Measurements with a flow direction boundary-layer probe in a two-dimensional laminar separation bubble

 Measurements with a directional sensitive hot-wire probe have been carried out in a two-dimensional laminar separation bubble caused by an adverse pressure gradient. The probe has three parallel, in plane wires and can be traversed in the boundary layer in all spatial directions. The central wire, operated as a conventional hot-wire in CTA mode, and two surrounding resistance wires measure the instantaneous magnitude and direction of the flow, respectively. The probe is calibrated and operated in a similar way as a single hot-wire probe for boundary layer measurements. The frequency response is high enough for measurements of naturally occurring instability waves in the bubble. The flow direction intermittency was measured inside the bubble and regions with reversed flow were mapped out. Prior to reattachment periodical oscillations of the flow direction are found associated with shedding of vortical structures from the bubble. Received: 13 March 1998/Accepted: 22 April 1998     

On near-wall hot-wire measurements

A specially constructed hot-wire probe was used to obtain very near-wall velocity measurements in both a fully developed turbulent channel flow and flat plate boundary layer flow. The near-wall hot-wire probe, having been calibrated in a specially constructed laminar flow calibration rig, was used to measure the mean streamwise velocity profile, distributions of streamwise and spanwise intensities of turbulence and turbulence kinetic energy k in the viscous sublayer and beyond; these distributions compare very favorably with available DNS results obtained for channel flow. While low Reynolds number effects were clearly evident for the channel flow, these effects are much less distinct for the boundary layer flow. By assuming the dissipating range of eddy sizes to be statistically isotropic and the validity of Taylor's hypothesis, the dissipation rate ɛ _iso in the very near-wall viscous sublayer region and beyond was determined for both the channel and boundary layer flows. It was found that if the convective velocity U _c in Taylor's hypothesis was assumed to be equal to the mean velocity Uˉ at the point of measurement, the value of (ɛ⁺ _iso)₁ thus obtained agrees well with that of (ɛ ⁺)_DNS for y ⁺ ≥ 80 for channel flow; this suggests the validity of assuming U _c=Uˉ and local isotropy for large values of y ⁺. However, if U _c was assumed to be 10.6u _τ , the value of (ɛ⁺ _iso)₂ thus obtained was found to compare reasonably well with the distribution of (ɛ⁺ _iso)_DNS for y ⁺≤ 15. Received: 31 May 1999/Accepted: 20 December 1999     

Examination of the flow around a hot-wire probe using particle image velocimetry

Previous work has shown that the k ² term in the effective cooling velocity equation for inclined hot-wires can become negative under certain probe configurations and wire length-to-diameter ratios. It was hypothesised that this was due to a downwash component of velocity along the wire when prong interference effects were expected to be minimal. Direct measurements of the flow around a typical hot-wire probe using digital particle image velocimetry have shown that this downwash velocity component does exist, leading to negative values of k ² as calculated from the angle of deviation from the free stream.List of symbols d diameter of hot-wire mm - k factor in equation for effective dimensionless velocity for inclined hot-wire - l length of hot-wire mm - Q effective velocity mm/s - U free stream velocity mm/s - angle between free stream and degrees wire normal - angle through which flow is degrees deflected at working section of wire     

Near-wall hot-wire measurements

This work continues the studies of Khoo et al. (Exp. Fluids 29: 448–460, 2001), where experiments were performed in turbulent-channel and flat-plate boundary-layer flows using near-wall hot-wire probes. The probability density function (pdf) of the wall-shear stress and streamwise velocity fluctuations in the viscous sublayer, buffer region and beyond were compared and analyzed. The convective velocity U _c of the streamwise velocity fluctuations in the very near-wall region was obtained using a two-point correlation technique. It was found that in the viscous sublayer, U _c is approximately constant at 13u _τ and 15u _τ , respectively, for the channel and boundary-layer flows. Spectra data for the viscous sublayer are presented for the first time, and the normalized spectral plots for different flow conditions collapse at high frequencies or wavenumbers, thus indicating the possible presence of small-scale universality at different Reynolds numbers. The integral time scale corresponding to the streamwise velocity fluctuations in the viscous sublayer is also presented. Received: 18 October 2000/Accepted: 2 April 2001     

Comparison of turbulent channel and pipe flows with varying Reynolds number

Single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ Re _τ ≤ 3,000. A total of 27 velocity profile measurements were taken with a systematic variation in the inner-scaled hot-wire sensor length l ⁺ and the hot-wire length-to-diameter ratio (l/d). It was observed that for constant l ⁺ = 22 and l/d >~200l/d \gtrsim 200, the near-wall peak in turbulence intensity rises with Reynolds number in both channels and pipes. This is in contrast to Hultmark et al. in J Fluid Mech 649:103–113, (2010), who report no growth in the near-wall peak turbulence intensity for pipe flow with l ⁺ = 20. Further, it was found that channel and pipe flows have very similar streamwise velocity statistics and energy spectra over this range of Reynolds numbers, with the only difference observed in the outer region of the mean velocity profile. Measurements where l ⁺ and l/d were systematically varied reveal that l ⁺ effects are akin to spatial filtering and that increasing sensor size will lead to attenuation of an increasingly large range of small scales. In contrast, when l/d was insufficient, the measured energy is attenuated over a very broad range of scales. These findings are in agreement with similar studies in boundary layer flows and highlight the need to carefully consider sensor and anemometry parameters when comparing flows across different geometries and when drawing conclusions regarding the Reynolds number dependency of measured turbulence statistics. With an emphasis on accuracy, measurement resolution and wall proximity, these measurements are taken at comparable Reynolds numbers to currently available DNS data sets of turbulent channel/pipe flows and are intended to serve as a database for comparison between physical and numerical experiments.     

Temperature compensation of hot-wire anemometer with photoconductive cell

A new temperature compensation technique for hot-wire anemometer is proposed in this article. In contrast to the available compensation techniques, a photoconductive cell is introduced here as a variable resistor in the bridge. The major advantage of adopting an active component such as photoconductive cell is that temperature compensation can be achieved by using any kind of temperature sensors, once the output of temperature sensor is given as a voltage. Validation experiments using a photoconductive cell with a thermocouple-thermometer are conducted in the temperature range from 30 to 50 °C and the velocity ranges from 8 to 18 m/s.List of symbols h(U) convective heat transfer coefficient of the wire at U - E _b bridge top voltage - E _w voltage across the wire - I heating current through the hot-wire - R _A resistance connected in tandem with the hot-wire in the bridge - R _B variable resistance for overheat-ratio setting of the hot-wire - R _C compensation resistance connected in series with R _B in the bridge, 1/(R _p ^–1 + R _CdS ^–1 - R _CdS photoconductive cell resistance - R _P resistance connected parallel with R _CdS - R _wf wire resistance at T _f - R _wa wire resistance at T _a - R _ww wire resistance at working temperature of T _w - R _w0 wire resistance at 0 °C - T _f fluid temperature - T _a ambient temperature - T _w working temperature of the wire - U flow velocity - V _c compensating voltage applied to the input side of the R _CdS Greek symbols _w temperature resistance coefficient of the hot-wire - V voltage across R _A, voltage difference between E _b and E _w Greek symbols ^* reference     

In situ calibration of hot wires close to highly heat-conducting walls

A calibration procedure has been derived that permits reliable hot-wire measurements close to walls. When hot wires are calibrated in a free flow and subsequently used for near-wall velocity measurements, erroneous velocity information results because of additional heat losses to the wall. On the other hand, laser-Doppler anemometry (LDA) measurements of local time mean velocities are very little affected by the presence of the wall and this readily suggests in situ calibration of hot wires located just behind the LDA measuring volume and at the same distance from the wall. Calibrations of this kind are described for highly heat-conducting walls and the results show good agreement with corresponding data obtained through numerical investigations. The present investigations permit a generally applicable correction curve to be suggested for hot-wire velocity measurements close to walls of high thermal conductivity. Received: 3 May 2000/Accepted: 24 November 2000     

Effects of imperfect spatial resolution on turbulence measurements in the very near-wall viscous sublayer region

 Experiments were carried out to study the effects of imperfect spatial resolution on turbulence measurements in the very near-wall region using hot wires of different lengths, l ⁺ (in wall units). Previous works have indicated that the distributions of the longitudinal velocity rms value, skewness and flatness factors are independent of l ⁺ in the buffer region and beyond provided l ⁺<20–25. Our results obtained using l ⁺=3, 6, and 22 in the viscous sublayer region show that generally the said distributions are dependent on l ⁺ and attentuate in magnitude with increasing l ⁺. Further experiments were also carried out at different Reynolds numbers (Re _c , based on centerline velocity and channel’s height) but with measurements made using hot wire of the same l ⁺. The latter shows that the rms value and other higher order moments of longitudinal velocity fluctuations are independent of Re _c , thereby extending similar findings by Johansson and Alfredsson (1983), valid in the buffer region into the viscous sublayer region. Received: 29 January 1996 / Accepted: 10 August 1996     

浮力对混合对流流动及换热特性的影响

用热线和冷线相结合的技术测量垂直圆管内逆混合对流流体的平均速度、 温度以及它们的脉动. 较详细地研究了浮力对逆混合对流的流动特性和传热特性的影响. 评 估了实验中采用的冷线测量温度补偿速度探头温度敏感的影响. 逆混合对流的传热结果用无 量纲参数Ω (Ω= Grd / Red2 )来表示，其中，基于管道直 径的雷诺数Red变化范围为900~18000, 浮力参数Ω变化范围为 0.004899~0.5047. 研究结果表明，浮力对逆混合对流的换热有强化作用. 随着葛拉晓夫数Grd的增加，温度脉动，流向雷诺正应力和流向温度通量增 大，并且在靠近壁面的流体区域尤其明显. 热线与冷线相结合的技术适合于研究非绝热的流 动测量，可以用于研究浮力对流动和换热特性的影响.     

On hot-wire diagnostics in Rayleigh–Taylor mixing layers

Two hot-wire flow diagnostics have been developed to measure a variety of turbulence statistics in the buoyancy driven, air-helium Rayleigh–Taylor mixing layer. The first diagnostic uses a multi-position, multi-overheat (MPMO) single wire technique that is based on evaluating the wire response function to variations in density, velocity and orientation, and gives time-averaged statistics inside the mixing layer. The second diagnostic utilizes the concept of temperature as a fluid marker, and employs a simultaneous three-wire/cold-wire anemometry technique (S3WCA) to measure instantaneous statistics. Both of these diagnostics have been validated in a low Atwood number (A _t  ≤ 0.04), small density difference regime, that allowed validation of the diagnostics with similar experiments done in a hot-water/cold-water water channel facility. Good agreement is found for the measured growth parameters for the mixing layer, velocity fluctuation anisotropy, velocity fluctuation p.d.f behavior, and measurements of molecular mixing. We describe in detail the MPMO and S3WCA diagnostics, and the validation measurements in the low Atwood number regime (A _t  ≤ 0.04). We also outline the advantages of each technique for measurement of turbulence statistics in fluid mixtures with large density differences.     

Tests of a fiber-optic velocity transducer

A novel transducer is developed and tested. The transducer utilizes optical fiber to measure mean and instantaneous flow rates in turbulent flows, and is capable of detecting flow reversal. Calibration of the transducer is conducted in both air and water. The dynamic response of the transducer is tested against hot-wire anemometery in the wake flow of a circular cylinder over a wide range of Reynolds number.List of symbols C _D drag coefficient - D diameter of cylinder - d diameter of fiber - E modulus of elasticity of the fiber - e output voltage - F drag force per unit length of a cylinder - f frequency (Hz) - L length of the fiber cantilever - M magnification factor - m mass per unit length of the fiber - Re Reynolds number - q dynamic pressure (= 1/2 U ²) - U free stream velocity - density - v kinematic viscosity     

Numerical simulation of transient response of heat transfer from a hot-wire anemometer transducer

Both the steady state and transient response of the Nusselt number to variations in Reynolds number over the range 1 to 40 are given by the analysis of a time dependent numerical simulation of a hot-wire anemometer transducer described here. Transducer response can be modelled suitably by considering the system to consist of a phase independent non-linearity followed by a non-linear differential equation whose coefficient (approximate time constant) is Nusselt number dependent. Errors associated with slip flow and free convection constrain the minimum size of a hot-wire which may be used in calibration anemometry while the wire thermal inertia and, to a lesser extent, the response of the Nusselt number to Reynolds number limits the use of large diameter wires. Thus, although the tendency has been to use finer and finer wires, the basic fluid mechanics suggests that a compromise in the choice of the wire diameter is appropriate. Thus development of even more sophisticated hot-wire anemometer control systems as well as accurate calibration techniques for measurement in flows containing large amplitude high frequency turbulence is required     

A novel perspective to high-speed cross-hot-wire calibration methodology

A practical cross-hot-wire calibration and data reduction methodology for instantaneous measurements of mass flux and flow angle is developed for two dimensional subsonic compressible flows. Historically, data reduction for flow conditions of 0.4?<?M?<?1.2 is regarded as problematic, even in the simplified case of flow normal mounted wires. Thus, in comparison with the incompressible and supersonic conditions, the literature addressing these flow regimes is quite limited. The present study addresses this void by relating the wire voltages to flow conditions through renormalized, Mach and overheating independent, nondimensional quantities. Therefore, a short and robust calibration can be performed in an unheated free jet facility with applicability toward a broad range of planar flow conditions. This disposes the need for typical closed loop calibration wind tunnels which vary flow velocity, density and temperature independently to parameterize the voltage dependency in a purely empirical manner.     

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.     

Experimental investigation on turbulent flow in a square-sectioned 90-degree bend

The development of steady, turbulent flow in a 90° section of a curved square duct was studied at a Reynolds number of 4 × 10⁴ by hot-wire anemometer. The curved duct has a cross-section measuring 80 × 80 mm and a curvature radius ratio of 4 and is connected with a long, straight duct at its both ends. The longitudinal and lateral components of mean and fluctuating velocities, and the Reynolds stresses were measured by the method of rotating a probe with an inclined hot-wire. The velocity fields of the primary and secondary flows, and the Reynolds stress distributions in the cross-section were illustrated in the form of contour map. The development of the primary flow was found to be connected with a strong pressure gradient near the outer and inner wall and a secondary flow induced in the cross-section of the bend by a pressure difference between the outer and inner wall and a centrifugal force acting on the fluid; the fluid is accelerated near the inner wall and decelerated near the outer wall between the bend angle ϕ ≅ 0° and ϕ ≅ 30°, but an increase and decrease of the fluid velocity are reversed between ϕ ≅ 30° and ϕ ≅ 90°. The fluctuating velocity correlations, i.e. the Reynolds stresses follow a complicated progress according to the complex development of the primary flow. The results obtained can be available to verify various types of turbulence models and to develop new models. Received: 10 May 1999/Accepted: 15 March 2000     

Direct Numerical Simulation of Transitional Turbulent Flow in a Closed Rotor-Stator Cavity

The transitional turbulent regime in confined flow between a rotating and a stationary disc is studied using direct numerical simulation. Besides its fundamental importance as a three-dimensional prototype flow, such flows frequently arise in many industrial devices, especially in turbomachinary applications. The present contribution extends the DNS simulation into the turbulent flow regime, to a rotational Reynolds number Re =3 × 10⁵. An annular rotor-stator cavity of radial extension ΔR and height H, is considered with L = 4.72(L = ΔR/H) and Rm = 2.33 (Rm = (R ₁+ R ₀)/ΔR). The direct numerical simulation is performed by integrating the time-dependent Navier–Stokes equations until a statistically steady state is reached. A three-dimensional spectral method is used with the aim of providing both very accurate instantaneous fields and reliable statistical data. The instantaneous quantities are analysed in order to enhance our knowledge of the physics of turbulent rotating flows. Also, the results have been averaged so as to provide target turbulence data for any subsequent modelling attempts at reproducing the flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Study of Density Effects in Turbulent Buoyant Jets Using Large-Eddy Simulation

Large-Eddy simulations (LES) of spatially evolving turbulent buoyant round jets have been carried out with two different density ratios. The numerical method used is based on a low-Mach-number version of the Navier–Stokes equations for weakly compressible flow using a second-order centre-difference scheme for spatial discretization in Cartesian coordinates and an Adams–Bashforth scheme for temporal discretization. The simulations reproduce the typical temporal and spatial development of turbulent buoyant jets. The near-field dynamic phenomenon of puffing associated with the formation of large vortex structures near the plume base with a varicose mode of instability and the far-field random motions of small-scale eddies are well captured. The pulsation frequencies of the buoyant plumes compare reasonably well with the experimental results of Cetegen (1997) under different density ratios, and the underlying mechanism of the pulsation instability is analysed by examining the vorticity transport equation where it is found that the baroclinic torque, buoyancy force and volumetric expansion are the dominant terms. The roll-up of the vortices is broken down by a secondary instability mechanism which leads to strong turbulent mixing and a subsequent jet spreading. The transition from laminar to turbulence occurs at around four diameters when random disturbances with a 5% level of forcing are imposed to a top-hat velocity profile at the inflow plane and the transition from jet-like to plume-like behaviour occurs further downstream. The energy-spectrum for the temperature fluctuations show both −5/3 and −3 power laws, characteristic of buoyancy-dominated flows. Comparisons are conducted between LES results and experimental measurements, and good agreement has been achieved for the mean and turbulence quantities. The decay of the centreline mean velocity is proportional to x ^−1/3 in the plume-like region consistent with the experimental observation, but is different from the x ⁻¹ law for a non-buoyant jet, where x is the streamwise location. The distributions of the mean velocity, temperature and their fluctuations in the near-field strongly depend upon the ratio of the ambient density to plume density ρ_a/ρ₀. The increase of ρ_a/ρ₀ under buoyancy forcing causes an increase in the self-similar turbulent intensities and turbulent fluxes and an increase in the spatial growth rate. Budgets of the mean momentum, energy, temperature variance and turbulent kinetic energy are analysed and it is found that the production of turbulence kinetic energy by buoyancy relative to the production by shear is increased with the increase of ρ_a/ρ₀. Received 16 June 2000 and accepted 26 June 2001     

Calibration ofX-probes for turbulent flow measurements

We compare two methods of calibrating the yaw response of hot-wire probes: (i) the assumption that an effective angle, independent of the flow speed, can be deduced; (ii) the more general approach of determining the yaw response at a number of different speeds. The first, simpler, approach is shown to give surprisingly reasonable results for the usual turbulence statistics, even in high turbulence intensity flows. Some differences in the distribution of the inclination of the instantaneous velocity vector are observed. There is no advantage in using thek ² factor to allow for longitudinal cooling.     

Turbulence in rough-wall boundary layers: universality issues

Wind tunnel measurements of turbulent boundary layers over three-dimensional rough surfaces have been carried out to determine the critical roughness height beyond which the roughness affects the turbulence characteristics of the entire boundary layer. Experiments were performed on three types of surfaces, consisting of an urban type surface with square random height elements, a diamond-pattern wire mesh and a sand-paper type grit. The measurements were carried out over a momentum thickness Reynolds number (Re _θ) range of 1,300–28,000 using two-component Laser Doppler anemometry (LDA) and hot-wire anemometry (HWA). A wide range of the ratio of roughness element height h to boundary layer thickness δ was covered (0.04 ￡ h/d ￡ 0.400.04 \leq h/\delta \leq 0.40). The results confirm that the mean profiles for all the surfaces collapse well in velocity defect form up to surprisingly large values of h/δ, perhaps as large as 0.2, but with a somewhat larger outer layer wake strength than for smooth-wall flows, as previously found. At lower h/δ, at least up to 0.15, the Reynolds stresses for all surfaces show good agreement throughout the boundary layer, collapsing with smooth-wall results outside the near-wall region. With increasing h/δ, however, the turbulence above the near-wall region is gradually modified until the entire flow is affected. Quadrant analysis confirms that changes in the rough-wall boundary layers certainly exist but are confined to the near-wall region at low h/δ; for h/δ beyond about 0.2 the quadrant events show that the structural changes extend throughout much of the boundary layer. Taken together, the data suggest that above h/δ ≈ 0.15, the details of the roughness have a weak effect on how quickly (with rising h/δ) the turbulence structure in the outer flow ceases to conform to the classical boundary layer behaviour. The present results provide support for Townsend’s wall similarity hypothesis at low h/δ and also suggest that a single critical roughness height beyond which it fails does not exist. For fully rough flows, the data also confirm that mean flow and turbulence quantities are essentially independent of Re _θ; all the Reynolds stresses match those of smooth-wall flows at very high Re _θ. Nonetheless, there is a noticeable increase in stress contributions from strong sweep events in the near-wall region, even at quite low h/δ.     

A Beale–Kato–Majda Criterion for Three Dimensional Compressible Viscous Heat-Conductive Flows

We prove a blow-up criterion in terms of the upper bound of (ρ, ρ ⁻¹, θ) for a strong solution to three dimensional compressible viscous heat-conductive flows. The main ingredient of the proof is an a priori estimate for a quantity independently introduced in Haspot (Regularity of weak solutions of the compressible isentropic Navier–Stokes equation, arXiv:1001.1581, 2010) and Sun et al. (J Math Pure Appl 95:36–47, 2011), whose divergence can be viewed as the effective viscous flux.