Numerical simulation of flow in a circular duct fitted with air‐jet vortex generators

Most of the fundamental studies of the use of air‐jet vortex generators (AJVGs) have concentrated on their potential ability to inhibit boundary layer separation on aerofoils. However, AJVGs may be of use in controlling or enhancing certain features of internal duct flows. For example, they may be of use in controlling the boundary layer at the entrance to engine air intakes, or as a means of increasing mixing and heat transfer. The objective of this paper is to analyse the flow field in the proximity of an air‐jet vortex generator array in a duct by using two local numerical models, i.e. a simple flat plate model and a more geometrically faithful sector model. The sector model mirrors the circular nature of the duct's cross‐section and the centre line conditions on the upper boundary. The flow was assumed fully turbulent and was solved using the finite volume, Navier–Stokes Code CFX 4 (CFDS, AEA Technology, Harwell) on a non‐orthogonal, body‐fitted, grid using the k–ε turbulence model and standard wall functions. Streamwise, vertical and cross‐stream velocity profiles, circulation and peak vorticity decay, peak vorticity paths in cross‐stream and streamwise direction, cross‐stream vorticity profiles and cross‐stream wall shear stress distributions were predicted. Negligible difference in results was observed between the flat plate and the sector model, since the produced vortices were small relative to the duct diameter and close to the surface. The flow field was most enhanced, i.e. maximum thinning of the boundary layer, with a configuration of 30° pitch and 75° skew angle. No significant difference in results could be observed between co‐ and counter‐rotating vortex arrays. Copyright © 2002 John Wiley & Sons, Ltd.     

Control of turbulent separated flow over a backward-facing step by local forcing

An experimental study was made of the flow over a backward-facing step. Excitations were given to separated flow by means of a sinusoidally oscillating jet issuing from a thin slit near the separation line. The Reynolds number based on the step height (H) varied 13000 Re _H 33000. Effect of local forcing on the flow structure was scrutinized by altering the forcing amplitude (0 A ₀ 0.07) and forcing frequency (0 St _H 5.0). Small localized forcing near the separation edge enhanced the shear-layer growth rate and produced a large roll-up vortex at the separation edge. A large vortex in the shear layer gave rise to a higher rate of entrainment, which lead to a reduction in reattachment length as compared to the unforced flow. The normalized minimum reattachment length (x _r )_min/x _x0 was obtained at St 0.01. The most effective forcing frequency was found to be comparable to the shedding frequency of the separated shear layer.List of symbols a ₀ forcing amplitude=(Q _forced–Q _unforced)/U ₀ - AR aspect ratio=W/H - C _p wall-pressure coefficient=(P-P ₀)/(l/2) U ₀ ² - ER expansion ratio=(2H+H)/2H - f _f forcing frequency, Hz - f _s shedding frequency, Hz - g slit width = 1.0 ± 0.1 mm - H step height = 50 mm - P wall-static pressure, Pa - P ₀ wall-static pressure at x/H= -2.0, Pa - Q _forced total velocity measured at reference position for forced flow, m/s - Q _unforced total velocity measured at reference position for unforced flow, m/s - Re _H Reynolds number based on H and U ₀,= U ₀ H/v - St _H Reduced forcing frequency, Strouhal number = f _f H/U ₀ - St Reduced forcing frequency based on the momentum thickness = f _f /U ₀ - U, V streamwise and vertical time-mean velocity, m/s - u streamwise fluctuation velocity, m/s - U ₀ free-stream velocity, m/s - r.m.s. intensity of streamwise velocity fluctuation, m/s - x _r reattachment length, m - X _{r 0} reattachment length for A ₀ = 0, m - x, y, z distance of streamwise, vertical and spanwise respectively, m - W width of test section = 625 mm Greek symbols boundary-layer thickness, cm - ^* displacement thickness, cm - _p forward-flow time fraction - density of air for measurement, kg/m³ - v kinematic viscosity of air for measurement, m²/s - momentum thickness, cm     

Computation of internal turbulent flow with a large separated flow region

An implicit two-equation turbulence solver, KEM. in generalized co-ordinates, is used in conjunction with the three-dimensional incompressible Navier–Stokes solver, INS3D, to calculate the internal flow in a channel and a channel with a sudden 2:3 expansion. A new and consistent boundary procedure for a low Reynolds number form of the κ-ε turbulence model is chosen to integrate the equations up to the wall. The high Reynolds number form of the equations is integrated using wall functions. The latter approach yields a faster convergence to the steady-state solution than the former. For the case of channel flow, both the wall-function and wall-boundary-condition approaches yield results in good agreement with the experimental data. The back-step (sudden expansion) flow is calculated using the wall-function approach. The predictions are in reasonable agreement with the experimental data.     

Heat transfer augmentation between impinging circular air jet and flat plate using finned surfaces and vortex generators

An experimental investigation is performed to study the effect of the finned surfaces and surfaces with vortex generators on the local heat transfer coefficient between impinging circular air jet and flat plate. Reynolds number is varied between 7000 and 30,000 based on the nozzle exit condition and jet to plate spacing between 0.5 and 6 nozzle diameters. Thermal infrared imaging technique is used for the measurement of local temperature distribution on the flat plate. Fins used are in the form of cubes of 2 mm size spaced at a pitch of 5 mm on the target plate and hexagonal prism of side 2.04 mm and height of 2 mm spaced at a pitch of 7.5 mm. Vortex generators in the form of a equilateral triangle of side 4 mm are used. Effect of number of rows of vortex generators, radius of a row, number of vortex generators in a row and inclination angle (i.e., the angle between the plane of the target plate and the plane of the vortex generators) on Nusselt number is studied. It is observed that the heat transfer coefficient between the impinging jet and the target plate is sensitive to the shape of the fin. The increase in the heat transfer coefficient up to 77% depending on the shape of the fin, nozzle plate spacing and the Reynolds number is observed. The augmentation in the heat transfer for the surfaces vortex generators are higher than that of the finned surfaces. The heat transfer augmentation in case of vortex generator is as high as 110% for a single row of six vortex generators at a radius of 1 nozzle diameter as compared to the smooth surface at a given nozzle plate spacing of 1 nozzle diameter and a Reynolds number of 25,000 at extreme radial location.     

Velocity gradients in a turbulent jet flow

We present a selection of results from experiments on an air turbulent jet flow, which included measurements of all the three velocity components and their nine gradients with the emphasis on the properties of invariant quantities related to velocity gradients (enstrophy, dissipation, enstrophy generation, etc.). This has been achieved by a 21 hot wire probe (5 arrays x 4 wires and a cold wire), appropriate calibration unit and a 3-D calibration procedure [1]. A more detailed account on the results will be published elsewhere.     

Scaling of the near-wall layer beneath turbulent separated flow

This paper is a continuation of an earlier paper [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438] in which it is proposed that each Reynolds stress has its own velocity scale. Two of these, $u_{\tau }^{\prime }$ and $w_{\tau }^{\prime }$, are directly related by definition to the r.m.s. of the wall-shear-stress fluctuations (${\tau }_x$ and ${\tau }_z$) in the streamwise and transverse directions. They are also velocity scales for the true dissipation of the turbulent kinetic energy and the Kolmogorov velocity and length scales at the surface. From asymptotic considerations it is shown that the other two scales are related to averages involving instantaneous gradients of wall-shear-stress fluctuations. The measurements, made using pulsed-wire anemometry into the viscous sublayer, show that $u_{\tau }^{\prime }$ and $w_{\tau }^{\prime }$ are also the velocity scales for the respective streamwise and transverse fourth-order velocity moments, together with the viscous velocity scale ($\nu /y$). Normalised, the fourth-order moments show an inner-layer-like behaviour independent of both position and direction, like that seen in the second-order moments [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438]. However, not surprisingly, the third order moments exhibit an effect of mean shear, seen in the skewing of the probability distributions. Though not measured directly, the measurements imply the behaviour of the averaged products of fluctuations in wall-shear-stress and wall-pressure-gradient ($\overline{{\tau }_x\partial p/\partial x}$ and $\overline{{\tau }_z\partial p/\partial z}$). Normalised, they also are independent of position and direction. Some of the results presented apply more generally to the near-wall region beneath turbulent flow.     

Heat transfer and friction in turbulent vortex flow

Summary This paper presents experimentally measured heat transfer and friction coefficients for air and water flowing through a pipe with several types of inserts designed to induce a swirl in the flow. It was observed that inside-surface heat transfer coefficients in swirling flow can, under favourable conditions, be at least four times as large as heat transfer coefficients at the same mass flow rate in purely axial flow. At the same time the pumping power per unit rate of heat transfer can be reduced. The increase in heat transfer coefficients was found to depend on the degree of swirl and on the density or temperature gradient. However, at comparable Reynolds numbers and swirling motions the heat transfer coefficients for air were found to be smaller than the coefficients for water. The reason for this difference is not definitely known, but the phenomenon is qualitatively compatible with that causing the cooling effect in Ranque-Hilsch vortex tubes. The observed phenomena are analyzed qualitatively and it is shown that they are primarily the result of a centrifugal force which induces a radial inward motion of warmer fluid and a radial outward motion of cooler fluid. The application of vortex flow to boiling heat transfer and other high heat flux systems is discussed briefly.

Nomenclature

Symbols c _p Specific heat at constant pressure, BTU/(lb)(deg F) - D _H Hydraulic diameter, (ft) - D Tube diameter, (ft) - f ₀ Fanning friction factor for axial flow, - f Fanning friction factor for swirling flow, - g Acceleration due to gravity, ft/(sec)² - G Mass velocity, lb/(sec) (sq ft) - h _i Inside surface coefficient of heat transfer, BTU/(hr)(sq ft)(deg F) - k Thermal conductivity, BTU/(hr)(sq ft)(deg F/ft) - L Characteristic length used in Grashof numbers, ft - p Frictional pressure drop in a duct, lbs/sq ft - r Radius of tube, ft - t Temperature potential in Grashof number, deg F - U _i Over-all coefficient of heat transfer based on inside tube area, BTU/(hr)(sq ft)(deg F) - V Axial velocity, ft/sec - Coefficient of thermal expansion, (deg F)^–1 - Absolute viscosity, (lbs)/(ft)(hr) - Density, lbs/(ft)³ - Angular velocity of fluid, rad/sec Dimensionless Parameters Nu ₀ Nusselt Number in axial flow, h _i D _H /k - Nu Nusselt Number in swirling flow, h _i D _H /k - Re Reynolds Number, VD _Hp / - Pr Prandtl Number, c _p /k - j Colburn j-Factor, (Nu/RePr)Pr ^2/3 Member of Technical Staff, Bell Telephone Laboratories, Murray Hill, N. J. formerly Baldwin Research Fellow, Lehigh University.     

Effect of air jet vortex generators on a shock wave boundary layer interaction

The effect of upstream injection by means of continuous air jet vortex generators (AJVGs) on a shock wave turbulent boundary layer interaction is experimentally investigated. The baseline interaction is of the impinging type, with a flow deflection angle of 9.5° and a Mach number M _e  = 2.3. Considered are the effects of the AJVGs on the upstream boundary layer flow topology and on the spatial and dynamical characteristics of the interaction. To this aim, Stereoscopic Particle Image Velocimetry has been employed, in addition to hot-wire anemometry (HWA) for the investigation of the unsteady characteristics of the reflected shock. The AJVGs cause a reduction of the separation bubble length and height. In addition, the energetic frequency range of the reflected shock is increased by approximately 50%, which is in qualitative agreement with the smaller separation bubble size.     

Numerical investigation of leading edge separated flow over cranked wings using a vortex lattice model

Numerical models based on the vortex lattice concept using free vortex lines have been developed for the calculation of separated flow about cranked wings. Various separated flow models are developed assuming the flow to be separated along the leading edges of (i) the inner wing, (ii) the entire wing and (iii) the inner wing and the outboard part of the outer wing. To illustrate the effects of separation, attached flow solutions are also obtained. Results are compared with available experimental results. Agreement with separated flow solutions is usually good except at very high incidence.     

Evolution of vortex structures in an electromagnetically excited separated flow

Time periodic wall parallel Lorentz forces have been used to excite the separated flow on the suction side of an inclined flat plate. Experiments for a Reynolds number of 10⁴ and an angle of attack of α = 13° are reported. The controlled flow is characterised by a small number of relatively large scale vortices, which are related to the control mechanism. The influence of the main parameters, i.e. the excitation frequency, amplitude and wave form on the suction side flow structures was investigated by analysing time resolved particle image velocimetry (TR-PIV) measurements using continuous wavelet analysis for vortex detection and characterisation. Statistical analysis of the coherent structures of the flow was performed on a large amount of data samples.     

Pressure distribution near wedges for separated supersonic turbulent flow

Summary A theoretical analysis of the pressure distribution in the vicinity of a wedge for separated turbulent flow is made. The solution is based on Vasiliu's analysis of the pressure distribution for step-induced separation using the Crocco-Lees mixing coefficient and Chapman's dividing streamline model. Theoretical results are compared with experimental data by Sterrett and Emery for Mach 5.8 and wedge angles of 28° and 34.17°.Nomenclature b mixing coefficient distribution factor - C _p pressure coefficient - F() defined by equation (3) - f ₁() defined by equation (5) - f() defined by equation (10) - I ₁ momentum integral, reference 4 - K mixing coefficient, defined by equation (4) - K _j jet flow parameter, reference 4 - K ₀ value of K at separation - K _0r value of K in the reattachment zone - () defined by equation (11) - M Mach number - M free stream Mach number - P pressure - P _S pressure at the separation point - P free stream pressure - r _S defined as P _S/P - X distance from the separation point - X _n distance from separation to reattachment point - X _W distance from separation point to wedge corner - wedge angle - specific heats ratio - mixing layer thickness - _j mixing layer thickness in jet flow solution - _j ^* displacement thickness in jet flow solution - _S boundary layer thickness at separation - dimensionless coordinate, defined as X/ _S - _n value of at the reattachment point - deflection angle of flow outside the mixing layer - jet flow parameter, reference 4 - dimensionless pressure, defined as P/P _S - [ _c ]_max jet flow parameter, reference 4 - _c jet spread factor, reference 4     

Numerical prediction of locally forced turbulent separated and reattaching flow

An unsteady numerical simulation was performed for locally forced separated and reattaching flow over a backward-facing step. The local forcing was given to the separated and reattaching flow by means of a sinusoidally oscillating jet from a separation line. A version of the k––f_μ model was employed, in which the near-wall behavior without reference to distance and the nonequilibrium effect in the recirculation region were incorporated. The Reynolds number based on the step height (H) was fixed at Re_H=33 000, and the forcing frequency was varied in the range 0St_H2. The predicted results were compared and validated with the experimental data of Chun and Chun. It was shown that the unsteady locally forced separated and reattaching flows are predicted reasonably well with the k––f_μ model. To characterize the large-scale vortex evolution due to the local forcing, numerical flow visualizations were carried out.     

Modelling turbulent separated flow in the context of aerodynamic applications

In contrast to rapid advances in computing, numerical methods and visualisation, the predictive capabilities of statistical models of turbulence are limited and improve only slowly, despite much intensive research in the recent past. The intuitive nature of turbulence modelling, its strong reliance on calibration and validation, the extreme sensitivity of model performance to seemingly minor variations in modelling details and flow conditions, and the fact that the non-local dynamics of turbulence are not well captured by single-point closure, all conspire to make turbulence modelling an especially demanding component of CFD, but one that is crucially important for the correct prediction of complex flows. This applies in particular to separation from streamlined bodies, which is, from a computational point of view, the most challenging flow feature in aeronautical CFD.This paper reviews some aspects of the foundation and application of turbulence models to flows that relate to aeronautical practice, with particular emphasis being placed on turbulence-transport models at a closure level higher than that based on the Boussinesq-viscosity hypothesis. Following a review of basic modelling issues, including aspects of linear-eddy-viscosity two-equation modelling, some recent experience and current work on predicting separation from continuous surfaces with non-linear eddy-viscosity models and second-moment closure are reported. The predictive performance of several anisotropy-resolving models is illustrated by reference to computational solutions for a number of flows, both two- and three-dimensional, some compressible and others incompressible.     

On turbulent separated flow past a truncated body of revolution

Results of testing a series of truncated bodies of revolution with convergent afterbodies in a hydrodynamic tunnel are presented. It is shown that the base pressure can be substantially raised and hence the total drag reduced by varying the shape and convergence of the afterbodies. This effect is caused by intense reverse jets formed as a result of the collision of flow particles moving toward the axis of symmetry.The turbulent flow past the bodies is calculated using the method of viscous-inviscid interaction. The formulas derived for the base pressure and drag coefficients agree satisfactorily with the experimental data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 50–55, November–December, 1996.     

Effects of flow width in nominally two-dimensional turbulent separated flows

Pulsed-wire measurements of mean and fluctuating wall shear stress have been measured beneath a nominally two-dimensional separated and reattaching flow, where the flow width has been varied by means of end plates. End effects are much larger near the surface than they are in the outer flow. Residual effects of the presence of the end walls on the mean wall shear stress are seen for a flow width as large as seven bubble lengths. It is inferred that the effects of the end-wall boundary layers extend to a substantially smaller distance. The influence of the end plates on the rms of the fluctuations is markedly less than that on the mean stress.     

Numerical study on evolution of subharmonic varicose low-speed streaks in turbulent channel flow

The evolution of two spanwise-aligned low-speed streaks in a wall turbulent flow, triggered by the instability of the subharmonic varicose (SV) mode, is studied by a direct numerical simulation (DNS) method in a small spatial-periodic channel. The results show that the SV low-speed streaks are self-sustained at the early stage, and then transform into subharmonic sinuous (SS) low-speed streaks. Initially, the streamwise vortex sheets are formed by shearing, and then evolve into zigzag vortex sheets due to the mutual induction. As the intensification of the SV low-speed streaks becomes prominent, the tilted streamwise vortex tubes and the V-like streamwise vortex tubes can be formed simultaneously by increasing \( + \frac{{\partial u}}{{\partial x}}\). When the SV low-speed streaks break down, new zigzag streamwise vortices will be generated, thus giving birth to the next sustaining cycle of the SV low-speed streaks. When the second breakdown happens, new secondary V-like streamwise vortices instead of zigzag streamwise vortices will be generated. Because of the sweep motion of the fluid induced by the secondary V-like streamwise vortices, each decayed low-speed streak can be divided into two parts, and each part combines with the part of another streak, finally leading to the formation of SS low-speed streaks.     

Control of diffuser jet flow: turbulent kinetic energy and jet spreading enhancements assisted by a non-thermal plasma discharge

An axisymmetric air jet exhausting from a 22-degree-angle diffuser is investigated experimentally by particle image velocimetry (PIV) and stereo-PIV measurements. Two opposite dielectric barrier discharge (DBD) actuators are placed along the lips of the diffuser in order to force the mixing by a co-flow actuation. The electrohydrodynamic forces generated by both actuators modify and excite the turbulent shear layer at the diffuser jet exit. Primary air jet velocities from 10 to 40 m/s are studied (Reynolds numbers ranging from 3.2 to 12.8 × 10⁴), and baseline and forced flows are compared by analysing streamwise and cross-stream PIV fields. The mixing enhancement in the near field region is characterized by the potential core length, the centreline turbulent kinetic energy (TKE), the integrated value of the TKE over various slices along the jet, the turbulent Reynolds stresses and the vorticity fields. The time-averaged fields demonstrate that an effective increase in mixing is achieved by a forced flow reattachment along the wall of the diffuser at 10 m/s, whereas mixing enhancement is realized by excitation of the coherent structures for a primary velocity of 20 and 30 m/s. The actuation introduces two pairs of contra-rotating vortices above each actuator. These structures entrain the higher speed core fluid toward the ambient air. Unsteady actuations over Strouhal numbers ranging from 0.08 to 1 are also studied. The results suggest that the excitation at a Strouhal number around 0.3 is more effective to enhance the turbulence kinetic energy in the near-field region for primary jet velocity up to 30 m/s.     

Numerical simulation on evolution of subharmonic low-speed streaks in minimal channel turbulent flow

The evolution of low-speed streaks in the turbulent boundary layer of the minimum channel flow unit at a low Reynolds number is simulated by the direct numer- ical simulation （DNS） based on the standard Fourier-Chebyshev spectral method. The subharmonic sinuous （SS） mode for two spanwise-aligned low-speed streaks is excited by imposing the initial perturbations. The possibilities and the physical realities of the turbulent sustaining in the minimal channel unit are examined. Based on such a flow field environment, the evolution of the low-speed streaks during a cycle of turbulent sus- taining, including lift-up, oscillation, and breakdown, is investigated. The development of streamwise vortices and the dynamics of vortex structures are examined. The results show that the vortices generated from the same streak are staggered along the streamwise direction, while the vortices induced by different streaks tilt toward the normal direction due to the mutual induction effect. It is the spatial variations of the streamwise vortices that cause the lift-up of the streaks. By resolving the transport dynamics of enstrophy, the strength of the vortices is found to continuously grow in the logarithmic layer through the vortex stretching mechanism during the evolution of streaks. The enhancement of the vortices contributes to the spanwise oscillation and the following breakdown of the low-speed streaks.