Moving-model technique used in automobile aerodynamics for measurement of ground effects

Efforts are currently underway in many laboratories to simulate correctly the ground effects which occur in windtunnels used for studies in automobile aerodynamics. An experimental approach which is sometimes used, the moving belt technique, is both complicated and expensive. On the other hand, if the model is rapidly accelerated along a stationary rail by a pneumatic launch system, the relative motion between the car and the road is simulated in an optimum manner with less effort and lower costs. The practical advantages and disadvantages of the moving-model technique in comparison with the moving belt in a windtunnel are discussed. Using a two-dimensional model car, the effect of the ground on the body pressure distribution was investigated. In addition, the distribution of the pressure on the surface of the ground board and the velocity profiles underneath the model were measured.List of symbols B model width - L model length - h distance between ground and lower side of model - H _m maximum model height at rear end - c _p pressure coefficient,=(p–p )/(/2·U ² - p static pressure - p static pressure of free stream - Re Reynolds number, = U · L · / - U model velocity - u streamwise velocity component - x streamwise coordinate, from front of model downstream - y transverse coordinate, from ground upwards - z spanwise coordinate, from centerline of model outwards - dynamic viscosity of air - density of air     

Elastico-viscous boundary-layer flow on the surface of a sphere

Summary The Prandtl boundary-layer theory is extended for an idealized elastico-viscous liquid. The boundary layer equations are solved approximately by Kármán-Pohlhausen technique for the case of a sphere. It is shown that the increase in the elasticity of the liquid causes a shift in the point of separation towards the forward stagnation point.

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Zusammenfassung Die Prandtlsche Grenzschicht-Theorie wird für eine idealisierte viskoelastische Flüssigkeit erweitert. Die Grenzschichtgleichungen werden für den Fall einer angeströmten Kugel näherungsweise mit Hilfe der Kármán-Pohlhausen-Methode gelöst. Es wird gezeigt, daß das Anwachsen der Flüssigkeitselastizität eine Verschiebung des Ablösepunktes auf den vorderen Staupunkt hin zur Folge hat.

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Nomenclature b ^ik arbitrary contravariant tensor - D non-dimensional boundary layer thickness - g _ik metric tensor of a fixed coordinate system - K curvature at any point on the generating curve - K ₀ elastico-viscous parameter - p arbitrary hydrostatic pressure - p _ik stress tensor - p ^ik part of stress tensor associated with the change of shape of material - R radius of the sphere - r radius of any transverse cross-section of the sphere - t time - U potential velocity around the body - U stream-velocity at a large distance from the body - u, w velocity components along (x, z) directions respectively - x distance measured along a generating line from the forward stagnation point - z distance measured along a normal to the surface - non-dimensional elastico-viscous parameter - density of the liquid - boundary layer thickness - convected time derivative - ₀ limiting viscosity for very small changes in deformation velocity - angle measured along the transverse direction - x/R - v kinematic coefficient of viscosity - T _s shearing stress on the surface of the sphere With 2 figures and 1 table     

Displacement effect of square-ended pitot tubes in shear flows

Measurements in uniformly sheared flows indicate that the displacement of total-pressure tube readings due to shear is roughly constant, even for values of the shear parameter smaller than previously believed.List of symbols D tube outer diameter - d tube inner diameter - h wind-tunnel height - K tube shear parameter - K _r reference tube shear parameter - L characteristic scale of turbulence - P pressure - P _D total pressure indicated by tube of diameter D - P ₀ free stream total pressure - P _r total pressure indicated by reference tube - P _s pressure indicated by static pressure tube - U mean velocity - U _c centerline mean velocity - U _D mean velocity indicated by tube of diameter D - U _r mean velocity indicated by reference tube - u r.m.s. velocity - y transverse coordinate - empirical coefficient - wind-tunnel shear parameter - displacement - fluid density     

Turbulence measurements in a merged jet from two opposing curved wall jets

A two-dimensional flow generated by the interaction of two opposing, symmetric curved wall jets is investigated experimentally. The overall flow field can be divided into the curved wall jet region, the interaction region, and the merged jet region; thus, the results of the measurement are discussed to characterize these three distinct regions. For the curved wall jet region, the Reynolds stress distribution, the correlation coefficient, , and the ratio of normal stresses, , are presented and the effects of curvature and adverse pressure gradient on these distributions are discussed. The Reynolds stress distributions in the interaction region are analyzed in detail to illuminate the negative production of the turbulent kinetic energy. The developing jet in this region is found to accelerate owing to the very high pressure arising from the collision of the two wall jets. A counter-gradient shear flow situation is also observed in this interacting region. Measured data in the merged jet region are often compared to those of plane jets and the development of the merged jet is discussed in that respect. The spreading rate of the present merged jet is found to be much larger than that of the plane jets. To account for the larger spreading rate, the intermittency distribution is also investigated.List of symbols b position of y where U = U _c/2 - f turbulent/non-turbulent interface crossing rate - f _max maximum interface crossing rate - h slot height of the wall jet, 10 mm - L _u integral length scale - P, P _a static and atmospheric pressure, respectively - P _u ² production rate of longitudinal normal stress - P _v ² production rate of lateral normal stress - r radial distance from the cylinder surface - R radius of curvature of the cylinder, 100 mm - r _1/2 position of r where U=U _m/2 - U streamwise velocity - U _c centerline velocity of the merged jet - U _m maximum velocity of the curved wall jet - U ₀ exit velocity - \] Reynolds stresses - V lateral velocity in the merged jet - x distance along the centerline of the merged jet - y lateral distance from the centerline of the merged jet - intermittency factor     

Developing laminar flow in the inlet length of a smooth pipe

The laminar flow phenomena in the inlet (entrance) region of circular pipe are investigated experimentally. New curves of friction factor versus Reynolds number, for various entry lengths, are obtained and compared with the standard curve for fully developed laminar flow. The relationship between the viscous friction, the energy loss due to the lengthwise rate of change of the kinetic energy coefficient and the total energy loss is investigated. The continuous variation of the velocity profile is analysed by using the concept of a non-Newtonian liquid whose shear sensitivity varies continuously along the pipe.Nomenclature A cross-sectional area - kinetic energy correction coefficient - D pipe diameter - boundary thickness - increment - f measured friction factor as defined by Darcy's law - f _k component of f due to change in kinetic energy only - f _v component of f due to viscous head loss only - f _L friction factor as computed from Langhaar's theory - g gravitational acceleration - h head loss - H _k component of h due to change in kinetic energy - H _v component of h due to viscous friction - K, n constants in the power law =K(dU/dr) ⁿ - v kinematic viscosity - viscosity - L length - L _e entry length - L _d developing (inlet) length - N _R Reynolds number - P pressure - Q volume discharge - r distance from the centre line of the pipe towards the wall - r ₀ radius - pressure - shear stress - U velocity - U _m mean velocity - U _c centre-line (maximum) velocity - x ₁ axial distance from entrance to the first pressure tapping point - x ₂ axial distance from entrance to the second pressure tapping point - Z dimensionless number=L/r ₀ - dimensionless number=Z/N _R     

Experimental investigations of steady and oscillating annular liquid curtains with different surface tensions

Experiments were performed on laminar, vertical, annular, liquid curtains to study the dynamics of steady curtains, and the onset and frequency of oscillating curtains. The experiments were conducted to observe the effects of inertia and pressure on liquid curtains with different surface tensions. For steady curtains, convergence lengths were measured as functions of Froude number and pressure differential for three different surface tensions. The factors causing the onset of oscillations in a pressurized curtain were observed and the frequency of the internal pressure fluctuations were measured for various Froude numbers and two surface tensions.List of symbols b local thickness of curtain sheet - b ₀ initial thickness of curtain or nozzle gap thickness (0.5 mm) - C _P pressure coefficient - Fr Froude number (V ₀ ² /g R ₀) - g gravitational acceleration - g gravitational acceleration - L convergence length of curtain - L ^* dimensionless convergence length (L/R ₀) - N _c convergence number (g ² R ₀ ² b ₀ /2v ₀ ² ) - P _e pressure outside the curtain (ambient) - P _i pressure inside the curtain - P pressure differential (P _i– P _e) - P _cr pressure differential at which curtain begins to oscillate - R local radius of curvature in the horizontal plane - R ₀ initial curtain radius or radius of nozzle exit (50 mm) - r _v local radius of curvature in the vertical plane - V local liquid velocity - V ₀ initial liquid velocity - V ^* dimensionless local liquid velocity (V/V ₀) - z axial distance from the nozzle - z ^* dimensionless axial distance from the nozzel (z/R ₀) - s differential length of curtain - differential angle in the horizontal plane - angle between the direction of the surface tension force in the vertical plane and the direction of r _v - deangle between the direction of the surface tension force in the horizontal plane and the direction of R - angle between r _vand R in the vertical plane - ₀ nozzle exit angle (zero degrees) - surface tension of liquid - liquid density (1.0 gm/cm³)     

Magnetohydrodynamic laminar flow between porous disks

The steady two-dimensional laminar flow of an incompressible conducting fluid between two parallel circular disks in the presence of a transverse magnetic field is investigated. A solution is obtained by perturbing the creeping flow solution and it is valid only for small suction or injection Reynolds numbers. Expressions for velocity, induced magnetic field, pressure, and shear stress distribution are determined and are compared with the creeping flow and hydrodynamic solutions. It is found that the overall effect of the magnetic field on the flow is the same as that in the Hartmann flow.Nomenclature stream function - 2h channel width - z, r axial and radial coordinates - radius of the disk - U _r radial component of velocity - U _r average velocity in the radial direction, U _r d - U _z axial component of velocity - U ₀ injection or suction velocity - dimensionless axial coordinate, z/h - f() function defined in (8) - density - coefficient of kinematic viscosity - electrical conductivity - magnetic permeability - H ₀ impressed magnetic field - h _r induced magnetic field, H _r /H ₀ - M Hartmann number, H ₀ h(/)^1/2 - R Reynolds number, U ₀ h/ - R _m magnetic Reynolds number, U ₀ r - A constant defined in (15) - K constant defined in (27) - C ₂ constant defined in (26) - p pressure - C _p pressure coefficient - C _f skin friction coefficient     

Measurements of thermally stratified pipe flow using image-processing techniques

The cross-correlation technique and Laser Induced Fluorescence (LIF) have been adopted to measure the time-dependent and two-dimensional velocity and temperature fields of a stably thermal-stratified pipe flow. One thousand instantaneous and simultaneous velocity and temperature maps were obtained at overall Richardson numberRi = 0 and 2.5, from which two-dimensional vorticity, Reynolds stress and turbulent heat flux vector were evaluated. The quasi-periodic inclined vortices (which connected to the crest) were revealed from successive instantaneous maps and temporal variation of vorticity and temperature. It has been recognized that these vortices are associated with the crest and valley in the roll-up motion.List of symbols A Fraction of the available light collected - C Concentration of fluorescence - D Pipe diameter - I Fluorescence intensity - L Sampling length along the incident beam - I ₀ Intensity of an excitation beam - I _c (T) Calibration curve between temperature and fluorescence intensity - I _ref Reference intensity of fluorescence radiation - Re _b Reynolds number based on bulk velocity,U _b D/v - Ri Overall Richardson number based on velocity difference,gDT/U ² - t Time - t Time interval between the reference and corresponding matrix - T Temperature - T ₁,T ₂ Temperature of lower and upper layer - T ^* Normalized temperature, (T–T ₁)/T - T _c (I) Inverse function of temperature as a function ofI _c - T _ref Reference temperature - T Temperature difference between upper and lower flow,T ₂ –T ₁ - U ₁ Velocity of lower stream - U ₂ Velocity of upper stream - U _b Bulk velocity - U _c Streamwise mean velocity atY/D=0 - U Streamwise velocity difference between upper and lower flow,U ₁–U ₂ - u, v, T Fluctuating component ofU, V, T - U, V Velocity component of X, Y direction - X Streamwise distance from the splitter plate - Y Transverse distance from the centerline of the pipe - Z Spanwise distance from the centerline of the pipe - Quantum yield - Absorptivity - vorticity calculated from a circulation - Kinematic viscosity - circulation     

An investigation of laminar radial flow between two parallel discs

Summary Experiments have been carried out to test recent theoretical predictions of the pressure distribution for laminar flow between parallel discs, including inertia effects. The experimental investigation covered the condition where the inertia effects were always completely dominant over the central region of the discs in contrast to other recent experimental work on the problem where the central injection diameter was considerably larger. The present experiments subject the theories to a stringent test, due to the dominance of the inertia effects, and it is found that the inertia effects predicted by the various theoretical analyses are significantly smaller than those shown by the experimental results. It is suggested that the theoretical approach requires further development before it will cover the conditions where the central injection diameter is small.Nomenclature r, y, cylindrical co-ordinates - u velocity in r direction - U _m mean velocity in r direction at radius r - density - coefficient of viscosity - Q volume flow per unit time - 2h gap between parallel discs - p static pressure - R r/h - P h ³ p/Q - R _e Q/h     

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     

Effect of angular inertia of lubricant in MHD hydrostatic thrust bearings

Summary Circumferential motion of a conducting lubricant in a hydrostatic thrust bearing is caused either by the angular motion of a rotating disk or by the interaction of a radial electric field and an axial magnetic field. Under the assumption that the fluid inertia due to radial motion is negligibly small in comparison with that due to angular motion, it is found analytically that the rotor causes an increase in flow rate and a decrease in load capacity, while both are increased by the application of an electric field in the presence of an axial magnetic field. The critical angular speed of the rotor at which the bearing can no longer support any load is obtained, and the possibility of flow separation in the lubricant is discussed.Nomenclature a recess radius - b outside disk radius - B ₀ magnetic induction of uniform axial magnetic field - E ₀ radial electric field at r=a - E _r radial electric field - h half of lubricant film thickness - M Hartmann number = (B ₀ ² h ²/)^1/2 - P pressure - P ₀ pressure at r=a - P _e pressure at r=b - Q volume flow rate of lubricant - Q ₀ flow rate of a nonrotating bearing without magnetic field - r radial coordinate - r _s position of flow separation on stationary disk - u, v fluid velocity components in radial and circumferential directions, respectively - W load carrying capacity of bearing - W ₀ load capacity of a nonrotating bearing without magnetic field - z axial coordinate - coefficient of viscosity - _e magnetic permeability - fluid density - electrical conductivity - electric potential - angular speed of rotating disk - _c critical rotor speed at which W=0     

Effects of the separating shear layer on the reattachment flow structure part 2: Reattachment length and wall shear stress

Measurements of reattachment length of a separated flow behind a backward-facing step for a range of Reynolds numbers (8000 < Re _H < 40,000) and initial boundary-layer thickness (0 < /H < 2) were performed with the purpose of explaining the scatter in existing (high quality) data sets and to understand the effect of the initial shear-layer structure on the reattachment zone. The reattachment length for the case of laminar boundary layers upstream of the step were 30% smaller than when the boundary layer upstream of the step was turbulent. Measured values of the mean wall shear stress in the reattachment zone were also measurably affected by the upstream boundary-layer state. The (rms) levels of fluctuating wall stress were not sensitive to boundary-layer state, but rather to /H, as was the case for the pressure profiles in part 1 (Adams and Johnston 1988).List of symbols C _* ^p normalized pressure, (C _p – C _{p, min})/(1 – C _{p, min}) - C _f skin friction coefficient, /0.5 U _ref ² - C _f level (rms) of fluctuation part of skin-friction coefficient - ER duct expansion ratio; outlet to inlet width - H step height - Re _d Reynolds number based on diameter - Re Reynolds number based on inlet boundary-layer momentum thickness, and U _ref - Re _H Reynolds number based on H and U _ref - x _r distance to reattachment - X ^* normalized distance, (x – x _r)/x _r (note: different from x/x _r in part 1) - /H ratio of inlet boundary-layer thickness to step height - gq ₀ momentum thickness upstream of step     

Turbulent kinetic energy balance in the wake of a self-propelled body

An experimental study of the turbulent wake of a self-propelled body in a wind tunnel is reported. A significant difference is formed between the turbulent kinetic energy balance in a wake with drag and in the wake of a self-propelled body: the production term is very small in comparison with the other terms of the turbulent kinetic energy balance, and this result seems to be typical of self-propulsion. The axial evolution of the wake radius and turbulent kinetic energy profiles are described. Sufficiently far downstream from the body, a self-similar profile is found. Particular attention is devoted to the turbulent kinetic energy balance; all the terms in the energy balance are evaluated experimentally.List of Symbols D diameter of the body - L axial length scale - l radial length scale - R radius of the body - r radial coordinate - r ^* radius of the wake - U mean axial velocity scale - Û defect velocity - U _e freestream velocity - u fluctuating velocity scale - x axial coordinate - dissipation rate - = r/r ^* radial relative direction - azimuthal coordinate - kinematic viscosity - density     

A cylindrical coaxial MHD generator

A MHD generator with a novel geometry is analyzed as a possible dc power source. The generator channel consists of two coaxial cylinders with a smooth annular space between them through which pressure driven ionized gas flows axially. Magnetic poles and electrodes separated by insulators are embedded in both the inner and outer cylinders. A one-dimensional steady state analysis is presented. It is shown that the internal impedance of the generator is a very sensitive function of the ratio of areas of the charge collecting electrodes to that of the magnetic poles. The generator efficiency analysis, on the other hand, indicates that there is an optimum area ratio corresponding to the maximum conversion efficiency. A comparison of the performance characteristics of this generator with those of a generator of rectangular cross section is presented. The average gas temperature and velocity, the magnetic flux density at the poles, and the volume displacement rate, etc., are assumed identical for the two cases in comparison. It is inferred that the novel channel analyzed herein is, in general, superior to the simple rectangular channel in the energy conversion scheme.Nomenclature a _n - 2a width of the rectangular channel - a _1n , a _2n , b _1n , b _2n constants - B magnetic flux density, both induced and applied - B _r0 maximum value of radial component of B at r=r _i - B ₀ applied magnetic field in the rectangular generator = B _r0 - 2b height of the rectangular channel - C _n r _i r _o ⁿ +r _o r _i ⁿ - C _–n r _i r _o ⁿ +r _o r _i ^–n - c integration constant - D _n - E electric field strength - maximum value of azimuthal component of E at r=r _i - G _n C _–n r _n +C _n r ^– _n - G _–n C _–n r _n –C _n r ^– _n - H _n G _n r ^–1 - H _–n G _–n r ^–1 - I _r total radial current between a pair of opposite electrodes - j electric current density - p pressure of the ionized gas - P number of magnetic poles in each cylinder of the generator - P _HT power loss due to heat transfer to the walls - P _i power input - P _o power output - R _ic internal impedance of the coaxial channel MHD generator consisting of an opposite pair of electrodes associated with the magnetic poles, insulators, and the channel in between, for a unit length of the channel - R _ir internal impedance of the rectangular generator for a unit length of the channel = a/b - R ₀ external load connected to the MHD generator - r radial coordinate of the cylindrical coordinate system - r _i, r _o radii of the inner and outer cylinders, respectively - V fluid velocity - z axial coordinate of the cylindrical coordinate system - _n nP/2 - azimuthal coordinate of the cylindrical coordinate system - _e electrode angular width - _pi pole-insulator angular width - electrical conductivity of the ionized gas - permeability of the medium - _v coefficient of viscosity - (r, ) electric potential - (r _i, )–(r _o, ) potential difference between an opposite pair of electrodes - conversion efficiency of a MHD generator A paper based on some of this material was presented at the International Electron Devices Meeting, Washington (D.C.) October 1967.     

Near-wall velocity distributions within a straight conical diffuser

The measured mean velocity profiles at the various stations along a conical diffuser (8° total divergence angle) were found to consist of log regions, half-power law regions and linear regions. The describing coefficients for the inner half-power law region (which followed a rather narrow log region) differed from the standard values due to the axi-symmetric geometry and lack of moving equilibrium of the flow as it attempted to adjust to a varying adverse pressure gradient. However, these coefficients (like those for the linear region) correlated with the local wall shear stress and the kinematic pressure gradient.List of symbols A, B coefficients in logarithmic law velocity distribution (Eq. (1)) - C, D coefficients in half-power law velocity distribution (Eq. (5)) - D_i inside diameter of feed pipe (10.16 cm) - d _p outer diameter of Preston tube - E, F coefficients in linear law velocity distribution (Eq. (10)) - P _s local static pressure - R local radius of diffuser, (D _i /2) + x _w sin 4° - Re Reynolds number, D _i U _b /v - U local mean velocity in the x _w direction - U _b cross-sectional average mean velocity (x-direction) in feed pipe - U _c mean velocity at the diffuser centerline - u ^* local friction velocity - u ⁺ dimensionless local mean velocity, U/u ^* - axial distance along diffuser centerline (measured from inlet to diffuser) Fig. (2) - _w distance along diffuser wall (measured from inlet to difusser (Fig. 2) - y _w distance from wall in direction orthogonal to wall (Fig. 2) - y ⁺ dimensionless position, y _w u ^*/v - kinematic (axial static) pressure gradient, (1/g9) dP _s/dx - ^* displacement thickness (Eq. (4)) - dimensionless pressure gradient parameter, x v/(u*) ³ - Von Karman constant (0.41) - density - kinematic viscosity - shear stress     

Measurements in the field of a spark excited compressible axisymmetric jet

Acoustic phase (ensemble) averaged measurements were performed in a constant temperature, axisymmetric, Mach 0.6 jet of air. These measurements show that the noise directly radiated by the coherent structure in the jet flow field was responsible for the directivity of the acoustic field.List of symbols D nozzle exit diameter - f frequency, Hz - r radial distance from the jet centerline - SPL sound pressure level (ref.: 20 micro pascals) - St Strouhal number, = f D/U - U jet exit velocity - x distance along the jet axis from the nozzle exit - t time - ensemble average quantity     

Some flow characteristics of lobed forced mixers at higher velocity ratios

The flow characteristics of two types of lobed forced mixers, the unscalloped and the scalloped mixers, have been examined at velocity ratios higher than unity, in relation to the variation of mass flux uniformity, the decay of the streamwise vorticity, the variation of turbulent kinetic energy and the growth of the shear layer with distance from the trailing edge. Three trailing edge configurations have also been considered for each type of mixer, namely a square wave, a semi-circular wave and a triangular wave. The analysis showed that the strength of the streamwise vorticity shed at the trailing edge and the subsequent decaying rate with downstream distance are found to be very important in studying the mixing effectiveness of the lobed mixers.List of Symbols C _I normalized streamwise circulation, _s/U _r h tan - _s streamwise circulation - k turbulent kinetic energy = 1/2(u²+v²+w²) - Re Reynolds number, U _r /=2.27×10⁴ - h (=) Lobe height, 33 mm - U ₁, U ₂ mean velocity of the slow and fast streams - U _r reference mean velocity, (U ₁ + U ₂)/2 = 10 m/s - U, u streamwise mean and the corresponding rms velocities - V, v horizontal mean and the corresponding rms velocities - W, w vertical mean and the corresponding rms velocities - x,y, z streamwise, horizontal and vertical directions - A _wake cross-sectional area bounded by the wake region. The wake region boundary is defined at the region bounded by one half of a lobe along the y/ direction and at the locations along the z/ direction where U ₂/U _r2 and U ₁/U _r1<0.95. - nominal lobe wavelength, 33 mm - half of the included divergent angle of the penetration region, 22° - U uniformity factor - momentum thickness Financial supports from the Applied Research Grant is gratefully acknowledged. The contribution of Mr. J. K. L. Teh, Dr. J. H. Yeo and Mr. T. H. Yip to the work presented here are sincerely appreciated.     

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     

Strong cylindrical shocks in a rotating gas

Similarity solutions describing the flow behind a diverging strong cylindrical shock wave, advancing into a nonuniform gas having solid body rotation, are studied. The effects of the angular velocity variation on the shock velocity are shown graphically. It is found that an increase in the initial angular velocity leads to a decrease in the shock velocity.Nomenclature c ₀ sound velocity in unperturbed state - c sound velocity in unperturbed state at the axis of symmetry - D nondimensional density in unperturbed state - E energy release per unit length - f nondimensional radial velocity in perturbed state - g nondimensional pressure in perturbed state - h nondimensional density in perturbed state - k nondimensional azimuthal velocity in perturbed state - M an integral - N another integral - P nondimensional pressure in unperturbed state - p pressure in perturbed state - p ₀ pressure in unperturbed state - p pressure at the axis in unperturbed state - p ₁ pressure immediately behind the shock front - R shock front radius - r radial coordinate - R ₀ a characteristic length parameter - t time coordinate - U shock front velocity - u particle velocity (radial) in perturbed state - u ₀ particle velocity (radial) in unperturbed state - u ₁ particle velocity (radial) immediately behind the shock front - v particle velocity (azimuthal) in perturbed state - v ₀ particle velocity (azimuthal) in unperturbed state - v ₁ particle velocity (azimuthal) immediately behind the shock - w nondimensional azimuthal velocity in unperturbed state - x a nondimensional independent variable - z axial coordinate of cylindrical coordinates - Z a nondimensional independent variable - ₀ angular velocity in unperturbed state - ₁ angular velocity immediately behind the shock - density in perturbed state - ₀ density in unperturbed state - ₁ density immediately behind the shock - density at r=0 in unperturbed state - adiabatic index of the gas - ₀ R ₀ ² ₀ ² /(c)²     

Aerodynamic behaviour of prismatic bodies with sharp and rounded edges

The aerodynamic behaviour of prismatic bodies in a wide range of angles of attack is addressed in the present work. In particular, we focus on bodies with a basically rectangular shape, either sharp or cylindrical edges and different thicknesses. In general, the thinnest bodies exhibit the largest lift-to-drag ratio at moderate angles of attack, which is further enhanced with rounded edges. At larger angles of attack, bodies with rounded edges exhibit smaller drag than bodies with sharp edges. Roughness was found to enhance the lift-to-drag ratio significantly at small angles, and drag is reduced at larger angles.List of symbols A Cross-sectional area - b Span width - c_D Drag coefficient - c_D,r Recalculated drag coefficient applying a different reference area - c_L Lift coefficient - c_L,r Recalculated lift coefficient applying a different reference area - c_M Pitching moment coefficient - D Drag area - F_D Drag force - F_L Lift force - H Height - L Lift area - l Reference length - M Pitching moment - q Dynamic pressure - Re Reynolds number - Re_Cx Critical Reynolds numbers - T Thickness - t Time - v Velocity - W Width - Angle of attack - , , Angles characterising posture and position of ski jumpers - Fluid density - Aspect ratio - kinematic viscosity