Double row vortical structures in the near field region of a plane wall jet

The qualitative and quantitative behaviour of double row vortical structures in the near field region of a plane wall jet are studied experimentally by flow visualization and hot-wire measurements. Ensemble averaging is employed to investigate the interaction of vortices with the wall. In the flow visualization study, a double row vortical structure, which includes a primary vortex formed in the outer layer region and a secondary vortex induced in the inner layer region, and the vortex lift-off phenomenon are clearly observed during the development of the wall jet. The phase averaged results of the velocity measurements show that the instability leading to induction of the secondary vortex is stimulated by the primary vortex. In the early stage of wall jet transition, the inflection point of the inner layer velocity profile moves transversely from the wall surface to the inner layer region due to passage of the well-organized primary vortex in the outer layer region. The inner layer instability is thus induced and the instability wave rolls up to form the secondary vortex. Furthermore, the secondary vortex will convect downstream faster than the primary vortex, and this difference in convective speed will lead to the subsequent phenomenon of vortex lift-off from the wall surface.List of symbols A1, A2, . . . primary vortex - B1,B2, . . . secondary vortex - fe forcing frequency - f fundamental frequency - H nozzle exit height - Re Reynolds number,U _j H/ - T period of the referred signal (=13.5 ms) - t, t time scale - U streamwise mean velocity - U _c convection speed - U _j jet exit velocity - U _m local maximum velocity - ut' streamwise turbulence intensity - uv turbulent shear stress - V transverse mean velocity - v transverse turbulence intensity - X streamwise coordinate - Y transverse coordinate - X _Ai streamwise location of vortexAi - X _Bi streamwise location of vortexBi - X _ave averaged streamwise location of the vortex - Y _m wall jet inner layer width, the distance from wall to whereU=U _m - Y _1/2 wall jet half-width, the distance from wall to whereU=1/2U _m in outer layer region - t time interval (=0.267 s) - phase averaged value     

Forcing a planar jet flow using MEMS

We present the results of an experimental study in which a planar laminar jet of air was forced by an array of micro-electromechanical systems (MEMS) micro-actuators. In the absence of forcing, the velocity profile of the experimental jet matched the classic analytic solution. Driving actuators on either side of the jet in-phase or anti-phase, respectively, excited the symmetric or anti-symmetric mode of instability of the jet. Asymmetric forcing, using MEMS actuators on only one side of the jet, was also investigated.List of symbols x, y, z Streamwise, cross-stream, and spanwise coordinates - u Streamwise velocity - d Exit slit width - U₀ Centerline streamwise velocity - b Jet half-width - v Kinematic viscosity - Re Reynolds number=U₀b/v - M Momentum flux - u Fluctuating velocity component in x direction - f Forcing frequency of MEMS actuators - Dimensionless frequency of velocity fluctuations=fb/U₀     

In the intermixing region behind circular cylinders with stepwise change of the diameter

The flow within the intermixing region behind circular cylinders with stepwise change of the diameter of diameter ratio d/D of 0.5 has been examined. Based on the statistical analysis and conditional sampling of the velocity fluctuations and of flow visualization, the vortex wakes associated with the big and small cylinders have been established. Both wakes are found under the dominant primary mode, which corresponds to the vortex shedding Strouhal number of two dimensional cylinder, and the less dominant secondary mode. The Strouhal number of the secondary mode of the big vortex wake is higher than that of the primary mode and the opposite is found for the small vortex wake. Both vortex wakes and their modes are found convecting downstream and into region behind the other cylinder. Both wakes are observed to be different from that of two dimensional cylinder.List of symbols D, d diameter of big and small cylinder - f frequency - R ₁₂ (f) cross-power spectral function - R ₁₁, R ₂₂ auto-power functions - Re _D, Re_d Reynolds numbers U ₀ D/v, U ₀ d/v - t time relative to triggering instant - U ₀ freestream mean velocity - U, V, W streamwise, lateral and spanwise mean velocity, respectively - u, v, w streamwise, lateral and spanwise velocity fluctuations, respectively - U _f phase velocity - U _T convection velocity - u _R, v_r recovered u and v velocity fluctuations - uv Reynolds stress - x, y, z streamwise, lateral, and spanwise coordinates, respectively - separation - ₁₂ ² (f) coherence function - _R recovered coherent vorticity fluctuation - phase - ₁₂ (f) phase spectral function     

Generating high freestream turbulence levels

This paper presents a method of generating a highly turbulent freestream flow, up to levels of 20% with a relatively uniform mean velocity field. This method was developed as a result of a combined water channel and wind tunnel study. The method for generating these high turbulence levels includes using high-velocity jets issuing into a mainstream cross-flow. A range of turbulence levels can be generated, using this same flow geometry, by adjusting the jet-to-mainstream velocity ratio or the Reynolds number of the flow.List of symbols b Grid bar width - D Turbulence generator jet hole diameter - Eu (f) Spectral energy for streamwise velocity fluctuations - f Frequency - H Channel height - L _u Dissipation length scale, - m Exponent for length scale growth - M Grid mesh size - n Exponent for turbulence decay - Re _D Reynolds number based on jet hole diameter - Re _T Turbulent Reynolds numbers,u _g /V - S Lateral spacing between the jet holes - T Integral time scale of turbulence - Tu Streamwise turbulence intensity,u/U - u RMS velocity in streamwise direction - U Mean local velocity in streamwise direction - U Freestream velocity in streamwise direction - v RMS velocity in normal direction - x Streamwise distance measured from the turbulence generator jets - y Vertical distance from the wall - z Spanwise distance - Boundary layer thickness (U = 0.99U ) - _x Longitudinal integral length scale of turbulence This project was supported by Wright Laboratory and Allied-Signal. The authors would also like to thank Mr. David Dotson for his help in constructing the turbulence generator and Mr. Don Schmidt for his help in procuring the blower. The first author would also like to thank Professor Sigmar Wittig and the Institut für Thermische Strömungsmaschinen for support while writing this paper     

Effect of velocity ratio on plane mixing layer development: Influence of the splitter plate wake

An experimental study has been conducted to investigate the effect of velocity ratio on the approach of a plane mixing layer to self-similarity. Plane mixing layers with five different velocity ratios (0.5, 0.6, 0.7, 0.8 and 0.9) were generated in a newly designed mixing layer wind tunnel with both initial boundary layers tripped. For each velocity ratio, mean flow and turbulence measurements were obtained at eight streamwise locations with a single cross-wire probe. The results indicate that the splitter plate wake plays a very dominant and, in some cases, a lasting role in the development of the mixing layer. For velocity ratios between 0.5 and 0.7, self-similarity of the mixing layer was observed with the asymptotic states comparable. Mixing layers with the higher velocity ratios failed to achieve a self-similar state within the measurement domain, although a slow approach to it was apparent. The development distance decreased with increasing velocity ratio up to 0.7, after which it appeared to increase. Almost all of the observed effects may be attributed to the presence of the splitter plate wake and its complex interaction with the mixing layer.List of symbols C _f boundary layer skin friction coefficient - H boundary layer shape factor - r velocity ratio of the two streams, (=U ₂/U ₁) - Re _L Reynolds number, (=UL/v) - R correlation coefficient in least squares fit - U, V, W mean velocity in the X, Y, Z directions, respectively - U ^* velocity parameter, [=(U–U ₂)/(U ₁–U ₂)] - U ₀ velocity difference, (=U ₁–U ₂) - U _e free-stream velocity in the wind tunnel - u, , w fluctuating velocity components in the X, Y, Z directions, respectively - u, , w instantaneous velocity in the X, Y, Z directions, respectively, e.g. u=U+u - X ₀ virtual origin of the mixing layer - X, Y, Z cartesian coordinates for streamwise, normal, and spanwise directions, respectively - Y ₀ centerline of mixing layer from error function fit - mixing layer width from error function fit - ₉₉ initial boundary layer thickness - similarity coordinate [=(Y–Y ₀)/] - initial boundary layer momentum thickness - modified velocity ratio [=(1–r)/(1+r)] - _n initial instability wavelength in the mixing layer - spreading parameter [=1/(d/dX)] - ₀ spreading parameter for single-stream mixing layer - - (overbar) Time-averaged quantity - ( )_max maximum value at given X-station - ( )_min minimum value at given X-station - ( )₁ value for high-speed side - ( )₂ value for low-speed side     

Quantitative liquid jet instability measurement system using asymmetric magnification and digital image processing

A new technique for measuring the growth of instabilities on the surface of liquid jets flowing into gas is demonstrated. A collimated beam of white light illuminates the jet from behind, forming a shadow image. A pair of cylindrical lenses are arranged to provide different magnifications in the streamwise and cross-stream directions. A number of streamwise diameters and one cross-stream diameter are thus captured with maximum resolution in a single image on a charge-coupled device (CCD) electronic camera. A short-duration spark is used to freeze the jet motion. A mask representing the theoretical edge-response of the imaging system is digitally convolved with the cross-stream gray scale data to obtain sub-pixel resolution of the jet edge profile. The method is demonstrated using the well-known capillary jet instability and a ratio of streamwise to cross-stream magnifications of 40. Well-resolved single images show the development of the instability from small perturbations through the formation of the first drop. The system forms an accurate automated method of measuring the development of liquid jet instabilities. It can readily be applied to practical problems including liquid jet atomization.List of symbols a undisturbed jet radius - k nondimensional wavenumber (= 2a/) - Q gas-to-liquid density ratio - r ₀ mean jet radius, from initial region of image - R Reynolds number (= 2Ua/) - U mean jet velocity - We Weber number - z streamwise coordinate, origin at jet orifice - temporal growth rate - _s measured spatial growth rate - nondimensional temporal growth rate - r absolute value of height of peaks or troughs relative to r ₀ - r ₁ height of first extremum in a particular record - instability wavelength - liquid viscosity - liquid density - surface tension of liquid-gas interface     

Convection velocity measurements in a cylinder wake

The convection velocity of vortices in the wake of a circular cylinder has been obtained by two different approaches. The first, implemented in a wind tunnel using an array of X-wires, consists in determining the velocity at the location of maximum spanwise vorticity. Four variants of the second method, which estimates the transit time of vortices tagged by heat or dye, were used in wind and water tunnels over a relatively large Reynolds number range. Results from the two methods are in good agreement with each other. Along the most probable vortex trajectory, there is only a small streamwise increase in the convection velocity for laminar conditions and a more substantial variation when the wake is turbulent. The convection velocity is generally greater than the local mean velocity and does not depend significantly on the Reynolds number.Nomenclature d diameter of circular cylinder - f frequency in spectrum analysis - f _v average vortex frequency - r _v vortex radius - Re Reynolds number U _o d/v - t time - Th , Th , Th _r thresholds for _zp, , and r _v respectively - U _o free stream velocity - U ₁ maximum value of (U _o – U) - U _c convection velocity of the vortex, as obtained either by Eq. (1) or Eq. (2) - U _co convection velocity used in Eq. (3) U _cd, U _cu average convection velocities of downstream and up-stream regions respectively of the vortex - U _cv the value of U _c at y = 0.5 - u, v the velocity fluctuations in x and y directions respectively - U, V mean velocity components in x and y directions respectively - U,V U = U + u, V = V + v - x, y, z co-ordinate axes, defined in Fig. 1 Greek Symbols circulation - mean velocity half-width - x spacing between two cold wires or grid spacing - ₁, ₂ temperature signals from upstream and downstream cold wires respectively - v kinematic viscosity - _c transit time for a vortex to travel a distance x - phase in the cross-spectrum of ₁ and ₂ - _z instantaneous spanwise vorticity - _zc cut-off vorticity used in determining the vortex size - _zp peak value of _z - a denotes conditional average, defined in Eq. (12) - a prime denoting rms value     

Unsteady forces on circular cylinders in a cross-flow

A three-axis piezoelectric load cell was used to measure the local unsteady forces induced on cylinders placed in a cross-flow. In conjunction with this, a single hot-wire was used to traverse the wake at a fixed distance behind the cylinder so that correlations between the induced forces on the cylinder and the wake velocity could be calculated to provide insight into the character of the flow-induced unsteady forces. Experiments were carried out on both two-dimensional and finite-span cylinders at a Reynolds number of 46,000. For the two-dimensional cylinder case, substantial evidence was obtained to demonstrate that the strength of the vortex roll-up along the span was quite uniform. Consequently, the lift-velocity correlation along the span remained unchanged. On the other hand, there was a total lack of correlation between the fluctuating drag and the wake velocity, thus indicating that the drag signal was not quite periodic. In the finite-span cylinder case, the separated flow from the top edge of the cylinder was found to suppress vortex shedding along the span of the cylinder, destroyed its coherence and caused the wake flow to oscillate in the stream direction. This oscillation induced a significant fluctuating drag on the cylinder. Consequently, the fluctuating drag far exceeded the fluctuating lift and the wake velocity was found to correlate well with the drag and not with the lift. This correlation remained intact along the span of the cylinder. Finally, the rms fluctuating lift and drag forces were found to vary along the cylinder span, with the lift increasing and the drag decreasing as the base of the cylinder is approached; thus suggesting that a submerged two-dimensional region exists near the base of the cylinder.List of symbols a span of active element on cylinder - C _D local rms drag coefficient, - C _L local rms lift coefficient, - C _D local mean drag coefficient - (C _D ) _2D spanwise-averaged mean drag coefficient for two dimensional cylinder - d diameter of cylinder (= 10.2 cm) - D fluctuating component of instantaneous drag - D local rms of fluctuating drag - E _D power spectrum of fluctuating drag, defined as - E _L power spectrum of fluctuating lift, defined as - E _U power spectrum of fluctuating streamwise velocity, defined as - f _L dominant frequency of lift spectrum - f _D dominant frequency of drag spectrum - f _u dominant frequency of velocity spectrum - h span of cylinder - H height of test section (= 30.5 cm) - L fluctuating component of instantaneous lift - L local rms of fluctuating lift - R _Du () cross-correlation function of streamwise velocity and local drag - R _Lu () cross-correlation function of streamwise velocity and local lift - Re Reynolds number, - S _L Strouhal number based on f _L , - S _D Strouhal number based on f _D , - S _U Strouhal number based on f _u , - t time - u fluctuating component of instantaneous streamwise velocity - u rms of streamwise fluctuating velocity - u rms of streamwise fluctuating velocity upstream of cylinder - U mean streamwise velocity - U mean stream velocity upstream of cylinder - x streamwise distance measured from axis of cylinder - y transverse distance measured from axis of cylinder - z spanwise distance measured from floor of test section - v kinematic viscosity of air - density of air - time lag in cross-correlation function - _D normalized spectrum of fluctuating drag - _L normalized spectrum of fluctuating lift - _U normalized spectrum of fluctuating streamwise velocity     

Streamwise pseudo-vortical structures and associated vorticity in the near-wall region of a wall-bounded turbulent shear flow

Streamwise pseudo-vortical motions near the wall in a fully-developed two-dimensional turbulent channel flow are clearly visualized in the plane perpendicular to the flow direction by a sophisticated hydrogen-bubble technique. This technique utilizes partially insulated fine wires, which generate hydrogen-bubble clusters at several distances from the wall. These flow visualizations also supply quantitative data on two instantaneous velocity components, and w, as well as the streamwise vorticity, _x . The vorticity field thus obtained shows quasi-periodicity in the spanwise direction and also a double-layer structure near the wall, both of which are qualitatively in good agreement with a pseudo-vortical motion model of the viscous wall-region.List of symbols C _i ,c _i ,d _i constants in Eqs. (2), (3) and (4) - H channel width (m) - Re _H Reynolds number (= U _c H/) - Re Reynolds number (= U _c /) - T period (s) - t time (s) - U mean streamwise velocity (m/s) - U _c center-line velocity (m/s) - u friction velocity (m/s) - u, , w velocity fluctuations (m/s) - x, y, z coordinates (m) - ^* displacement thickness (m) - momentum thickness (m) - mean low-speed streak spacing (m) - kinematic viscosity (m²/s) - phase difference - _x streamwise vorticity fluctuation (1/s) - ( )⁺ normalized by u and - (^–) root mean square value - (^–) statistical average This paper was presented at the Ninth Symposium on Turbulence, University of Missouri-Rolla, October 1–3, 1984     

Measurement of turbulent wall velocity gradients using cylindrical waves of laser light

A new optical instrument has been developed for direct measurement of instantaneous velocity gradients at the bounding wall. Light emerging from two tiny optical slits in the surface is used to form a fan of fringes in the region very near the wall. Doppler frequency of the light scattered by the seed particles is directly proportional to the velocity gradient. The system has been used to measure the statistics of the streamwise and spanwise velocity gradients in a turbulent boundary layer. The streamwise and spanwise rms fluctuations were found to be 38% and 11% of the mean streamwise value respectively. The latter result is subject to a large uncertainty.List of symbols a slit width - B transfer function of the instrument - B ^* normalized transfer function - path-averaged value of the normalized transfer function - c constant in logarithmic velocity profile - C _f skin friction coefficient - d _f fringe spacing - f ₁,f₂ frequencies at the downstream and upstream slits resp. - f _d heterodyne Doppler frequency of the signal - g(t) instantaneous wall velocity gradient - G Clauser shape factor - mean wall velocity gradient - g rms value of the wall velocity gradient - H boundary layer shape factor - i, j, k unit vectors along x, y, z axes - wavenumber of laser light - L major axis of the elliptic cross-section of the laser sheet at the slit - l length of each slit - N number of cycles in a signal - N ₀ number of cycles without frequency-shifting - n difference of the unit vectors u ₁and u ₂ - P power transmitted through a slit - P _o power incident on a slit - Re ₁ Reynolds number based on displacement thickness and free-stream velocity - Re ₂ Reynolds number based on momentum thickness and free-stream velocity - S spacing between the slits - S ^* normalized spacing between the slits - u streamwise velocity - u ₁,u₂ unit vectors along the local directions of propagation of the two cylindrical waves - u _l linear term in the streamwise velocity profile - u _nl nonlinear terms in the streamwise velocity - u _nl ^* normalized value of nonlinear streamwise velocity - u _nl ^* mean streamwise velocity - u friction velocity - u⁺ mean velocity normalized with friction velocity - v velocity component normal to the wall - v ^* normal velocity normalized with streamwise velocity - V velocity vector - w spanwise component of velocity - W minor axis of the elliptic cross-section of the laser sheet at the slit - x streamwise distance - ± x _m limiting values of streamwise distance for a signal - x ^* normalized streamwise distance - x ^* normalized value of x _m - y normal distance - y ⁺ normal distance normalized with friction length scale - z spanwise distance - z ⁺ spanwise distance normalized with friction length scale - half-spreading angle of the cylindrical waves - boundary layer thickness in Coles' profile - ₁ displacement thickness of the boundary layer - ₂ momentum thickness of the boundary layer - ₃ energy thickness of the boundary layer - constant in logarithmic velocity profile - wavelength of laser light - kinematic viscosity - coefficient of wake function in Coles' profile Currently at LSTM, Universitat Erlangen-Nürnberg, Cauerstraße 4, W-8520 Erlangen, BRD     

Selective control of flow coherence in triangular jets

The triangular jet was investigated for use as a passive device to enhance fine-scale mixing and to reduce the coherence of large-scale structures in the flow. The suppression of the structures is vital to the enhancement of molecular mixing, which is important for efficient chemical reactions including combustion. The sharp corners in the jet injector introduced high instability modes into the flow via the non-symmetric mean velocity and pressure distribution around the nozzle. Both aerodynamic and hydrodynamic flows showed the difference between the flow at the corner (vertex) and at the flat side. While highly coherent structures could be generated at the flat side, the corner flow was dominated by highly turbulent small-scale eddies. The flow characteristics were tested using hotwire anemometry for mean flow and turbulence analysis, and flow visualization in air and water.List of symbols D inlet duct diameter - D _e equivalent diameter - D _i inside diameter - E _v velocity fluctuation energy - f _F forcing frequency - f _j preferred mode frequency - L length - Re Reynolds number - R _e equivalent radius (same area) - r _0.5 jet half-width - R _1.2 cross-correlation factor - r radial coordinate (circular duct) - St _e most energetic Strouhal number - St _j preferred mode Strouhal number - U _m centerline (maximum) velocity in radial u-profile - U ₀ jet exit velocity - u local axial mean velocity - x axial coordinate - X ₁ axial position of first of two hot-wires for axial cross-correlation - + y _F lateral coordinate at flat side of triangular duct - - y _V lateral coordinate at vertex side of triangular duct - (E _V)_j preferred mode energy - X axial distance between hot-wires - r radial distance between two hot-wires (circular jet) - y lateral distance between two hot-wires (triangular jet) - P/P pressure amplitude - momentum thickness - time     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some large-scale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u/U).List of symbols a speed of sound - b total mixing layer thickness between U ₁ – 0.1 U and U ₂ + 0.1 U - f normalized third moment of u-velocity, f u³/(U)³ - g normalized triple product of u² , g u²/(U)³ - h normalized triple product of u ², h u ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁ = ₂), M _c (U ₁ – U ₂)/(a ₁ + a ₂) - P static pressure - r freestream velocity ratio, r U ₂/U ₁ - Re unit Reynolds number, Re U/ - s freestream density ratio, s ₂/₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation of u-velocity, uu – U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - average of freestream velocities, (U ₁ + U ₂)/2 - U freestream velocity difference, U U ₁ – U ₂ - instantaneous transverse velocity - v deviation of -velocity, – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y – y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U – U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

Simultaneous measurements of velocity and temperature fluctuations in thermal boundary layer in a drag-reducing surfactant solution flow

The mechanism of turbulent heat transfer in the thermal boundary layer developing in the channel flow of a drag-reducing surfactant solution was studied experimentally. A two-component laser Doppler velocimetry and a fine-wire thermocouple probe were used to measure the velocity and temperature fluctuations simultaneously. Two layers of thermal field were found: a high heat resistance layer with a high temperature gradient, and a layer with a small or even zero temperature gradient. The peak value of was larger for the flow with the drag-reducing additives than for the Newtonian flow, and the peak location was away from the wall. The profile of was depressed in a similar manner to the depression of the profile of in the flow of the surfactant solution, i.e., decorrelation between v and compared with decorrelation between u and v. The depression of the Reynolds shear stress resulted in drag reduction; similarly, it was conjectured that the heat transfer reduction is due to the decrease in the turbulent heat flux in the wall-normal direction for a flow with drag-reducing surfactant additives.List of symbols ensemble averaged value - (·)⁺ normalized by the inner wall variables - (·) root-mean-square value - C concentration of cetyltrimethyl ammonium chloride (CTAC) solution - c _p heat capacity - D hydraulic diameter - f friction factor - H channel height - h heat transfer coefficient - j _H Colburn factor - l length - Nu Nusselt number, h - Pr Prandtl number, c _p/ - q _w wall heated flux - Re Reynolds number, U _b/ - T temperature - T _b bulk temperature - T _i inlet temperature - T _w wall temperature - T friction temperature, q _w /c _p u - U local time-mean streamwise velocity - U ₁ velocity signals from BSA1 - U ₂ velocity signals from BSA2 - U _b bulk velocity - u streamwise velocity fluctuation - u1 velocity in abscissa direction in transformed coordinates - u friction velocity, - v wall-normal velocity fluctuation - v1 velocity in ordinate direction in transformed coordinates - var(·) variance - x streamwise direction - y wall-normal direction - z spanwise direction - _j junction diameter of fine-wire TC - _w wire diameter of fine-wire TC - angle of principal axis of joint probability function p(u,v) - _f heat conduction of fluid - _w heat conduction of wire of fine-wire TC - kinematic viscosity - local time-mean temperature difference, T _w –T - temperature fluctuation - standard deviation - density - _w wall shear stress     

Aspect ratio effect on flow-induced forces on circular cylinders in a cross-flow

Finite-span circular cylinders with two different aspect ratios, placed in a cross-flow, are investigated experimentally at a cylinder Reynolds number of 46,000. Simultaneous measurements of the flow-induced unsteady forces on the cylinders and the stream velocity in the wake are carried out. These results together with mean drag measurements along the span and available literature data are used to evaluate the flow mechanisms responsible for the induced unsteady forces and the effect of aspect ratio on these forces. The coherence of vortex shedding along the span of the cylinder is partially destroyed by the separated flow emanating from the top and by the recirculating flow behind the cylinder. As a result, the fluctuating lift decreases drastically. Based on the data collected, it is conjectured that the fluctuating recirculating flow behind the cylinder is the flow mechanism responsible for the unsteady drag and causes it to increase beyond the fluctuating lift. The fluctuating recirculating flow is a direct consequence of the unsteady separated flow. The unsteady forces vary along the span, with lift increasing and drag decreasing towards the cylinder base. When the cylinder span is large compared to the wall boundary layer thickness, a submerged two-dimensional region exists near the base. As the span decreases, the submerged two-dimensional region becomes smaller and eventually vanishes. Altogether, these results show that fluctuating drag is the dominant unsteady force in finite-span cylinders placed in a cross-flow. Its characteristic frequency is larger than that of the vortex shedding frequency.List of symbols a span of active element on cylinder, = 2.5 cm - C _D local rms drag coefficient, 2D/ U ² da - C _L local rms lift coefficient, 2l/ U ² da - C _D local mean drag coefficient, 2D/ U ² da - C _D spanwise-averaged C _D for finite-span cylinder - (C _D ) _2D spanwise-averaged mean drag coefficient for two-dimensional cylinder - C _p pressured coefficient - -(C _p ) _b pressure coefficient at = - d diameter of cylinder, = 10.2 cm - D fluctuating component of instantaneous drag - D local rms of fluctuating drag - D local mean drag - E _D power spectrum of fluctuating drag, defined as - E _L power spectra of fluctuating lift, defined as - f _D dominant frequency of drag spectrum - f _L dominant frequency of lift spectrum - f _u dominant frequency of velocity spectrum - h span of cylinder - H height of test section, = 30.5 cm - L fluctuating component of instantaneous lift - L local rms of fluctuating lift - R _Du () cross-correlation function of streamwise velocity and local drag, - R _Lu () cross-correlation function of stream wise velocity and local lift, - Re Reynolds number, U d/y - S _L Strouhal number based on f _L ,f _L d/U - S _D Strouhal number based on f _D ,f _D d/U - S _u Strouhal number based on f _u , f _u d/U - t time - u fluctuating component of instantaneous streamwise velocity - U mean streamwise velocity - mean stream velocity upstream of cylinder - x streamwise distance measured from axis of cylinder - y transverse distance measured from axis of test section - z spanwise distance measured from cylinder base - angular position on cylinder circumference measured from forward stagnation - kinematic viscosity of air - density of air - time lag in cross-correlation function - _D normalized spectrum of fluctuating drag - _L normalized spectrum of fluctuating lift     

Quantitative detection of turbulent reattachment using a surface mounted hot-film array

A robust method to detect the mean turbulent reattachment location with a flush surface-mounted array of hot-film sensors is presented. The method has the advantages of requiring no sensor calibration, no dependence on the presence of a dominant frequency or oscillation period and it requires no qualitative interpretation of sensor time-series signals. The method is developed by investigating the flow downstream of a backward-facing step. Through computation of the time of flight of convected flow disturbances over adjacent sensor pairs, the method offers a quantitative resolution of the mean location of reattachment for turbulent flows.Nomenclature AR backward-facing step aspect ratio; =w/h - f frequency - G_pp(f) autospectral density function - G_pq(f) cross-spectral density function - h step height - Ma Mach number - n_d number of ensembles - Re_c Reynolds number based on external velocity and body chord - Re_h Reynolds number based on external velocity and step height - Re Reynolds number based on external velocity and momentum thickness - t time of flight - u mean streamwise velocity component - U_c phase velocity - U freestream velocity - w span of backward-facing step - x streamwise coordinate - x_R mean reattachment length - y wall-normal coordinate - z spanwise coordinate - x adjacent hot-film sensor spacing - _R random error in phase estimates - linear coherence spectrum - _pq(f) phase spectrum - momentum thickness - HFA hot-film array - LDV laser Doppler velocimetry     

Pulsed-wire measurements in the near-wall layer in a reattaching separated flow

Pulsed-wire velocity measurements have been made in the near-wall layer, including the viscous sublayer, beneath a separated flow. A method for correcting the error caused by fluctuations in velocity gradient is given, extending the work of Schober et al. (1998). The measurements show that the r.m.s. of the streamwise velocity fluctuations scale closely in accordance with an inner-layer scaling, where the velocity scale, , is based on the r.m.s. of the wall shear stress fluctuations (measured by means of a pulsed-wire shear stress probe), rather than the mean wall shear stress. The effects of velocity gradient are only significant beneath of 10 or less.List of symbols C Calibration constant - f Function representing mean velocity - h_f Height of fence above splitter plate surface - L Length scale of outer-layer structures - s Distance between pulsed and sensor wires - u r.m.s. of U - Velocity scale based on r.m.s of wall shear stress fluctuation - U Instantaneous velocity in x-direction - U_m Instantaneous measured velocity in x-direction - U_r Free-stream reference velocity - x Streamwise direction from separation point - y Distance from splitter plate surface, in normal direction - X_r Length of separation bubble - ₀ Thickness scale in oscillating layer - Blasius laminar boundary layer parameter - Density - Wall shear stress - r.m.s. of wall shear stress fluctuation - Frequency of oscillating layer - Kinematic viscosity - Overbar denotes time average     

Helium jets discharging normally into a swirling air flow

The characteristics of helium jets injected normally to a swirling air flow are investigated experimentally using laser Doppler and hot-wire anemometers. Two jets with jet-to-crossflow momentum flux ratios of 0.28 and 12.6 are examined. The jets follow a spiral path similar to that found in the swirling air flow alone. Swirl acts to decrease jet penetration, but this is being counteracted by the lighter jet fluid density which is being pressed towards the tube center by the inward pressure gradient. Consequently, in spite of the large variation in momentum flux ratio, jet penetration into the main flow for the two jets investigated is about the same. The presence of the jet is felt only along the spiral path and none at all outside this region. Upstream of the jet, the oncoming swirling flow is essentially unaffected. These characteristics are quite different from jets discharging into a uniform crossflow at about the same momentum flux ratios, and can be attributed to the combined effects of swirl and density difference between the jet fluid and the air stream. Finally, the jets lose their identity in about fifteen jet diameters.List of symbols C mean volume concentration of helium - C _j mean volume concentration of helium at jet exit - c fluctuating volume concentration of helium - instantaneous volume concentration of helium - c RMS volume concentration of helium - D _j jet nozzle diameter - D _T diameter of tube - F flatness factor of c - J = _j U _j ² / _a U _a ^{gn 2} jet-to-crossflow momentum flux ratio - P(c) probability density function of c - r radial coordinate measured from tube centerline - R = D _T /2 radius of tube - Re _j = D _j U _j / _j jet Reynolds number - S = = tan swirl number - Sk skewness of c - instantaneous axial velocity - u RMS axial velocity - U mean axial velocity - local average mean axial velocity across tube - U _j jet exit velocity - U _a overall average mean axial velocity across tube - instantaneous circumferential velocity - w RMS circumferential velocity - W mean circumferential velocity - x axial coordinate measured from exit plane of swirler - x ₁ axial coordinate measured from centerplane of normal jet - y normal distance measured from tube wall - _j jet fluid kinematic viscosity - _a air density - _j jet fluid density - vane angle (constant)     

Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers

An experimental investigation of the moderate Reynolds number plane air jets was undertaken and the effect of the jet Reynolds number on the turbulent flow structure was determined. The Reynolds number, which was defined by the jet exit conditions, was varied between 1000 and 7000. Other initial conditions, such as the initial turbulence intensity, were kept constant throughout the experiments. Both hot-wire and laser Doppler anemometry were used for the velocity measurements. In the moderate Reynolds number regime, the turbulent flow structure is in transition. The average size and the number of the large scale of turbulence (per unit length of jet) was unaffected by the Reynolds number. A broadening of the turbulent spectra with increasing Reynolds number was observed. This indicated that there is a decrease in the strength of the large eddies resulting from a reduction of the relative energy available to them. This diminished the jet mixing with the ambient as the Reynolds number increased. Higher Reynolds numbers led to lower jet dilution and spread rates. On the other hand, at higher Reynolds numbers the dependence of jet mixing on Reynolds number became less significant as the turbulent flow structure developed into a self-preserving state.List of symbols b _u velocity half-width of the jet - C _u, C _u,0 constants defining the velocity decay rate - D nozzle width - E _u one dimensional power spectrum of velocity fluctuations - f frequency - K _u, K _u,0 constants defining the jet spread rate - k wavenumber (2f/U) - L longitudinal integral scale - R ₁₁ correlation function - r separation distance - Re jet Reynolds number (U ₀ D/v) - St Strouhal number (fD/U ₀) - t time - U axial component of the mean velocity - U _m mean velocity on the jet axis - U ₀ mean velocity at the jet exit - u the rms of u - u fluctuating component of the axial velocity - V lateral component of the mean velocity - fluctuating component of the lateral velocity - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - v kinematic viscosity - time lag A version of this paper was presented as paper no. 86-0038 at the AIAA 24th Aerospace Sciences Meeting, Reno NV, USA, January 1986     

Turbulent wall pressure fluctuations over wavy surfaces

Measurements of the spectral characteristics of the wall pressure fluctuations produced by a turbulent boundary layer flow over solid sinusoidal surfaces of moderate wave amplitude to wave-length ratios have been obtained. The wave amplitudes were sufficiently small so that the flow remained attatched. The results show that the root mean square pressure level reaches a maximum on the adverse pressure gradient side of the wave at a position somewhat before the trough. Spectral analysis of the pressure fluctuations in narrow frequency bands reveals considerable differences in low and high frequency behavior. At low frequencies, the peak fluctuation amplitude was found at the trough whereas at high frequencies, the peak occurs just after the crest and a minimum is found at the trough. Pressure fluctuations having streamwise correlation lengths on the order of or larger than the wavelength of the surface do not return to their equilibrium (crest) amplitudes as they travel the length of a wave. Pressure fluctuations having streamwise correlation lengths about one order of magnitude less than a wavelength return exactly to their equilibrium amplitudes. Two-point correlation measurements show a decrease in longitudinal coherence on the adverse pressure gradient side of the wave at low frequencies and a considerable increase over a broad frequency range on the positive pressure gradient side. No change is found in the lateral coherence.List of symbols C _f skin friction coefficient - C _p pressure coefficient - C _n Fourier amplitudes of the pressure coefficient - C _dp pressure drag coefficient - d pinhole diameter - f frequency - h half the crest to trough distance - h ₊ nondimensional wave amplitude = - k _n wavenumber = - k fundamental wavenumber = - l _p pressure correlation length - p _s mean surface pressure - P ambient pressure - p fluctuating pressure - p ² mean square pressure - q dynamic head = 1/2 U ² - R space-time correlation - P Reynolds number based on wavelength = - R Reynolds number based on momentum thickness = - t time - R free stream velocity - U mean streamwise velocity - U _e streamwise velocity at the edge of the boundary layer - u ^* friction velocity = - x streamwise coordinate - y wall-normal coordinate - z spanwise coordinate - ⁺ non-dimensional wavelength = ^*) - phase of the cross-spectral density - ^* boundary layer displacement thickness - _long longitudinal coherency - _lat lateral coherency - wavelength of wavy surface - v kinematic viscosity - radian frequency = 2 f - spectral or cross-spectral density - _n phase of the Fourier series - density - time delay - _w wall shear stress - boundary layer momentum thickness     

Prediction of stagnation point heat transfer for a slot jet impinging on a flat surface

The fluid flow and heat transfer for a slot jet impinging on a flat plate has been analysed for different nozzle-to-plate spacing. The available potential flow solution has been used to solve the boundary layer and energy equations by using the Blasius-Frossling series solution method. The friction factor and Nusselt number have been evaluated as a function of the dimensionless distance from the stagnation point. Correlation for the Stanton number at the Stagnation point, is obtained in terms of velocity gradient at the stagnation point and Reynolds number.

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Berechnung des Wärmeübergangs am Staupunkt für einen Strahl, der senkrecht auf eine ebene Fläche trifft

Zusammenfassung Für einen Fluidstrahl, der senkrecht auf eine ebene Platte trifft, wurden für verschiedene Anordnungen von Düse und Platte Strömung und Wärmeübertragung untersucht. Die beschreibende Potentialtheorie wurde verwendet, um die Grenzschicht und Energiegleichungen mit Hilfe der Blasius-Frossling-Reihenentwicklung zu lösen. Reibungsfaktor und Nusseltzahl sind als eine Funktion des dimensionslosen Abstandes vom Staupunkt dargestellt. Die Beziehung für die Stanton-Zahl am Staupunkt ist in den Ausdrücken des Geschwindigkeitsgradienten am Staupunkt und der Reynoldszahl enthalten.

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Nomenclature A ₁ dimensionless coefficient - a dimensionless parameter - b dimensionless parameter - C _f friction factor,C _f= ₀/(1/2w ² ) - C _p specific heat at constant pressure - F ₀ function ofPr and - G ₄ function ofPr and - f ₁ function of - h heat transfer coefficient - k thermal conductivity - l half-width of slot nozzle - Nu Nusselt number,Nu=hl/k - Pr Prandtl number,Pr=v/ - Re Reynolds number,Re=w l/v - St Stanton number,St=Nu/(Re · Pr) - t temperature - t _w wall temperature - t ambient temperature - U dimensionless velocity,U=u/w - U _f dimensionless free-stream velocity,U _f =u _f /w - U _s dimensionless mainstream velocity along the plate,U _s =u _s /w - u velocity component inx-direction - u _f free stream velocity - u _s mainstream velocity along the plate - w velocity component inz-direction - w velocity at the nozzle exit - x coordination along the plate - X dimensionless distance from the stagnation point along the plate,X=x/l - Y ratio ofU _s andU _f ,Y=U _s /U _f - z coordinate perpendicular to the plate - z _n height of the nozzle above the plate - Z dimensionless height of the nozzle above the plate,Z=z _n /l - thermal diffusivity,=k/( C _p) - dimensionless parameter - dimensionless coordinate perpendicular to the plate - viscosity - kinematic viscosity - ₀ shear stress at the wall - stream function