Control of low-speed turbulent separated flow using jet vortex generators

A parametric study has been performed with jet vortex generators to determine their effectiveness in controlling flow separation associated with low-speed turbulent flow over a two-dimensional rearward-facing ramp. Results indicate that flow-separation control can be accomplished, with the level of control achieved being a function of jet speed, jet orientation (with respect to the free-stream direction), and jet location (distance from the separation region in the free-stream direction). Compared to slot blowing, jet vortex generators can provide an equivalent level of flow control over a larger spanwise region (for constant jet flow area and speed).Nomenclature C _p pressure coefficient, 2(P-P_)/V ² - C _Q total flow coefficient, Q/ v - D ₀ jet orifice diameter - Q total volumetric flow rate - R Reynolds number based on momentum thickness - u fluctuating velocity component in the free-stream (x) direction - V free-stream flow speed - VR ratio of jet speed to free-stream flow speed - x coordinate along the wall in the free-stream direction - jet inclination angle (angle between the jet axis and the wall) - jet azimuthal angle (angle between the jet axis and the free-stream direction in a horizontal plane) - boundary-layer thickness - momentum thickness - lateral distance between jet orifices A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 Sept. 1990     

Rheology of molten polymers

Summary TheCross equation describes the flow of pseudoplastic liquids in terms of an upper and a lower Newtonian viscosity corresponding to infinite and zero shear, and ₀, and of a third material constant related to the mechanism of rupture of linkages between particles in the intermediate, non-Newtonian flow regime, Calculation of of bulk polymers is important, since it cannot be determined experimentally. The equation was applied to the melt flow data of two low density polyethylenes at three temperatures.Using data in the non-Newtonian region covering 3 decades of shear rate to extrapolate to the zero-shear viscosity resulted in errors amounting to about onethird of the measured ₀ values. The extrapolated upper Newtonian viscosity was found to be independent of temperature within the precision of the data, indicating that it has a small activation energy.The ₀ values were from 100 to 1,400 times larger than the values at the corresponding temperatures.The values of were large compared to the values found for colloidal dispersions and polymer solutions, but decreased with increasing temperature. This shows that shear is the main factor in reducing chain entanglements, but that the contribution of Brownian motion becomes greater at higher temperatures.

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Zusammenfassung Die Gleichung vonCross beschreibt das Fließverhalten von pseudoplastischen Flüssigkeiten durch drei Konstante: Die obereNewtonsche Viskosität (bei sehr hohen Schergeschwindigkeiten), die untereNewtonsche Viskosität ₀ (bei Scherspannung Null), und eine Materialkonstante, die vom Brechen der Bindungen zwischen Partikeln im nicht-Newtonschen Fließbereich abhängt. Die Berechnung von ist wichtig für unverdünnte Polymere, wo man sie nicht messen kann.Die Gleichung wurde auf das Fließverhalten der Schmelzen von zwei handelsüblichen Hochdruckpolyäthylenen bei drei Temperaturen angewandt. Die Werte von ₀, durch Extrapolation von gemessenen scheinbaren Viskositäten im Schergeschwindigkeitsbereich von 10 bis 4000 sec^–1 errechnet, wichen bis 30% von den gemessenen ₀-Werten ab. Die Aktivierungsenergie der war so klein, daß die-Werte bei den drei Temperaturen innerhalb der Genauigkeit der Extrapolation anscheinend gleich waren. Die ₀-Werte waren 100 bis 1400 mal größer als die-Werte.Im Verhältnis zu kolloidalen Dispersionen und verdünnten Polymerlösungen war das der Schmelzen groß, nahm aber mit steigender Temperatur ab. Deshalb wird die Verhakung der Molekülketten hauptsächlich durch Scherbeanspruchung vermindert, aber der Beitrag derBrownschen Bewegung nimmt mit steigender Temperatur zu.

     

Penetration depth of a jet injected into an oncoming supersonic flow

The geometrical characteristics of jets injected through an opening in a flat plate into an oncoming supersonic flow have been studied on a number of occasions [1, 3]. However, the results were analyzed under different suppositions about the important dimensionless parameters. In [1], the degree of underexpansion of the jet, characterized by n = p _a /p, was regarded as decisive; in [3], the experimental points were plotted against the relative dynamic head _a u² _a /(u² ) of the jet. In the present paper, dimensional considerations are used to determine the dimensionless parameters which influence the flow field when an injected jet interacts with an oncoming supersonic gas flow. The influence of these determining dimensionless parameters on the depth of penetration of injected jets into a flow was investigated experimentally. It is shown that the relative depth of penetration is determined basically by the relative specific impulse of the jet, the injection angle, and the shape of the blowing nozzle section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 151–154, July–August, 1980.     

Flow in porous media III: Deformable media

Stokes flow in a deformable medium is considered in terms of an isotropic, linearly elastic solid matrix. The analysis is restricted to steady forms of the momentum equations and small deformation of the solid phase. Darcy's law can be used to determine the motion of the fluid phase; however, the determination of the Darcy's law permeability tensor represents part of the closure problem in which the position of the fluid-solid interface must be determined.Roman Letters A interfacial area of the- interface contained within the macroscopic system, m² - A interfacial area of the- interface contained within the averaging volume, m² - A _e area of entrances and exits for the-phase contained within the macroscopic system, m² - A ^* interfacial area of the- interface contained within a unit cell, m² - A _e ^* area of entrances and exits for the-phase contained within a unit cell, m² - E Young's modulus for the-phase, N/m² - e i unit base vectors (i = 1, 2, 3) - g gravity vector, m²/s - H height of elastic, porous bed, m - k unit base vector (=e ₃) - characteristic length scale for the-phase, m - L characteristic length scale for volume-averaged quantities, m - n unit normal vector pointing from the-phase toward the-phase (n = -n ) - p pressure in the-phase, N/m² - P p – g·r, N/m² - r ₀ radius of the averaging volume, m - r position vector, m - t time, s - T total stress tensor in the-phase, N/m² - T ⁰ hydrostatic stress tensor for the-phase, N/m² - u displacement vector for the-phase, m - V averaging volume, m₃ - V volume of the-phase contained within the averaging volume, m³ - v velocity vector for the-phase, m/s Greek Letters V /V, volume fraction of the-phase - mass density of the-phase, kg/m³ - shear coefficient of viscosity for the-phase, Nt/m² - first Lamé coefficient for the-phase, N/m² - second Lamé coefficient for the-phase, N/m² - bulk coefficient of viscosity for the-phase, Nt/m² - T –T ⁰ , a deviatoric stress tensor for the-phase, N/m²     

Instantaneous visualization of surface flows

An experimental system is described for visualizing the surface flow of a wing, using an oil smoke tracer technique. The method leads to the determination of the instantaneous velocity direction at the output of surface injectors. A preliminary investigation is made on a flat plate to optimize the conditions of oil smoke injection. Then, the visualization is performed on the upperside of a sweptback wing in the vicinity of the reattachment of the vortex flow. This visualization technique can be applied to other types of wall flows — separated or not — around various bodies.List of symbols b wing span - c _n normal (to leading edge) chord - c _r streamwise (or root) chord - d diameter of the injectors - distance from the apex along the leading edge - relative distance from the apex along the leading edge ( = /C _d) - sweep angle - e injector geometric parameter (e = d/l) - angle of attack - K injection parameter - l length of the injectors - v kinematic viscosity - P _t, P_s total and static pressure of the flow - P _inj injection pressure - P _r reduced pressure (P _r = (P_inj – P_t)/(P_t – P_s)) - Re flow Reynolds number (Re = V ·c _n/v) - Re _i injector Reynolds number (Re = V ·d/v) - s curvilinear distance along c _d - s relative curvilinear distance along c _d(s = s/c _d) - V infinite upstream flow velocity     

Outflow of an unexpanded jet into counter supersonic and subsonic flows

The article gives the results of an experimental investigation of the geometric structure of an opposing unexpanded jet. It discusses flow conditions with interaction between the jet and sub- and supersonic flows. It is shown that, with the outflow of an unexpanded jet counter to a supersonic flow, there are unstable flow conditions. For stable flow conditions with one roll, dependences are proposed determining the form of a jet in a supersonic opposing flow. A generalized dependence is obtained for the distribution of the pressure at the surface of a body with a jet, flowing out counter to a subsonic flow. The range of change in the determining parameters are the following: Mach numbers at outlet cross section of nozzle, M _a = 1 and 3; Mach numbers of opposing flow, M = 0.6–0.9 and 2.9; degree of effectiveness of jet, n = p _a /p = 0.5–800 (p _a and p are the static pressures at the outlet cross section of the nozzle and in the opposing flow); the ratios of the specific heat capacities, _a = = 1.4; the drag temperatures of the jet and the flow, T_o = T_oa = 290°K.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 89–96, January–February, 1977.     

Experimental investigation of the flow in the mixing layer in the initial section of an underexpanded jet in a parallel stream

The results are given of an experimental investigation of the flow in the initial section of a turbulent underexpanded jet exhausting from a profiled nozzle with Mach number M _a = 2.56 at the exit into a parallel stream with Mach number M = 3.1. Analysis of the results of measurement of the fields of the total head p₀ and the stagnation temperature T₀ in conjunction with results of calculation of a jet of an ideal gas make it possible to construct the velocity profile in the mixing layer of the underexpanded jet in the parallel supersonic flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 161–163, January–February, 1981.     

Critique of the computational Preston tube method

The general validity of the Computational Preston Tube Method (CPM) proposed by Nitsche et al. is disputed. The method involves the determination of both the skin-friction coefficient c _f and the von Karman constant from fitting two near-wall mean velocity measurements to a generalized van Driest family of velocity profiles. It is demonstrated by a detailed examination of measured mean velocity profiles that for at least one flow situation for which success with the CPM has been claimed, the laminar-turbulent transition of a flat-plate boundary layer, the method must either fail completely or lead to non-unique results. It is concluded that the applicability of the CPM is restricted to flows for which the normal law-of-the-wall is valid.     

A experimental investigation of turbulent flow and heat transfer in elliptical duets

Fully developed turbulent flow and heat transfer to air and water in ducts of elliptical cross section have been investigated experimentally. For the ducts of aspect ratio 2.5 1 and larger, a reduction in the overall heat transfer rate was found in the lower turbulent Reynold's number range (Re<25,000). Similar effects have been noted by investigators of narrow triangular cross sections where flow measurements indicated the possible co-existence of laminar and turbulent flow resulting in localised increases in thermal resistance. It was found that the analogy between momentum and heat transfer could not be applied directly to the larger aspect ratio ducts where significant circumferential variations of wall temperature occurred.

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Zusammenfassung Voll entwickelte turbulente Strömung und Wärmeübertragung an Luft und Wasser in elliptischen Kanälen wurden experimentell untersucht. Für Kanäle mit Achsenverhältnissen von 2,5 1 und größer fand man eine Verringerung des Wärmedurchgangs im Bereich geringer Reynolds-Zahlen (Re < 25 000). Ähnliche Effekte waren von anderen Autoren in engen Dreieckskanälen gefunden worden, wobei man aus Strömungsmessungen das gleichzeitige Auftreten von laminarer und turbulenter Strömung mit örtlicher Zunahme des thermischen Widerstandes folgern konnte. Die Analogie zwischen Impuls- und Wärmeübertragung konnte nicht unmittelbar auf Kanäle mit großem Achsenverhältnis, bei denen die Umfangstemperatur beträchtlich variierte, angewendet werden.

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Nomenclature A cross-sectional area - b duct wall thickness - C_p specific heat at constant pressure - d_e equivalent diameter of noncircular cross-section (=4A/p) - f Fanning friction coefficient - h local heat transfer coefficient (=q_w/(T_w-T_b)) - ¯h average circumferential heat transfer coefficient - k thermal conductivity of fluid - k_w thermal conductivity of wall material - K^* wall conductivity parameter (= k_wb/kd_e) - p wetted perimeter - q_w wall heat flux - T_b bulk fluid temperature - T_w local wall temperature - absolute viscosity - kinematic viscosity (=/) - mass density - Nu Nusselt number (= h d_e/k) - Nu average circumferential Nusselt number (= ¯h d_e/k) - Pr Prandtl number (= C_p/k) - Re Reynolds number (= d_e/) - St Stanton number (= Nu/Re · Pr)     

A Turbulence Model Sensitivity Study for CH4/H2 Bluff-Body Stabilized Flames

The objective of this work is to assess the performances of different turbulence models in predicting turbulent diffusion flames in conjunction with the flamelet model.The k– model, the Explicit Algebraic Stress Model (EASM) and the k– model withvaried anisotropy parameter C (LEA k– model)are first applied to the inert turbulent flow over a backward-facing step, demonstrating the quality of the turbulence models. Following this, theyare used to simulate the CH₄/H₂ bluff-body flame studied by the University of Sydney/Sandia.The numerical results are compared to experimental values of the mixture fraction, velocity field, temperature and constituent mass fractions.The comparisons show that the overall result depends on the turbulence model used, and indicate that theEASM and the LEA k– models perform better than the k– model and mimic most of the significant flow features.     

Interaction of a vortex couple with a free surface

The characteristics of three-dimensional flow structures (scars and striations) resulting from the interaction between a heterostrophic vortex pair in vertical ascent and a clean free surface are described. The flow features at the scar-striation interface (a constellation of whirls or coherent vortical structures) are investigated through the use of flow visualization, a motion analysis system, and the vortex-element method. The results suggest that the striations are a consequence of the short wavelength instability of the vortex pair and the helical instability of the tightly spiralled regions of vorticity. The whirls result from the interaction of striations with the surface vorticity. The whirl-merging is responsible for the reverse energy cascade leading to the formation and longevity of larger vortical structures amidst a rapidly decaying turbulent field.List of symbols A _c Area of a vortex core (Fig. 6b) - AR Aspect ratio of the delta wing model - B base width of delta wing - b ₀ initial separation of the vortex couple - d ₀ depth at which the vortex pair is generated - c average whirl spacing in the x-direction - E energy density - Fr Froude number ( ) - g gravitational acceleration - L length of the scar band - L _ko length of the Kelvin oval - N _w number of whirls in each scar band - P _c Perimeter of a vortex core - q surface velocity vector - r _c core size of the whirl ( = 2A _c/P _c) - Re Reynolds number ( = ) - Rnd a random number - s inboard edge of the scar front (Fig. 6 a) - t time - u velocity in the x-direction - velocity in the y-direction - V _b velocity imposed on a scar by the vortex couple (Fig. 6 a) - V ₀ initial mutual-induction velocity of the vortex couple (=₀/2b ₀) - V _t tangential velocity at the edge of the whirl core - w width of the scar front (Fig. 6 a) - z complex variable - z _k position of the whirl center - half included angle of V-shaped scar band - wave number - _m initial mean circulation of the whirls - ₀ initial circulation of the vortex pair - _w circulation of a whirl - _min minimum survival strength of a whirl - t time step - gDz increment of z - gD change in vorticity - cut-off distance in velocity calculations - critical merging distance - curvature of the surface - wavelength - kinematic viscosity - angular velocity of a whirl core     

Consecutive chemical reactions in an annular reactor with non-newtonian flow

The purpose of this paper is to analyze the homogeneous consecutive chemical reactions carried out in an annular reactor with non-Newtonian laminar flow. The fluids are assumed to be characterized by a Ostwald-de Waele (powerlaw) model and the reaction kinetics is considered of general order. Effects of flow pseudoplasticity, dimensionless reaction rate constants, order of reaction kinetics and ratio of inner to outer radii of reactor on the reactor performances are examined in detail.Nomenclature c _A concentration of reactant A, g.mole/cm³ - c _B concentration of reactant B, g.mole/cm³ - c _A0 inlet concentration of reactant A, g.mole/cm³ - C ₁ dimensionless concentration of A, c _A/c _A0 - C ₂ dimensionless concentration of B, c _B/c _A0 - C ₁ dimensionless bulk concentration of A - C ₂ dimensionless bulk concentration of B - D _A molecular diffusivity of A, cm²/sec - D _B molecular diffusivity of B, cm²/sec - k _A first reaction rate constant, (g.mole/cm³)^1–m /sec - k _B second reaction rate constant, (g.mole/cm³)^1–n /sec - K ₁ dimensionless first reaction rate constant, k _A r ₀ ² c _A0 ^m–1 /D _A - K ₂ dimensionless second reaction rate constant, k _B r ₀ ² c _A0 ^n–1 /D _B - K apparent viscosity, dyne(sec) ^m /cm² - m order of reaction kinetics - n order of reaction kinetics - P pressure, dyne/cm² - r radial coordinate, cm - r _i radius of inner tube, cm - r _max radius at maximum velocity, cm - r _o radius of outer tube, cm - R dimensionless radial coordinate, r/r _o - s reciprocal of rheological parameter for power-law model - u local velocity, cm/sec - u _max maximum velocity, cm/sec - u bulk velocity, cm/sec - U dimensionless velocity, u/u - z axial coordinate, cm - Z dimensionless axial coordinate, zD _A/r ₀ ² /u - ratio of molecular diffusivity, D _B/D _A - ratio of inner to outer radius of reactor, r _i/r _o - ratio of radius at maximum velocity to outer radius, r _max/r _o     

Correlations between porous medium flow data and turbulent tube flow results for aqueous hydroxypropylguar solutions (Part 2)

Turbulent tube flow and the flow through a porous medium of aqueous hydroxypropylguar (HPG) solutions in concentrations from 100 wppm to 5000 wppm is investigated. Taking the rheological flow curves into account reveals that the effectiveness in turbulent tube flow and the efficiency for the flow through a porous medium both start at the same onset wall shear stress of 1.3 Pa. The similarity of the curves = ( _w ) and = ( _w ), respectively, leads to a simple linear relation / =k, where the constantk or proportionality depends uponc. This offers the possibility to deduce (for turbulent tube flow) from (for flow through a porous medium). In conjunction with rheological data, will reveal whether, and if yes to what extent, drag reduction will take place (even at high concentrations).The relation of our treatment to the model-based Deborah number concept is shown and a scale-up formula for the onset in turbulent tube flow is deduced as well.     

About the origin of sharkskin

Summary Some new results of experimental study of linear polyethylene melt flow instabilities are given. Two effects, the main flow instability and the sharkskin phenomenon, are presented in terms of relaxation oscillator theory, and permit an understanding of the influence of experimental parameters on the period of the oscillatory flow. Sharkskin is interpreted to be the same phenomenon as the other instability, but to occur in the die entry region rather than in the whole die itself. Various aspects of sharkskin characteristics are considered.

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Zusammenfassung Es werden einige neue Ergebnisse einer experimentellen Untersuchung betreffend die Instabilität des Fließverhaltens von Polyäthylen hoher Dichte in geschmolzenem Zustand mitgeteilt. Zwei Effekte, die Haupt-Fließinstabilität und das sogenannte Sharkskin-Phänomen, werden mit Hilfe der Theorie der Relaxations-Schwingungen erklärt. Diese Theorie erlaubt es, die Wirkung der experimentellen Parameter auf die Fließschwingungsdauer zu verstehen. Man findet, daß Sharkskin und Haupt-Fließinstabilität im wesentlichen das gleiche Phänomen darstellen, daß aber Sharkskin im Düseneintritt entsteht statt in der ganzen Düse. Die Intensität von Sharkskin wird zu der Schwingungsperiode in Beziehung gesetzt.

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A cross section of the barrel - C capacity - l length of the real die - l ₁ length of the equivalent die corresponding to die entry region - l ₂ length of that part of the die for which the pressure gradient is constant - n flow index - P pressure in the reservoir - Q _ex exit flow rate or flow rate within the die - Q _in inlet flow rate - Q ₁ ,Q ₂ upper and lower boundary of the oscillation of flow rate - Q _SS flow rate at which the sharkskin phenomenon occurs - Q _MFI flow rate at which the main flow instability occurs - Q flow rate at which the main flow instability disappears - r ₁ radius of the equivalent die corresponding to die entry region - r ₂ orr radius of the real die - R resistance - S _p plunger speed - S wall shear stress - S _ss critical die wall shear stress at which sharkskin first occurs - S _MF critical die wall shear stress at which the main flow instability first occurs - T oscillation period - T ₀ die auto-oscillation period - t time - t _eq time necessary for reaching equilibrium conditions - t _c that part of the period during which pressure is increasing - t _d that part of the period during which pressure is decreasing - z distance between die and plunger - mass density - apparent shear viscosity - bulk compressibility With 11 figures and 3 tables     

Error estimates for Rayleigh scattering density and temperature measurements in premixed flames

Rayleigh scattering has become an accepted technique for the determination of total number density during the combustion process. The interpretation of the ratio of total Rayleigh scattering signal as a ratio of densities or temperatures is hampered by the changing composition through a flame, since the average Rayleigh scattering cross-section depends on the gas composition. Typical correction factors as a function of degree of reaction, fuel and equivalence ratio were calculated. The fuels considered were H₂, CH₄, C₂H₄, C₂H₆ and C₃H₈. Factors as low as 0.7 and 0.56 were found for the heaviest hydrocarbon fuel at large equivalence ratio for interpreting the Rayleigh scattering intensity as gas density and inverse temperature, respectively. This is primarily due to the presence of CO and H₂ as intermediates. As CO and H₂ are subsequently oxidized to CO₂ and H₂O, these factors approach 1.0. Conversely, the worst case, when using H₂ as a fuel, occurs in the post flame zone. However, the correction factors for H₂ are near 1.0 and the errors involved will, in general, remain within the expected experimental accuracy of a typical Rayleigh scattering system. Linear correlations of correction factors with equivalene ratio and with the product of equivalence ratio and fuel molecular weight were found and presented. The interpretation of Rayleigh scattering as temperature was found to have larger errors than the interpretation as density. Corrections for changes in gas composition were applied to Rayleigh scattering temperature measurements in the post flame region of CH₄ and C₃H₈ flames with equivalence ratios of 0.75 and 1.0. The corrected temperatures were in excellent agreement with thermocouple measurements.List of symbols A ₁, A ₂ correlation coefficients - B ₁, B ₂ correlation coefficients - C ₁, C ₂ correlation coefficients - D ₁, D ₂ correlation coefficients - C calibration constant for Rayleigh scattering optics - H total enthalpy - Î I _R /I _RO - I _i incident laser intensity - I _R Rayleigh scattering intensity - I _R0 Rayleigh scattering intensity at reference condition - N total number density of gas - N ₀ total number density of gas at reference condition - n _i index of refraction of species i - – T/T _O - T temperature - T _a adiabatic flame temperature - T ₀ reference temperature - t time - W/W ₀ - W mean molecular weight - W ₀ mean molecular weight at reference condition - W _ij rate of production of species i by reaction j - X _i mole fraction of species i - degree of reaction (T – T ₀)/(T _a – T ₀) - laser wavelength - ₀ Loschmidt number - /₀ - density - ₀ density at reference condition - dimensionless mean Rayleigh scattering cross-section - _Ri Rayleigh scattering cross-section of species i - scattering angle measured from the electromagnetic field vector - equivalence ratio     

Flow Structure of Lifted Swirling Jet Flames

Swirling combustion is widely applied in various applications such as gas turbines, utility boilersor waste incinerators. This article contributes to the ongoing research by providing experimentaldata that are gathered in the mixing zone of a lifted swirling premixed natural gas flame. Theobjective of this paper is fivefold: (1) to introduce the lifted swirling flame featuring lowNO _x emissions (2) to provide experimental data such as major species distributions, temperature and streamlines of the flow pattern, (3) to report on velocity bias in probability density function (PDF) distributions and to present PDF sequences of velocities in medium scale swirling flows, (4) to make an assessment on the local small-scale turbulence that is present in the swirling mixinglayer and (5) to provide new experimental data for model verification and development.The PDFs are corrected in order to compensate for the velocity bias phenomenon, which is typicalfor randomly sampled LDA data. Sequences of axial PDF data are presented and measurement locationsof interest are selected to look at the PDF characteristics of the internal and externalrecirculation zones, the mixing layer and the onset of the reacting flow into detail. The mixinglayer PDFs covered a wide velocity range and revealed bimodality; even the concept ofmulti-modality is suggested and explored. Analysis showed that a sum of two Gaussian distributionscan accurately envelop the experimental PDFs. The reason for this broadband turbulence behavior isto be found in combination of precessing and flapping motion of the flow structures, and also incombustion generated instabilities of the lifted flame. As a result, the flame brush is wide (largescale motion) and the mixing (small-scale turbulence) flattens any high temperatures in thecombustion process.The multi-scale turbulence concept is subsequently used to make anassessment of the local turbulence characteristics in the mixing layer.The idea is that the PDFs capture both contributions of the flow-inherent fine grain turbulence (u _l ) which is superposed on slowlarge scale fluctuating structures. It is this u _l that will be of interest in continued research on the classification of the lifted flame into acombustion regime diagram (e.g. Borghi diagram). Finally, the bimodalitycharacter in reacting flows and the prediction of large-scale structuresmay be a challenge for LES researchers.     

Mixing enhancement in axisymmetric turbulent isothermal and buoyant jets

Measurements of the velocity and concentration in axisymmetric, turbulent, isothermal and buoyant jets have been performed with laser-Doppler velocimetry and planar and point laser-induced fluorescence to quantify the mixing enhancement achieved by periodic forcing when the jet exit has a fully-developed turbulent pipe flow, a situation less well-studied than the case of laminar initial conditions. It was found that forcing at Strouhal numbers around 0.6 enhances mixing in the developing region of the jet and this enhancement increased with increasing amplitude of excitation, consistent with results of initially-laminar jets. The initial turbulence intensity did not have any effect, but an increase in the initial lengthscale of the turbulence, controlled by a perforated plate inside the nozzle, caused faster mixing. In agreement with previous experiments, the initial conditions of the jet did not affect the far-field rate of decay, but the jet-fluid concentration there was significantly reduced by forcing due to the increased mixing during the early stages of development, an effect that can be described by a smaller virtual origin in decay laws of jet decay. These results are independent of the Froude number because the initial conditions have an influence only in the early stages where the flow is still momentum dominated.List of Symbols A normalised excitation amplitude, defined by A = u'/U ₀ - D nozzle diameter - f jet-fluid concentration - F mean f - f r.m.s. f - Fd Froude number, defined by Fd=U ₀ ² /(gDT ₀) - g acceleration of gravity - I fluorescent intensity - I _inc incident light intensity - I _ref light intensity of the reference flow - K decay constant - L _hf concentration halfwidth - M mixing enhancement, defined by U _cl/U _cl,st=0 at x/D=5 - r radial coordinate - Re Reynolds number, defined by Re=U ₀ D/v - [Rh] concentration of Rhodamine B - St Strouhal number, defined by St=D/U ₀ - T ₀ temperature of jet fluid - T temperature of outer fluid - T ₀ temperature difference (= T ₀–, T ) - u r.m.s. axial velocity - u r.m.s. of the sinusoidal velocity fluctuation due to forcing - U mean axial velocity - U _cl mean axial centreline velocity - U _cl,st=0 mean axial centreline velocity for an unforced jet - U _max U at the centre of the nozzle exit - U ₀ bulk velocity at nozzle exit - x streamwise coordinate - X ₀ virtual origin Greek coefficient of thermal expansion - kinematic viscosity of the jet fluid - forcing frequency The experiments described here have been performed together with Mr. J. Sakakibara. Acknowledgments are also due to Prof. H. Longmire, of the University of Minnesota, for helpful discussions on forcing. This work was done while E.M. visitied Keio University with the financial assistance of TEPCO.     

A flow field study of an elliptic jet in cross flow using DPIV technique

The digital particle image velocimetry (DPIV) technique has been used to investigate the flow fields of an elliptic jet in cross flow (EJICF). Two different jet orientations are considered; one with the major axis of the ellipse aligned with the cross flow (henceforth referred to as a low aspect ratio (AR) jet), and the other with the major axis normal to the cross flow (henceforth referred to as a high aspect ratio jet). Results show that the vortex-pairing phenomenon is prevalent in the low aspect ratio jet when the velocity ratio (VR)3, and is absent in the high aspect ratio jet regardless of the velocity ratio. The presence of vortex pairing leads to a substantial increase in the leading-edge peak vorticity compared to the lee-side vorticity, which suggests that vortex pairing may play an important role in the entrainment of ambient fluid into the jet body, at least in the near-field region. In the absence of vortex pairing, both the leading-edge and the lee-side peak vorticity increase monotonically with velocity ratio regardless of the aspect ratio. Moreover, time-averaged velocity fields for both AR=0.5 and AR=2 jets reveal the existence of an unstable focus (UF) downstream of the jet, at least for VR2. The strength and the location of this focus is a function of both the velocity ratio and aspect ratio. In addition, time-averaged vorticity fields show a consistently higher peak-averaged vorticity in the low aspect ratio jet than in the high aspect ratio jet. This behavior could be due to a higher curvature of the vortex filament facing the cross flow in the low aspect ratio jet, which through mutual interaction may lead to higher vortex stretching, and therefore higher peak-averaged vorticity.Nomenclature A nozzle or jet cross-sectional area - AR aspect ratio, defined as the ratio of the nozzle cross-stream dimension to its streamwise dimension, =H/L - D characteristic jet diameter (for circular jet only) - D_h hydraulic diameter, =4A/P - D_major major axis of an elliptic nozzle - D_minor minor axis of an elliptic nozzle - H cross-stream dimension of the nozzle - L streamwise dimension of the nozzle - P perimeter of the nozzle - Re_j jet Reynolds number, =V_jD/ - VR velocity ratio, =V_j/V - V_j mean jet velocity - V mean cross-flow velocity - x downstream distance from jet center - X cross-plane vorticity - kinematic viscosity     

On the prediction of riblet performance with engineering turbulence models

The paper reports the outcome of a numerical study of fully developed flow through a plane channel composed of ribleted surfaces adopting a two-equation turbulence model to describe turbulent mixing. Three families of riblets have been examined: idealized blade-type, V-groove and a novel U-form that, according to computations, achieves a superior performance to that of the commercial V-groove configuration. The maximum drag reduction attained for any particular geometry is broadly in accord with experiment though this optimum occurs for considerably larger riblet heights than measurements indicate. Further explorations bring out a substantial sensitivity in the level of drag reduction to the channel Reynolds number below values of 15 000 as well as to the thickness of the blade riblet. The latter is in accord with the trends of very recent, independent experimental studies.Possible shortcomings in the model of turbulence are discussed particularly with reference to the absence of any turbulence-driven secondary motions when an isotropic turbulent viscosity is adopted. For illustration, results are obtained for the case where a stress transport turbulence model is adopted above the riblet crests, an elaboration that leads to the formation of a plausible secondary motion sweeping high momentum fluid towards the wall close to the riblet and thereby raising momentum transport.Nomenclature c _f Skin friction coefficient - c _f Skin friction coefficient in smooth channel at the same Reynolds number - k Turbulent kinetic energy - K ⁺ k/ _w - h Riblet height - S Riblet width - H Half height of channel - Re Reynolds number = volume flow/unit width/ - Modified turbulent Reynolds number - R _t turbulent Reynolds numberk ²/ - P _k Shear production rate ofk, _t (U _i /x _j + U _j /x _i ) U _i /x _j - dP/dz Streamwise static pressure gradient - U _i Mean velocity vector (tensor notation) - U Friction velocity, _w/ where _w=–H dP/dz - W Mean velocity - W _b Bulk mean velocity through channel - y ⁺ yU /v. Unless otherwise stated, origin is at wall on trough plane of symmetry - Kinematic viscosity - _t Turbulent kinematic viscosity - Turbulence energy dissipation rate - Modified dissipation rate – 2(k ^1/2/x _j )² - Density - _k , Effective turbulent Prandtl numbers for diffusion ofk and      

Constituency measurements in the mixing region of a cross flow jet using a laser velocimeter

The velocities in the mixing region of a cross flow jet injected into a freestream were studied in detail with a laser velocimeter. Three jet to freestream momentum ratios were used (3.1, 8.1, 16.2). By purposely seeding the jet and freestream separately (as well as both simultaneously), marking the fluid was feasible. Thus, determining the velocities that emanated from the different streams was possible. By methodically analyzing the three sets of dependent data, the size and location of the mixing region was determined. The mixing regions for the three momentum ratios were found to be of different sizes and at different locations. By proper scaling, however, the regions for the three momentum ratios were found to collapse to one scaled region. Because of the intermittent behavior of the mixing, conventional turbulence models for such mixing may not be applicable; however, detailed velocities and turbulence quantities are included for benchmarking predictions.List of symbols B slot width - H channel height - MR momentum ratio, jet to free stream = _j V _j ²/ U ² - Re _H Reynolds number, U H/v - U free stream velocity - u axial velocity - u rms of axial velocity fluctuation - v transverse velocity - v rms of transverse velocity fluctuation - V _j slot exit transverse velocity - x axial direction (Fig. 3) - x _c x-center of mixing region - scaled value of x, = x/B - y transverse direction (Fig. 3) - y _c y-center of mixing region - scaled value of y, = y/ MRB - _x mixing region width in x-direction - _y mixing region width in y-direction - scaled mixing region width in x-direction, = _x /B - scaled mixing region width in y-direction, = _y / MRB - free stream density - _j slot exit density - v kinematic viscosity of freestream This research was sponsored in part by the Fulbright Commission (Bonn, Germany), the Institut für Thermische Strömungsmaschinen, Universität Karlsruhe (Karlsruhe, Germany), and the Rotating Machinery and Controls Industrial Research Program, University of Virginia (Charlottesville, VA, USA)