary layer flow were made on a smooth wall and on two types of rough walls with a wide range of roughness heights. The ratio of the boundary layer thickness (δ) to the roughness height (k) was 16≤δ/k≤110 in the present study, while the ratio of δ to the equivalent sand roughness height (k _s) ranged from 6≤δ/k _s≤91. The results show that the mean velocity profiles for all the test surfaces agree within experimental uncertainty in velocity-defect form in the overlap and outer layer when normalized by the friction velocity obtained using two different methods. The velocity-defect profiles also agree when normalized with the velocity scale proposed by Zagarola and Smits (J Fluid Mech 373:33–70, 1998). The results provide evidence that roughness effects on the mean flow are confined to the inner layer, and outer layer similarity of the mean velocity profile applies even for relatively large roughness.     

Characterizing developing adverse pressure gradient flows subject to surface roughness

An experimental study was conducted to examine the effects of surface roughness and adverse pressure gradient (APG) on the development of a turbulent boundary layer. Hot-wire anemometry measurements were carried out using single and X-wire probes in all regions of a developing APG flow in an open return wind tunnel test section. The same experimental conditions (i.e., T _∞, U _ref, and C _p) were maintained for smooth, k ⁺ = 0, and rough, k ⁺ = 41–60, surfaces with Reynolds number based on momentum thickness, 3,000 < Re _θ < 40,000. The experiment was carefully designed such that the x-dependence in the flow field was known. Despite this fact, only a very small region of the boundary layer showed a balance of the various terms in the integrated boundary layer equation. The skin friction computed from this technique showed up to a 58% increase due to the surface roughness. Various equilibrium parameters were studied and the effect of roughness was investigated. The generated flow was not in equilibrium according to the Clauser (J Aero Sci 21:91–108, 1954) definition due to its developing nature. After a development region, the flow reached the equilibrium condition as defined by Castillo and George (2001), where Λ = const, is the pressure gradient parameter. Moreover, it was found that this equilibrium condition can be used to classify developing APG flows. Furthermore, the Zagarola and Smits (J Fluid Mech 373:33–79, 1998a) scaling of the mean velocity deficit, U _∞δ*/δ, can also be used as a criteria to classify developing APG flows which supports the equilibrium condition of Castillo and George (2001). With this information a ‘full APG region’ was defined.     

A Device Enhancement for the Dry Sliding Friction Coefficient Measurement Between Steel 1080 and VascoMax with Respect to Surface Roughness Changes

An enhancement of an existing tribometer device developed by Philippon et al. (Wear 257:777–784, 2004) is presented in this work. This experimental device is made up of a dynamometer ring and a specific load sensor allowing to apply an apparent normal force on specimens and to measure frictional forces respectively. A set of strain gauges are added to the upgraded dynamometer ring in this new configuration. The apparent normal force can be recorded accurately during the sliding process. The setup is adapted on a hydraulic testing machine to carry out steel-on-steel dry sliding tests. The first set of standard Steel on standard Steel specimens (XC 38 French standard steel) with two apparent normal pressures are imposed (8 and 80 MPa) as the range of sliding velocities varies from 0.12 to 3.72 m/s for the same contact conditions. The main set of experiments with low sliding velocities (varying from 0 to 3 m/s) for the Steel 1080 on Steel VascoMax are performed in the same tested setup. The recordings of normal and tangential forces leading to the friction coefficient determination are discussed. The values of dry friction coefficient μ according to the experimental parameters are in good agreement with those observed in the literature. Using this new configuration, the effects of the sliding velocity on the surface roughness changes and on the dry fiction coefficient are also investigated. Additionally the surface roughness changes are also investigated. Performing the scans with use of the scanning electron microscope in particular locations of the specimens show the roughness decrease and reveal the occurrence of the wear phenomenon. Moreover, very interesting relations between wear and sliding velocity are observed.     

Turbulent film condensation on a horizontal elliptical tube

An investigation has been made of turbulent film condensation on a horizontal elliptical tube. The present study is based on Colburn analogy [1] and potential flow theory to determine the high tangential velocity of vapor flow at the boundary layer and to define the local interfacial shear owing to high velocity vapor flow across the tube surface. The condensate film flow and local/or mean heat transfer characteristics from a horizontal elliptical tube with variable ellipticities, e, under the influence of Froude number, sub-cooling parameter and system pressure have been performed. The present result for dimensionless mean heat transfer coefficient reduces to the same result obtained by Sarma et al.s [2] e=0 (circular tube). Compared with laminar model by Yang and Hsu [3], the present turbulent model shows in better agreement with Michaels experimental data [4] (for e=0). The dependence of mean Nusselt coefficient on the effect of n (power of Reynolds) [1] is also discussed.     

Effects of Strong Irregular Roughness on the Turbulent Boundary Layer

Some recent studies with irregular roughness suggest that the Nikuradse [Nikuradse, J., NACA TM 1292, National Advisory Committee on Aeronautics (1933)] equivalent sand-grain roughness measure gives inconsistent results of the flow characteristics. In situations where the roughness is very strong to stifle or diminish the viscous effects the viscous scaling laws alone will not be very meaningful. The present study aims to find an alternative scaling parameter for such cases. Here, the measured mean and turbulent velocity profiles on a nonuniform roughness surface, simulating a gas turbine blade roughness, are presented. A nonzero wall normal pressure gradient is caused which is believed to contribute to the velocity deficit in the near-wall rough boundary layer velocity profile. The surface pressure variation is also directly influenced by the local roughness. The normal turbulent stresses are increased on the rough surface, the vertical component more than the longitudinal component. A pressure gradient velocity scale (similar to that proposed for adverse pressure gradient boundary layer modeling by Durbin and Belcher [Durbin, P.A. and Belcher, S.E., J. Fluid Mech. 238 (1992), 699-722] is defined to capture the pressure effects induced by such roughness on the inner layer properties.     

Turbulent thermal diffusion in a multi-fan turbulence generator with imposed mean temperature gradient

We studied experimentally the effect of turbulent thermal diffusion in a multi-fan turbulence generator which produces a nearly homogeneous and isotropic flow with a small mean velocity. Using particle image velocimetry and image processing techniques, we showed that in a turbulent flow with an imposed mean vertical temperature gradient (stably stratified flow) particles accumulate in the regions with the mean temperature minimum. These experiments detected the effect of turbulent thermal diffusion in a multi-fan turbulence generator for relatively high Reynolds numbers. The experimental results are in compliance with the results of the previous experimental studies of turbulent thermal diffusion in oscillating grid turbulence (Buchholz et al. 2004; Eidelman et al. 2004). We demonstrated that the turbulent thermal diffusion is an universal phenomenon. It occurs independently of the method of turbulence generation, and the qualitative behavior of particle spatial distribution in these very different turbulent flows is similar. Competition between turbulent fluxes caused by turbulent thermal diffusion and turbulent diffusion determines the formation of particle inhomogeneities.     

The weak shear kinetic phase diagram for nematic polymers

We study the shear problem for nematic polymers as modeled by the molecular kinetic theory of Doi (1981), focusing on the anomalous slow flow regime. We provide the kinetic phase diagram of monodomain (MD) attractors and phase transitions vs normalized nematic concentration (N) and weak normalized shear rate (Peclet number, Pe). We then overlay all rheological features typically reported in experiments: alignment properties, normal stress differences and shear stress. These features play a critical role in the synthesis between theory and experiment for nematic polymers (Larson 1999; Doi and Edwards 1986). MD type is routinely used for rheological shear characterization: cf., flow-aligning 5CB (Mather et al. 1996a), tumbling PBT (Srinivasarao and Berry 1991), and 8CB (Mather et al. 1996b), evidence for a wagging regime (Mewis et al. 1997), out-of-plane kayaking modes (Larson and Ottinger 1991), and evidence for chaotic major director dynamics (Bandyopadhyay et al. 2000). MD transitions correlate with sign changes in normal stresses (Larson and Ottinger 1991; Magda et al. 1991; Kiss and Porter 1978, 1980). Furthermore, structure formation in shear devices appears to be correlated with monodomain precursor dynamics (Tan and Berry 2003; Forest et al. 2002a). In this paper we combine seminal kinetic theory results (Kuzuu and Doi 1983, 1984; Larson 1990; Larson and Ottinger 1991; Faraoni et al. 1999; Grosso et al. 2001), symmetry observations (Forest et al. 2002b), and mesoscopic results on the fate of orientational degeneracy in weak shear (Forest and Wang 2003; Forest et al. 2003a), together with our resolved numerical simulations, to provide the kinetic flow-phase diagram of Doi theory in the weak shear regime, 0<Pe<1, for infinitely thin rods. We report the "birth" of key rheological features at the onset of flow: sign changes and local maxima and minima in normal stress differences (N₁ and N₂) associated with MD transitions. These results serve as the basis for continuation of the kinetic phase diagram to Pe>1 ; as the definitive benchmark for any mesoscopic or continuum model; and experimental data can be compared in order to determine accuracy and limitations of the Doi theory in weak shear.     

A velocity dependent effective angle method for calibration of X-probes at low velocities

A velocity dependent effective angle (VDEA) method for the calibration of yaw response of hot-wire X-probes at low flow velocities (0.5–6 m/s) is presented. Comparisons with a full velocity vs. yaw-angle method (Österlund 1999) in a smooth wall channel flow indicate that there is only moderate advantage in using the latter method, which is considerably more laborious. Comparisons with direct numerical simulations (DNS) (Moser et al. 1999) and the more common fixed effective angle method (FEA) show that the VDEA method significantly improves estimates of Reynolds stresses compared to the FEA method.     

EXTENDED SELF SIMILARITY OF PASSIVE SCALAR IN RAYLEIGH-BNARD CONVECTION FLOW BASED ON WAVELET TRANSFORM

Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al., to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that, by extending the formula which was proposed by A. Arneodo et al. for extracting the scaling exponent ζ(q) of velocity data to temperature data, a newly defined formula which is also based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTMM (wavelet transform maximum modulus) ξ(q) correctly can be extracted.     

Experiments on the Flow Field and Acoustic Properties of a Mach number 0·75 Turbulent Air Jet at a Low Reynolds Number

In this paper we present the experimental results of a detailed investigation of the flow and acoustic properties of a turbulent jet with Mach number 0·75 and Reynolds number 3·5 10³. We describe the methods and experimental procedures followed during the measurements, and subsequently present the flow field and acoustic field. The experiment presented here is designed to provide accurate and reliable data for validation of Direct Numerical Simulations of the same flow. Mean Mach number surveys provide detailed information on the centreline mean Mach number distribution, radial development of the mean Mach number and the evolution of the jet mixing layer thickness both downstream and in the early stages of jet development. Exit conditions are documented by measuring the mean Mach number profile immediately above the nozzle exit. The fluctuating flow field is characterised by means of a hot-wire, which produced radial profiles of axial turbulence at several stations along the jet axis and the development of flow fluctuations through the jet mixing layer. The axial growth rate of the jet instabilities are determined as function of Strouhal number, and the axial development of several spectral components is documented. The directivity of the overall sound pressure level and several spectral components were investigated. The spectral content of the acoustic far field is shown to be compatible with findings of hot-wire experiments in the mixing layer of the jet. In addition, the measured acoustic spectra agree with Tam’s large-scale similarity and fine-scale similarity spectra (Tam et al., AIAA Pap 96, 1996).     

Turbulent Flow Produced by Piston Motion in a Spark-ignition Engine

Turbulence produced by the piston motion in spark-ignition engines is studied by 2D axisymmetric numerical simulations in the cylindrical geometry as in the theoretical and experimental work by Breuer et al. (Flow Turbul Combust 74:145, 2005). The simulations are based on the Navier–Stokes gas-dynamic equations including viscosity, thermal conduction and non-slip at the walls. Piston motion is taken into account as a boundary condition. The turbulent flow is investigated for a wide range of the engine speed, 1,000–4,000 rpm, assuming both zero and non-zero initial turbulence. The turbulent rms-velocity and the integral length scale are investigated in axial and radial directions. The rms-turbulent velocity is typically an order-of-magnitude smaller than the piston speed. In the case of zero initial turbulence, the flow at the top-dead-center may be described as a combination of two large-scale vortex rings of a size determined by the engine geometry. When initial turbulence is strong, then the integral turbulent length demonstrates self-similar properties in a large range of crank angles. The results obtained agree with the experimental observations of Breuer et al. (Flow Turbul Combust 74:145, 2005).     

Vasculature based model for characterizing the oxygen transport in skin tissues – analogy to the Weinbaum-Jiji bioheat equation

Based on the conceptual three-layer microvascular structure of skin tissues proposed by Weinbaum et al. [20–25] and in analogy to the well known Weinbaum-Jiji (W-J) bioheat equation, a new oxygen transport model was established in this paper, which collectively included the contributions of the vascular geometry and the blood flow condition. The new one-dimensional three-layer oxygen transport model was then applied to predict the average oxygen concentration distribution in skin tissues and numerical solutions for the boundary value problem coupling the three layers were obtained. A simple expression for the tensor diffusivity (D_eff) of oxygen transport over the deep tissue layer was presented, which was orders of magnitude higher than the intrinsic diffusivity (D_t) in tissue without blood flow. Effects of blood flow velocity and vascular geometry to the oxygen transport were investigated. Calculations indicated that the vascular geometry had significant effects on oxygen transport. The oxygen exchange between the arteries and veins was relatively small for the deep tissue layer. Further, the average oxygen concentration gradient appears low in intermediate layer due to large capillary perfusion. The theoretical results were implemented to interpret some previous experimental results and a better understanding on the oxygen transport across the vascularized living tissues was obtained. The strategy proposed in this paper may provide a feasible way to comprehensively characterize the oxygen transport behaviors in living tissues with real and complex vasculature.     

Degradation of homogeneous polymer solutions in high shear turbulent pipe flow

This study quantifies degradation of polyethylene oxide (PEO) and polyacrylamide (PAM) polymer solutions in large diameter (2.72 cm) turbulent pipe flow at Reynolds numbers to 3 × 10⁵ and shear rates greater than 10⁵ 1/s. The present results support a universal scaling law for polymer chain scission reported by Vanapalli et al. (2006) that predicts the maximum chain drag force to be proportional to Re ^3/2, validating this scaling law at higher Reynolds numbers than prior studies. Use of this scaling gives estimated backbone bond strengths from PEO and PAM of 3.2 and 3.8 nN, respectively. Additionally, with the use of synthetic seawater as a solvent the onset of drag reduction occurred at higher shear rates relative to the pure water solvent solutions, but had little influence on the extent of degradation at higher shear rates. These results are significant for large diameter pipe flow applications that use polymers to reduce drag.     

Large Eddy Simulation of an Initially-Confined Triangular Oscillating Jet

This paper reports the first large eddy simulation (LES) of a self-excited oscillating triangular jet (OTJ) issuing from a fluidic nozzle that consists of a small triangular orifice inlet followed by a large circular chamber and an orifice outlet. The case simulated is identical to that measured experimentally by England et al. (Exp Fluids 48(1):69–80, 2010). The present prediction agrees well with the previous measurement. The simulation reveals that the central oscillating jet exhibits axis-switching in the cross-section and rotates by 60° approximately over a downstream distance of x = 0.5D (chamber diameter). Three strong longitudinal vortices occur associated with the three vertices of the inlet triangle. These vortices strongly interact with the central jet and also the surroundings, in the region at x/D ≤ 1, and appear to merge finally with the outer secondary swirling flow. These observations are consistent with the deduction from previous experiments.