Study of the flow around surface-mounted pyramids

The turbulent flow around square-based wall-mounted pyramids in thin and thick boundary layers was experimentally investigated as a function of the pyramid apex angle, ‘, and angle of attack, f, based on mean flow surface patterns, pressure and velocity measurements. For thin boundary layers, wake periodicity is observed. For slender pyramids (15°<‘<75°), the periodic formation and shedding of vortices is observed. The shedding frequency scales with the length scale L=w'(w'/h)^-1/4, where h is the pyramid height and w' is the frontal (projected) base width. For broad pyramids, wake periodicity exists but cannot be related to vortex shedding. Vortex shedding appears related to the existence of a double vortex structure along the side faces of the slender pyramids. The location of the separation point upstream and the attachment point downstream of the obstacle also scales with L. For thick boundary layers, no wake periodicity is observed and the mean flow structure in the wake differs from that seen for thin boundary layers. The location of the separation and attachment points scales only approximately with L.     

4D Magnetic resonance velocimetry for mean velocity measurements in complex turbulent flows

An adaptation of a medical magnetic resonance imaging system to the noninvasive measurement of three-component mean velocity fields in complex turbulent engineering flows is described. The aim of this paper is to evaluate the capabilities of the technique with respect to its accuracy, time efficiency and applicability as a design tool for complex turbulent internal geometries. The technique, called 4D magnetic resonance velocimetry (4D-MRV), is used to measure the mean flow in fully developed low-Reynolds number turbulent pipe flow, Re=6400 based on bulk mean velocity and diameter, and in a model of a gas turbine blade internal cooling geometry with four serpentine passages, Re=10,000 and 15,000 based on bulk mean velocity and hydraulic diameter. 4D-MRV is capable of completing full-field measurements in three-dimensional volumes with sizes on the order of the magnet bore diameter in less than one hour. Such measurements can include over 2 million independent mean velocity vectors. Velocities measured in round pipe flow agreed with previous experimental results to within 10%. In the turbulent cooling passage flow, the average flow rates calculated from the 4D-MRV velocity profiles agreed with ultrasonic flowmeter measurements to within 7%. The measurements lend excellent qualitative insight into flow structures even in the highly complex 180° bends. Accurate quantitative measurements were obtained throughout the Re=10,000 flow and in the Re=15,000 flow except in the most complex regions, areas just downstream of high-speed bends, where velocities and velocity fluctuations exceeded MRV capabilities for the chosen set of scan parameters. General guidelines for choosing scanning parameters and suggestions for future development are presented.     

The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet

The flow at the outer boundary of a submerged self-similar turbulent jet at Re=2᎒³ is investigated experimentally by means of combined particle image velocimetry (PIV) laser-induced fluorescence (LIF) measurements. The jet fluid contains a fluorescent dye so that the LIF data can be used to discriminate between the jet fluid and the ambient fluid. The axial velocity, Reynolds stress, and vorticity are determined relative to the jet boundary. The results are compared against the conventional profiles, and the results of a direct numerical simulation of the turbulent far-wake behind a flat plate. The results show a sharp transition between rotational and irrotational fluid at the fluid interface, and the existence of a layer of irrotational velocity fluctuations outside the turbulent region.     

Propagation of shear-layer structures in the near-wall region of a turbulent boundary layer

Two non-intrusive techniques, namely laser Doppler anemometry (LDA) and the electrochemical method, have been used for simultaneous measurements of the instantaneous streamwise velocity (U) and longitudinal wall shear stress (S), evaluated in a zero pressure gradient turbulent boundary layer. The space-time correlation between the fluctuating velocity and shear stress suggests that the coherent flow structures are propagated (i) under a slight angle of 5° in the near-wall region and (ii) at an average angle of 15.5° for y⁺>30. It is shown that the time shift obtained from the correlation between the LDA and the electrochemical signals is due to the dynamic behaviour of the electrodiffusion probe, but also to the leaning character of the coherent structures.     

Effect of a suspension of magnesium particles on the detonation characteristics of methane-oxygen-nitrogen mixtures at elevated initial pressures

Effect of addition of magnesium particles on the detonation characteristics of methane-oxygen-nitrogen mixtures at elevated initial pressures is predicted by numerical calculations. Two rich (r=3, Z_N2/Z_O2=5 and r=2.8, Z_N2/Z_O2=2.9) mixtures under 40 bar initial pressure are considered. It is shown that an increase of the detonation velocity of the reactive mixture may be achieved with a proper choice of size and mass concentration of particles. For particle diameters larger than a critical value, magnesium addition is not able to provide an augmentation of the detonation velocity of the reactive mixture. Results are discussed in relation with performance enhancement of Ram accelerators.     

Experimental analysis of turbulent flow structure in a fully developed rib-roughened rectangular channel with PIV

An experimental study was carried out to investigate the turbulent water-flow structure over one-side micro-repeated ribs in a narrow two-dimensional rectangular channel by particle image velocimetry (PIV). Two rib pitch-to-height ratios p/k of 10 and 20 were investigated while the rib height was held constant at 4 mm. The rib height-to-channel equivalent diameter ratio k/D_e was 0.1. The streamwise mean velocity and turbulent kinetic energy fields in the fully developed flow region of the channel were calculated at three different positions of x=0, 3.8, and -6.2 mm, which corresponded to center, downstream, and upstream of the rib, respectively, and for two Reynolds numbers Re of 7,000 and 20,000. A large-scale turbulent eddy was generated by the rib promoter and then propagated into the mainstream flow, which led to the deformation of the velocity profile. Downstream of the rib, rotating and counter-rotating eddies were also generated by the rib promoter. The enhancement of the turbulent kinetic energy was not changed when the Reynolds number increased from 7,000 to 20,000 between p/k=20 and 10. The reattachment length L_R was measured from velocity vector fields in the developing, fully developed, and exit regions of the flow over the range Re=1,400-50,000. The results showed that the ratio p/k and the Reynolds number had no significant effect on the reattachment length beyond a critical value of Re=15,000, where L_R was found to be approximately 4 times the rib height.     

Particle image velocimetry measurements of a backward-facing step flow

Particle image velocimetry (PIV) measurements were carried out on a backward-facing step flow at a Reynolds number of Re_h=U_Xh/9=4,660 (based on step height and freestream velocity). In-plane velocity, out-of-plane vorticity, Reynolds stress and turbulent kinetic energy production measurements in the x-y and x-z planes of the flow are presented. Proper orthogonal decomposition was performed on both the fluctuating velocity and vorticity fields of the x-y plane PIV data using the method of snapshots. Low-order representations of the instantaneous velocity fields were reconstructed using the velocity modes. These reconstructions provided insight into the contribution that the various length scales make to the spatial distribution of mean and turbulent flow quantities such as Reynolds stress and turbulent kinetic energy production. Large scales are found to contribute to the Reynolds stresses and turbulent kinetic energy production downstream of reattachment, while small scales contribute to the intense Reynolds stresses in the vicinity of reattachment.     

Effect of different initial conditions on a turbulent round free jet

Velocity measurements were made in two jet flows, the first exiting from a smooth contraction nozzle and the second from a long pipe with a fully developed pipe flow profile. The Reynolds number, based on nozzle diameter and exit bulk velocity, was the same (䏪,000) in each flow. The smooth contraction jet flow developed much more rapidly and approached self-preservation more rapidly than the pipe jet. These differences were associated with differences in the turbulence structure in both the near and far fields between the two jets. Throughout the shear layer for x<3d, the peak in the v spectrum occurred at a lower frequency in the pipe jet than in the contraction jet. For x́d, the peaks in the two jets appeared to be nearly at the same frequency. In the pipe jet, the near-field distributions of f(r) and g(r), the longitudinal and transverse velocity correlation functions, differed significantly from the contraction jet. The integral length scale L_u was greater in the pipe jet, whereas L_v was smaller. In the far field, the distributions of f(r) and g(r) were nearly similar in the two flows. The larger initial shear layer thickness of the pipe jet produced a dimensionally lower frequency instability, resulting in longer wavelength structures, which developed and paired at larger downstream distances. The regular vortex formation and pairing were disrupted in the shear layer of the pipe jet. The streamwise vortices, which enhance entrainment and turbulent mixing, were absent in the shear layer of the pipe jet. The formation of large-scale structures should occur much farther downstream in the pipe jet than in the contraction jet.     

Combined natural convection and radiation in a vertical annulus

This paper presents a numerical study of the effects of thermal radiation on the heat transfer of steady natural convection in a participating fluid contained inside a cylindrical annulus. The fluid absorbs and emits radiation energy. Uniform temperature difference is imposed across the inner and outer cylinder walls. The radiation part of the problem is treated by using the two-dimensional P-1 approximation. The numerical calculations were executed using the PROJECTION algorithm with a power law scheme. The analysis are performed for Rayleigh number ranging from 10⁴ to 10⁶, aspect ratio varying between 2 and 10, and the radius ratio ranging from 1.25 to 10 for N=0.1, 1, and X where N is the conduction-to-radiation parameter. The thermal radiation greatly influences the flow field and temperature distribution inside the enclosure for different aspect ratio and radius ratios. Those results are presented vividly by the streamlines and isotherms. Based on the results, the average Nusselt number is correlated by a relation of the form N¥ˆ=a+b ln A and N¥ˆ=c+d exp(m-/e). The coefficients for various N are tabulated. Zusammenfassung Ziel der numerischen Studie ist es, die Einflüsse der Wärmestrahlung auf den Wärmeübergang durch stationäre, natürliche Konvektion an ein, in einem zylindrischen Ringraum befindlichen Fluid zu bestimmen, das Strahlungsenergie absorbiert und emittiert. Innere und äußere Zylinderwand werden auf unterschiedlichen, aber konstanten Temperaturen gehalten. Der Strahlungstransport wird mittels der zweidimensionalen P-1-Approximation erfaßt; die numerischen Berechnungen erfolgten unter Verwendung des PROJECTION-Algorithms nach einem Potenzgesetzschema. Die Untersuchung erstreckt sich auf Rayleigh-Zahlen von 10⁴ bis 10⁶, auf Seitenverhältnisse von 2 bis 10 und auf Radienverhältnisse von 1,25 bis 10. Der Leitungs/Strahlungs-Parameter N hatte die Werte 0,1-1,0 und X. Die Wärmestrahlung hat im Variationsbereich des Seiten-und des Radienverhältnisses großen Einfluß auf das Strömungsverhalten und die Temperaturverteilung im Ringspalt, was sich sehr gut durch Stromlinien-und Isothermenfeld-Darstellungen belegen läßt. Die Resultate stützen Berechnungsgleichungen für die gemittelte Nusselt-Zahl der Form N¥ˆ=a+b ln A und N¥ˆ=e+d exp(-/e). Die einzelnen Koeffizienten sind für verschiedene N-Werte in Tabellen zusammengestellt.     

Traversing field of view and AR-PIV for mid-field wake vortex investigation in a towing tank

Wake vortex flow experiments are performed in a water tank where a 1:48 scaled model of a large transport aircraft A340-300 is towed at the speed of 3 and 5 ms^-1 with values of the angle of attack !={2°, 4°, 8°}. Particle image velocimetry (PIV) measurements are performed in a plane perpendicular to the towing direction describing the streamwise component of the wake vorticity. The instantaneous field of view (I-FOV) is traversed vertically with an underwater moving-camera device tracking the vortex core during the downward motion. An adaptive resolution (AR) image-processing technique is introduced that enhances the PIV interrogation in terms of spatial resolution and accuracy. The main objectives of the investigation are to demonstrate the applicability of PIV diagnostics in wake vortex research with towing-tank facilities. The specific implementation of the traversing field-of-view (T-FOV) technique and the AR image processing are driven by the need to characterize the vortex wake global properties as well as the vortex decay phenomenon in the mid- and far-field. Relevant aerodynamic information is obtained in the mid-field where the time evolution of the vortex structure (core radius and tangential velocity) and of the overall vortex wake (vortex trajectory, descent velocity, circulation) are discussed.     

An Existence Theorem¶for the Navier-Stokes Flow¶in the Exterior of a Rotating Obstacle

We consider the three-dimensional Navier-Stokes initial value problem in the exterior of a rotating obstacle. It is proved that a unique solution exists locally in time if the initial velocity possesses the regularity L^1/2. This regularity assumption is the same as that in the famous paper of Fujita &; Kato. An essential step for the proof is the deduction of a certain smoothing property together with estimates near t˸ of the semigroup, which is not an analytic one, generated by the operator \Cal Lu = -P[\De u+(\om×x)·\na u-\om×u]\Cal Lu= -P\left[\De u+(\om\times x)\cdot\na u-\om\times u\right] in the space L², where y stands for the angular velocity of the rotating obstacle and P denotes the projection associated with the Helmholtz decomposition.     

L1 Continuous Dependence Property¶for Systems of Conservation Laws

This paper is concerned with the uniqueness and L¹ continuous dependence of entropy solutions for nonlinear hyperbolic systems of conservation laws. We study first a class of linear hyperbolic systems with discontinuous coefficients: Each propagating shock wave may be a Lax shock, or a slow or fast undercompressive shock, or else a rarefaction shock. We establish a result of L¹ continuous dependence upon initial data in the case where the system does not contain rarefaction shocks. In the general case our estimate takes into account the total strength of rarefaction shocks. In the proof, a new time-decreasing, weighted L¹ functional is obtained via a step-by-step algorithm. To treat nonlinear systems, we introduce the concept of admissible averaging matrices which are shown to exist for solutions with small amplitude of genuinely nonlinear systems. Interestingly, for many systems of continuum mechanics, they also exist for solutions with arbitrary large amplitude. The key point is that an admissible averaging matrix does not exhibit rarefaction shocks. As a consequence, the L¹ continuous dependence estimate for linear systems can be extended to nonlinear hyperbolic systems using a wave-front tracking technique.     

Perpendicular ultrasound velocity measurement by 2D cross correlation of RF data. Part A: validation in a straight tube

An ultrasound velocity assessment technique was validated, which allows the estimation of velocity components perpendicular to the ultrasound beam, using a commercially available ultrasound scanner equipped with a linear array probe. This enables the simultaneous measurement of axial blood velocity and vessel wall position, rendering a viable and accurate flow assessment. The validation was performed by comparing axial velocity profiles as measured in an experimental setup to analytical and computational fluid dynamics calculations. Physiologically relevant pulsating flows were considered, employing a blood analog fluid, which mimics both the acoustic and rheological properties of blood. In the core region (|r|/a < 0.9), an accuracy of 3 cm s⁻¹ was reached. For an accurate estimation of flow, no averaging in time was required, making a beat to beat analysis of pulsating flows possible.     

On the First Boundary Value Problem for Quasilinear Parabolic Equations with Two Independent Variables

This paper is concerned with the global solvability of the first initial boundary value problem for the quasilinear parabolic equations with two independent variables: a(t,x,u,u_xINF>)u_xxm u_t=f(t,x,u,u_xINF>). We investigate the case when the growth of [(|f(t,x,u,p)|)/(a(t,x,u,p))]{{|f(t,x,u,p)|}\over {a(t,x,u,p)}} with respect to p is faster than p² when |p|M X. Conditions which guarantee the global classical solvability of the problem are formulated.     

Comparison of molecular tagging velocimetry data and direct simulation Monte Carlo simulations in supersonic micro jet flows

We present results of a combined experimental computational study of free jet flow produced by a 1 mm (height)ǹ mm (span) nominally Mach 2 supersonic jet. Two-dimensional maps of u_x, the component of velocity parallel to the principal flow axis, are obtained experimentally, by acetone molecular tagging velocimetry (MTV), and computationally, by the direct simulation Monte Carlo (DSMC) method, at a stagnation pressure and temperature of 10 torr and 300 K, respectively. In all cases, direct comparison of the experimental data and the predictions from DSMC showed excellent agreement, with only minor deviations which, in most cases, can be ascribed to either the inherent uncertainty in the MTV or small uncertainties in the measured wall pressures.     

On multiple-path sonic anemometer measurement theory

In this paper, a model of the measuring process of sonic anemometers with more than one measuring path is presented. The main hypothesis of the work is that the time variation of the turbulent speed field during the sequence of pulses that produces a measure of the wind speed vector affects the measurement. Therefore, the previously considered frozen flow, or instantaneous averaging, condition is relaxed. This time variation, quantified by the mean Mach number of the flow and the time delay between consecutive pulses firings, in combination with both the full geometry of sensors (acoustic path location and orientation) and the incidence angles of the mean with speed vector, give rise to significant errors in the measurement of turbulence which are not considered by models based on the hypothesis of instantaneous line averaging. The additional corrections (relative to the ones proposed by instantaneous line-averaging models) are strongly dependent on the wave number component parallel to the mean wind speed, the time delay between consecutive pulses, the Mach number of the flow, the geometry of the sensor and the incidence angles of mean wind speed vector. Kaimal´s limit k_W1=1/l (where k_W1 is the wave number component parallel to mean wind speed and l is the path length) for the maximum wave numbers from which the sonic process affects the measurement of turbulence is here generalized as k_W1=C_l/l, where C_l is usually lesser than unity and depends on all the new parameters taken into account by the present model.     

Step and steady shear responses of nearly monodisperse highly entangled 1,4-polybutadiene solutions

Nonlinear relaxation dynamics of highly entangled solutions of high molecular weight 1,4-polybutadiene (PB) in a PB oligomer are studied in steady shear and step shear flows. Polymer entanglement densities vary in the range 14hN/N_e(J)⣴, allowing systematic investigation of entanglement effects on nonlinear rheological response. In agreement with previous steady shear studies using well entangled polystyrene solutions, a flow regime is found where both the steady-state shear stress and first normal stress difference remain constant or increase quite slowly with shear rate, leading to a plateau in the steady-state orientation angle. The magnitude of the average orientation angle in the plateau range is in accordance with predictions of a recent theory by Islam and Archer (2001). In step shear, the nonlinear relaxation modulus G(t,%) is approximately factorable into time-dependent G(t) and strain-dependent h(%) functions only at long times, t>5_k, where 5_k,O(F_d0). This finding is consistent with earlier observations for entangled polystyrene solutions; however the complex crossing pattern in G(t,%)h^-1(%) that precede factorability in the latter materials is not observed. For all but the most entangled sample, apparent shear damping functions h (%,t)=(G(t,%))/(G(t)) immediately following imposition of shear are in nearly quantitative accord with the damping function h_DEIA predicted by Doi-Edwards theory.     

The accuracy of turbulent velocity component measurements by multi-sensor hot-wire probes: a new approach to an old problem

The measurement accuracy of different hot-wire probes possessing between two and 12 sensors is analyzed. Experimental data were sampled in a round free jet and in a zero-pressure-gradient turbulent boundary layer by a 12-sensor hot-wire probe. Testing of the various hot-wire configurations is enabled by selectively considering different combinations of the 12 available anemometer output voltages. The influence on the measurement accuracy of neglecting the velocity gradients as well as neglecting one velocity component is analyzed. Two approaches were applied. One is based on expressions that relate the instantaneous velocity components and velocity gradients, and the other is based on a simple least-squares regression method. It is found that neglecting the instantaneous fluctuations of the velocity gradients for the measurement of the cross-stream velocity component, V, has a crucial influence and results in large errors. It is also shown that this influence is less significant or even negligible for the measurement accuracy of the other two velocity components, U and W.     

On the Riemann Problem for Non-Conservative Hyperbolic Systems

We consider the construction and the properties of the Riemann solver for the hyperbolic systemu_t + f(u)_x = 0, (0.1) u_t + f(u)_x = 0, (0.1) assuming only that Df is strictly hyperbolic. In the first part, we prove a general regularity theorem on the admissible curves T_i of the i-family, depending on the number of inflection points of f: namely, if there is only one inflection point, T_i is C^(1,1). If the i-th eigenvalue of Df is genuinely nonlinear, it is well known that T_i is C^(2,1). However, we give an example of an admissible curve T_i which is only Lipschitz continuous if f has two inflection points. In the second part, we show a general method for constructing the curves T_i, and we prove a stability result for the solution to the Riemann problem. In particular we prove the uniqueness of the admissible curves for (0.1). Finally we apply the construction to various approximations to (0.1): vanishing viscosity, relaxation schemes and the semidiscrete upwind scheme. In particular, when the system is in conservation form, we obtain the existence of smooth travelling profiles for all small admissible jumps of (0.1).     

Quantitative temperature imaging in gas-phase turbulent thermal convection by laser-induced fluorescence of acetone

In this paper, an acetone planar laser-induced fluorescence (PLIF) technique for nonintrusive temperature imaging is demonstrated in gas-phase (Pr = 0.72) turbulent Rayleigh-Bénard convection at Rayleigh number Ra = 1.3᎒⁵. The PLIF technique provides quantitative spatially correlated temperature data without the flow intrusion or time lag associated with physical probes, and without the significant path averaging that plagues most optical heat-transfer diagnostic tools, such as the Mach-Zehnder interferometer, thus making PLIF an attractive choice for quantitative thermal imaging in easily perturbed, complex three-dimensional flow fields. The "instantaneous" (20-ns integration time) thermal images presented have a spatial resolution of 176쐀아 µm and a single-pulse temperature measurement precision of - 2.5 K, or 2.5% of the total temperature difference. These images represent a two-dimensional slice through a complex three-dimensional flow, allowing for thermal structure of the turbulence to be quantified. Statistics such as the horizontally averaged temperature profile, root-mean square (rms) temperature fluctuation, two-point spatial correlations, and conditionally averaged plume structures are computed from an ensemble of 100 temperature images. The profiles of the mean temperature and rms temperature fluctuation are in good agreement with previously published data, and the results obtained from the two-point spatial correlations and conditionally averaged temperature fields show the importance of large-scale coherent structures in this turbulent flow.