Forced convection of turbulent flow in triangular ducts with different angles and surface roughnesses

The experimental investigations were consisting of two parts. The first part was carried out to study the effect of corner geometry on the steady-state forced convection inside horizontal isosceles triangular ducts with sharp corners. The electrically-heated triangular duct was used to simulate the triangular passage of a plate-fin compact heat exchanger. The isosceles triangular ducts were manufactured with duralumin, and fabricated with the same length of 2.4 m and hydraulic diameter of 0.44 m, but five different apex angles (i.e. θ _a =15^∘,30^∘, 40^∘,60^∘, and 90^∘) respectively. The investigation was performed under turbulent flow condition covering a wide range of Reynolds number (i.e. 7000≤Re _D ≤20000). It was found that the best thermal performance is achieved with the apex angle of 60^∘. The second part was performed to investigate the effect of surface roughness on the forced convection of the same system. Horizontal equilateral triangular ducts with an apex angle of 60^∘ were fabricated with the same length and hydraulic diameter, but different average surface roughnesses of 1.2 m,3.0 m and 11.5 m respectively. It was concluded that the duct with a higher surface roughness will have a better heat transfer performance. Non-dimensional expressions for the determination of the heat transfer coefficient of the triangular ducts with different apex angles and surface roughnesses were also developed. Received on 15 December 1997     

Measurements and scaling of wall shear stress fluctuations

Measurements of velocity and wall shear stress fluctuations were made in an external turbulent boundary layer developed over a towed surface-piercing flat plate. An array of eight flush-mounted wall shear stress sensors was used to compute the space-time correlation function. A methodology for in situ calibration of the sensors for ship hydrodynamic applications is presented. The intensity of the wall shear stress fluctuations, τ _rms/τ _avg was measured as 0.25 and 0.36 for R _θ =3,150 and 2,160 respectively. The probability density is shown to exhibit positive skewness, and lack of flow reversals at the wall. Correlations between velocity and wall shear stress fluctuations are shown to collapse with outer boundary layer length and velocity scales, verifying the existence of large-scale coherent structures which convect and decay along the wall at an angle of inclination varying from 10 to 13° over the range of Reynolds numbers investigated. The wall shear stress convection velocity determined from narrow band correlation measurements is shown to scale with outer variables. The space-time correlation of the wall shear is shown to exhibit a well-defined convective ridge, and to decay 80% over approximately 3δ for R _θ =3,150. Published online: 7 November 2002     

Flow field characteristics in the near field region of particle-laden coaxial jets

The effects of solid particles on the flow structure in the near field region of a coaxial water jet are investigated non-intrusively using molecular tagging velocimetry. Glass beads of 240 μm and specific gravity SG of 2.46 are used at three volume loadings of γ_v=0.03, 0.06, and 0.09% in the central water jet with a Reynolds number of 4.1×10⁴. Measurements are acquired for four annular to central jet velocity ratios in the range 0.11≤ U _o/U _i≤1.15 at downstream distances up to six inner jet diameters and the results are analyzed for the effects of solid particles on the characteristics of flow. It is found that the addition of particles does not affect the mean fluid velocity profile in this region. The results also indicate a small and moderate enhancement of axial turbulent velocity and radial gradients of velocity fluctuations, respectively, due to the presence of particles.     

Numerical simulation of fluid flow and heat transfer characteristics in channel with V corrugated plates

A detailed numerical study is carried out to investigate fluid flow and heat transfer characteristics in a channel with heated V corrugated upper and lower plates. The parameters studied include the Reynolds number (Re = 2,000–5,500), angles of V corrugated plates (θ = 20°, 40°, 60°), and constant heat fluxs (q″ = 580, 830, 1,090 W/m²). Numerical results have been validated using the experimented data reported by Naphon, and a good agreement has been found. The angles of V corrugated plates (θ) and the Reynolds number are demonstrated to significantly affect the fluid flow and the heat transfer rate. Increasing the angles of V corrugated plates can make the heat transfer performance become better. The increasing Reynolds number leads to a more complex fluid flow and heat transfer rate. The numerical calculations with a non-equilibrium wall function have a better accuracy than with a standard wall function for solving high Reynolds numbers or complex flow problems.     

Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence

A survey is made of the standard deviation of the streamwise velocity fluctuations in near-wall turbulence and in particular of the Reynolds-number-dependency of its peak value. The following canonical flow geometries are considered: an incompressible turbulent boundary layer under zero pressure gradient, a fully developed two-dimensional channel and a cylindrical pipe flow. Data were collected from 47 independent experimental and numerical studies, which cover a Reynolds number range of R _θ=U _∞ θ/v=300−20,920 for the boundary layer with θ the momentum thickness and R ⁺=u _*R/v=100-4,300 for the internal flows with R the pipe radius or the channel half-width. It is found that the peak value of the rms-value normalised by the friction velocity, u _*, is within statistical errors independent of the Reynolds number. The most probable value for this parameter was found to be 2.71±0.14 and 2.70±0.09 for the case of a boundary layer and an internal flow, respectively. The present survey also includes some data of the streamwise velocity fluctuations measured over a riblet surface. We find no significant difference in magnitude of the normalised peak value between the riblet and smooth surfaces and this property of the normalised peak value may for instance be exploited to estimate the wall shear stress from the streamwise velocity fluctuations. We also consider the skewness of the streamwise velocity fluctuations and find its value to be close to zero at the position where the variance has its peak value. This is explained with help of the equations of the third-order moment of velocity fluctuations. These results for the peak value of the rms of the streamwise velocity fluctuations and also the coincidence of this peak with the zero value of the third moment can be interpreted as confirmation of local equilibrium in the near-wall layer, which is the basis of inner-layer scaling. Furthermore, these results can be also used as a requirement which turbulence models for the second and triple velocity correlations should satisfy. The authors are indebted to Prof. P. Bradshaw for making available his list of references on this topic and for his remarks on “active” and “inactive” motions. We also gratefully acknowledge discussions with Prof. I. Castro regarding the value of σ _u ⁺ above rough walls.     

Forced convection from a straight elliptical tube

The paper deals with the problem of two-dimensional laminar forced convection heat transfer from a straight isothermal tube of elliptic cross-section placed in a uniform stream. The study is based on numerical solutions of the conservation equations of mass, momentum, and energy which covers the entire flow domain including the wake region. The parameters influencing the heat transfer process are essentially the Reynolds number, Re, the tube geometry represented by its minor to major axis ratio, Ar, and the angle of inclination, λ. The study focuses on the effect of Re, Ar, and λ on the heat transfer process in the range of Re from 20 to 500. The study reveals that the rate of heat transfer reaches its maximum when λ=0^∘ while the minimum occurs when λ=90^∘. The results also show that smaller axis ratio gives higher heat transfer rate when λ=0^∘. The local Nusselt number and surface vorticity distributions are plotted for a number of cases and the effect of vortex shedding on the overall rate of heat transfer is briefly discussed. Received on 20 September, 1997     

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001     

Influence of stress triaxiality and temperature on void growth and ductile/brittle transition behavior of 40 Cr steel

Examined experimentally are the influence of stress triaxiality and temperature on the growth of microvoids and the ductile/brittle transition (DBT) macrobehavior of 40 Cr steel subjected to two different heat treatments. This is accomplished by testing more than 300 smooth and notched specimens over a temperature range of 20°C to −196°C. Changes in the microstructure morphology are examined by scanning electron microscopy (SEM) and identified with fracture data on a surface constructed from the uniaxial strain ε_c at fracture, the stress triaxiality R_σ and the temperature T. While stress triaxiality has a significant influence on the DBT temperature T_c, it does not affect the ratio of the average radius of voids R_o to that of inclusions R_i. The ratio R_o/R_i is found to increase with temperature and remains constant in specimens with different notch radii regardless of the temperature. Empirical relations between T_c and R_σ⁻ and R_o/R_i and T are proposed to better understand how macrofracture parameters are influenced by microstructure entities.     

Equilibrium states in homogeneous turbulence with baroclinic instability

The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ?U _i /?x _j  = S δ _i1 δ _j3, a system rotation about the vertical axis with rate Ω, Ω _i  = Ωδ _i3, and uniform buoyancy gradients in the spanwise ${(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)}The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ∂U _i /∂x _j  = S δ _i1 δ _j3, a system rotation about the vertical axis with rate Ω, Ω _i  = Ωδ _i3, and uniform buoyancy gradients in the spanwise (?B/?x₂ = N_h² = -2WS){(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)} and vertical (?B/?x₃ = N_v²){(\partial B{/}\partial x_3\,{=}\,N_v^2)} directions. Computations based on the rapid distortion theory (RDT) are performed for several values of the rotation number R = 2Ω/S and the Richardson number R_i = N_v²/S² < 1{R_i\,{=}\,N_v^2/S^2 <1 }. It is shown that, during an initial phase, the energies and the buoyancy fluxes are sensitive to the effects of pressure and viscosity. At large time, the ratios of energies, as well as the normalized fluxes, evolve to an asymptotically constant value, while the pressure–strain correlation scaled with the product of the turbulent kinetic energy by the shear rate approaches zero. Accordingly, an analytical parametric study based on the “pressure-less” approach (PLA) is also presented. The analytical study indicates that, when R _i  < 1, there is an exponential instability and equilibrium states of turbulence, in agreement with RDT. The energies and the buoyancy fluxes grow exponentially for large times with the same rate (γ in St units). The asymptotic value of the ratios of energies yielded by RDT is well described by its PLA counterpart derived analytically. At R _i  = 0, the asymptotic value of γ increases with increasing R approaching 2 for high rotation rates. At low rotation rates, an important contribution to the kinetic energy comes from the streamwise kinetic energy, whereas, at high rotation rates, the contribution of the vertical kinetic energy is dominant. When 0 < R _i  < 1 and R 1 0{R\ne 0}, the asymptotic value of γ decreases as R _i increases so as it becomes zero at R _i  = 1.     

Similarities Between Rotation and Stratification Effects on Homogeneous Shear Flow

Linear theory is applied to examine rotation and buoyancy effects on homogeneous turbulent shear flows with given vertical velocity shear, S=d/dx ₃. In the rotating shear case (where the rotation vector is perpendicular to the plane of the mean flow, Ω _i =Ωδ _{i 2}), general solutions for the Fourier components of the fluctuating velocity are proposed. These solutions are compared with those proposed in the literature for the Fourier components of the fluctuating velocity and density in the case of a homogeneous stratified shear flow with vertical density gradient, S _ρ=d/dx ₃. It is shown that from the normal mode stability stand point the Bradshaw parameter B=2Ω/S(1+2Ω/S) (in the rotating shear case) and the Richardson number R _i (in the statified shear case) play similar roles in identifying the stability for all the wave components except in the case where Ω·k=0, for which rotation has no effects on the flow. Analysis of the long-time behavior of the non-dimensional spectral density of energy, e ^g , is carried out. In the stable case, e ^g has decaying oscillations or undergoes a power law decay in time. Analytical solutions for the streamwise two-dimensional energy ℰ _ii ¹/2 (i.e. the limit at k ₁=0 of the one-dimensional energy spectra) are proposed. At large time, ℰ _ii ¹(t)/ℰ _ii ¹(0) oscillates around the value (3R _i +1)/(4R _i ) except at R _i =1 it stays constant in time. Similar behavior for ℰ _ii ¹(t)/ℰ _ii ¹(0) is also observed in the rotating shear case (ℰ _ii ¹(t)/ℰ _ii ¹(0) oscillates around the value (1+4B)/(4B)). Due to the behavior of the dimensionless spectral density of energy in both flow cases, the turbulent kinetic energy, /2, the production rate, ?, and the rate due to the buoyancy forces, ℬ, are split into two parts, , ?=?₁+?₂, ℬ=ℬ₁+ℬ₂ (in the stratified shear case, both ?₁ and ℬ₁ vanish when R _i >?, while in the rotating shear case one has ℬ=0). It is shown that when rotation is “cyclonic” (i.e. Ω/S>0), part reaches maximum magnitudes at St ≈2, independent of the B value, and the first time to a zero crossing of ?₂ occurs at this particular value. When rotation is “anticyclonic” (i.e. Ω/S<0) one finds St ≈1.6 instead of St ≈2. In the stratified shear case, both ?₂ and ℬ₂ cross zero at Nt=St ≈2, and part reaches maximum magnitudes at this particular value. These results and in particular those for the turbulent kinetic energy are compared with previous direct numerical simulation (DNS) results in homogeneous stratified shear flows. Received 30 July 2001 and accepted 19 February 2002     

Effects of Large Scales Motion in Unstable Stratified Shear Flows

Homogeneous turbulence under unstable uniform stratification (N ² < 0) and vertical shear is investigated by using the linear theory (or the so-called rapid distortion theory, RDT) for an initial isotropic turbulence over a range −∞ ≤ R _i =N ²/S ² ≤ 0. The initial potential energy is zero and P _r =1 (i.e. the molecular Prandtl number).One-dimensional (streamwise) k ₁−spectra, especially Θ₃₃(k ₁) (i.e., that of the vertical kinetic energy, are investigated. In agreement with previous experiments, it is found that the unstable stratification affects the turbulence quantities at all scales. A significant increase of the vertical kinetic energy is observed at low wavenumbers k ₁ (i.e. large scales) due to an increase of the stratification . The effect of the shear (S) is appreciable only at high wavenumbers k ₁ (i.e. small scales).Based on the importance of the spectral components with k ₁ = 0, the asymptotic forms of Θ _ij (k ₁ = 0) or equivalently the so-called “two-dimensional” energy components (2DEC) are analyzed in detail. The asymptotic form for the ratio of 2DEC is compared to the long-time limit of the ratio of real energies. In the unstable stratified shearless case (S=0,N ² ≠ 0) the variances and the covariances of the velocity and the density are derived analytically in terms of the Weber functions, while when S ≠ 0 and N ² ≠ 0 they are obtained numerically (−100 ≤ R _i <0 and . The results are discussed in connection to previous experimental results in unstable stratified open channel flows cooled from above by Komori et al. Phy Fluids 25, 1539–1546 (1982).It is shown that the Richardson number dependence of the long-time limit of the ratios of real energies is well described by this “simple” model (i.e. the dependence of the long-time limit of 2DEC on R _i ). For example, the ratio of the potential energy to the kinetic energy (q ²/2), approaches −R _i /(1−R _i ), the ratio of turbulent energy production by buoyancy forces to production by shearing forces (i.e. the flux Richardson number, R _if ), approaches R _i . Also, the Richardson number dependence of the principal angle (β) of the Reynolds stress tensor and the angle (β_ρ) of the scalar flux vector is fairly predicted by this model .On the other hand, it is found that the above ratios are insensitive to viscosity, while the ratios ɛ /q ² and , depend on the viscosity and they evolve asymptotically like t ⁻¹. The turbulent Froude number, F _rt =(L _Oz /L _E )^2/3, where L _Oz and L _E are the Ozmidov length scale and the Ellison length scale, respectively, evolves asymptotically like t ^−1/3.     

Turbulent flow around a rotating cylinder in a quiescent fluid

 Hot-wire measurements have been carried out in the turbulent flow around a rotating circular cylinder in still air for Reynolds numbers Re=∣U _w ∣D/ν=1.5×10⁴ to 10⁵. The experimental results confirm the analysis derived by asymptotic theory for high Reynolds numbers. Two different ways of deriving the friction law from the experiments (via shear stress and via velocity distribution) resulted practically in the same law. It is shown, that in spite of the curvature of the streamlines the universal logarithmic velocity distribution is still valid near the wall. Received: 8 August 1996/Accepted: 24 April 1998     

Effect of different sized transverse square grooves on a turbulent boundary layer

The effect of three different sized transverse square grooves (5, 10, and 20 mm) on a turbulent boundary layer was investigated at two values of momentum thickness Reynolds numbers (R _θ =1,000 and 3,000) using hot-wire anemometry. The ratios of the groove depth to the boundary layer thickness (d/δ ₀) are approximately 0.07, 0.13, and 0.27. Wall shear stress (τ _w), mean velocity (U), and turbulence intensity downstream of the grooves are compared to those on a corresponding smooth wall The effects of the grooves are more significant at the higher R _θ , with the most pronounced effects caused by the largest size groove. There is an increase in mean velocity (U), streamwise (u′/U ₀), and wall-normal (ν′/U ₀) turbulence intensities in the near-wall region immediately downstream of the grooves. The increase propagates outwards in the layer as the streamwise distance increases downstream of the grooves. The increase in ν′/U ₀ is much more significant than that of u′/U ₀, which is also evident in the spectra of u′ and ν′. There is an increase in τ _w over the smooth wall value immediately downstream of the grooves at R _θ =1,000, with the increase being more pronounced as the groove size increases. The growth of the internal layer downstream of the grooves is found to scale with the groove size, and is more rapid at R _θ =3,000. Published online: 23 November 2002     

Numerical analysis of simulation accuracy for hypersonic heat transfer in subsonic jets of dissociated nitrogen

One-dimensional problems of the flow in a boundary layer of finite thickness on the end face of a model and in a thin viscous shock layer on a sphere are solved numerically for three regimes of subsonic flow past a model with a flat blunt face exposed to subsonic jets of pure dissociated nitrogen in an induction plasmatron [1] (for stagnation pressures of (10⁴–3·10⁴) N/m² and an enthalpy of 2.1·10⁷ m²/sec²) and three regimes of hypersonic flow past spheres with parameters related by the local heat transfer simulation conditions [2, 3]. It is established that given equality of the stagnation pressures, enthalpies and velocity gradients on the outer edges of the boundary layers at the stagnation points on the sphere and the model, for a model of radius R_m=1.5·10^–2 m in a subsonic jet the accuracy of reproduction of the heat transfer to the highly catalytic surface of a sphere in a uniform hypersonic flow is about 3%. For surfaces with a low level of catalytic activity the accuracy of simulation of the nonequilibrium heat transfer is determined by the deviations of the temperatures at the outer edges of the boundary layers on the body and the model. For this case the simulation conditions have the form: dU_e/dx=idem, p₀=idem, T_e=idem. At stagnation pressuresP ₀2·10⁴ N/m² irrespective of the catalycity of the surface the heat flux at the stagnation point and the structure of the boundary layer near the axis of symmetry of models with a flat blunt face of radius R_m1.5·10^–2 m exposed to subsonic nitrogen jets in a plasmatron with a discharge channel radius R_c=3·10^–2 m correspond closely to the case of spheres in hypersonic flows with parameters determined by the simulation conditions [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 135–143, March–April, 1990.     

Experimental investigations on a 1–2 heat exchanger with wire-wound tubes

This paper deals with experimental investigations on a 1–2 shell and tube heat exchanger, to study the effect of spiral turbulators on its performance. The heat exchanger has its tubes wound with copper wire, so that the winding acts as an augmenting device. Experiments were conducted with various winding wire diameters and pitches and the heat transfer coefficients were evaluated for a wide range of temperature levels and flow rates of the shell side fluid. The experimental results are discussed in detail and correlations are proposed to predict the shell side Nusselt number of the exchanger with varying winding pitches and diameters. The existence of optimum winding is also discussed in this paper. The present results are based on over 250 experimental observations made in the laminar range of flow.

---

Experimentelle Untersuchungen an einem 1–2-Wärmetauscher mit drahtumwickelten Rohren

Zusammenfassung Diese Arbeit befaßt sich mit experimentellen Untersuchungen an einem 1–2-Zylindermantel/Rohrwärmetauscher und hat die Klärung des Einflusses von spiralförmigen Turbulenzpromotoren auf das Übertragungsverhalten zum Ziel. Die Rohre des Wärmetauschers sind mit Kupferdraht umwickelt, dessen Windungslagen den Austausch befördern. Die Experimente wurden mit verschiedenen Drahtdurchmessern und Steigungen durchgefürht und hieraus Wärmeübergangskoeffizienten in einem weiten Bereich der Temperaturniveaus und der Mengenströme des die Rohre umströmenden Fluids bestimmt. Die experimentellen Befunde werden eingehend diskutiert und Korrelationen zur Bestimmung der Nusselt-Zahl auf der Rohraußenseite in Abhängigkeit von Steigung und Durchmesser der Drahtwindungen angegeben. Die Ergebnisse basieren auf mehr als 250 Messungen im Bereich der Laminarströmung und belegen die Existenz einer optimalen Windungskonfiguration.

---

Nomenclature A _o heat transfer surface area outside the tube, m² - A _i heat transfer surface area inside the tube, m² - d _o outer diameter of the tube, m - D inner diameter of the shell, m - D _e equivalent diameter of shell for heat transfer, m - d _w diameter of the winding wire, m - F _T LMTD correction factor [8] - h _i inside heat transfer coefficient, W/m² K - h _o outside heat transfer coefficient, W/m² K - k _o thermal conductivity of water outside tube, W/mK - L length of the shell, m - l _t tube length, m - l _w length of the winding wire, m - LMTD logarithmic mean temperature difference, K - m mass flow rate of cold fluid, kg/h - N number of tube passes - Nu _i inside Nusselt number for the tube - Nu _o outside Nusselt number for the tube - Nu _o * outside Nusselt number, average over the temperature range - n _t number of tubes per pass - P pitch of the winding wire, m - Pr _t Prandtl number, tube side - Q heat transfer rate, W - Re _t tube side Reynolds number - Re _s shell side Reynolds number for heat transfer - T corrected mean temperature difference, K [8] - Th _i inlet temperature of hot water, °C - Th _o exit temperature of hot water, °C - Ti _i inlet temperature of cold water, °C - Tc _o exit temperature of cold water, °C - U _o overall heat transfer coefficient, W/m² K     

Development of a turbulent boundary layer after a step from smooth to rough surface

The flow developing downstream of a step change from smooth to rough surface condition is studied in the light of Townsend’s wall similarity hypothesis. Previous studies seem to support the hypothesis for channel and pipe flows, but there are considerable controversies about its application to boundary layers and in particular to surface roughness formed by spanwise bars. It has been suggested that this controversy arises from insufficient separation of scales between the boundary layer thickness and the roughness length scale. An experimental investigation has therefore been undertaken where the flow evolves from a fully developed smooth wall boundary layer at high Reynolds numbers over a step in surface roughness (Re _θ = 13,400 at the step). The flow is mapped through the development of the internal layer until the flow is fully developed over the rough wall. The internal layer is found to grow as δ ∼ X ^0.73, and after about 15 boundary layer thicknesses at the step, the internal layer has reached the outer edge of the incoming layer. At the last rough wall measurement station, the Reynolds number has grown to Re _θ ≈ 32,600 and the ratio of boundary layer to roughness length scales is δ/k ≈ 140. The outer layer differences between the smooth and the rough wall data were found to be sufficiently small to conclude that for this setup the Townsend’s wall similarity hypothesis appears to hold.     

Motion of a sphere in an electrically conducting rotating fluid

The combined effect of rotation and magnetic field is investigated for the axisymmetric flow due to the motion of a sphere in an inviscid, incompressible electrically conducting fluid having uniform rotation far upstream. The steady-state linearized equations contain a single parameter α=1/2βR _m, β being the magnetic pressure number and R _m the magnetic Reynolds number. The complete solution for the flow field and magnetic field is obtained and the distribution of vorticity and current density is found. The induced vorticity is O(α⁴) and the current density is O(R _m) on the sphere.     

High-resolution imaging of turbulence structures in jet flames and non-reacting jets with laser Rayleigh scattering

A comparative study of the length scales and morphology of dissipation fields in turbulent jet flames and non-reacting jets provides a quantitative analysis of the effects of heat release on the fine-scale structure of turbulent mixing. Planar laser Rayleigh scattering is used for highly resolved measurements of the thermal and scalar dissipation in the near fields of CH₄/H₂/N₂ jet flames (Re _d  = 15,200 and 22,800) and non-reacting propane jets (Re _d  = 7,200–21,700), respectively. Heat release increases the dissipation cutoff length scales in the reaction zone of the flames such that they are significantly larger than the cutoff scales of non-reacting jets with comparable jet exit Reynolds numbers. Fine-scale anisotropy is enhanced in the reaction zone. At x/d = 10, the peaks of the dissipation angle PDFs in the Re _d  = 15,200 and 22,800 jet flames exceed those of non-reacting jets with corresponding jet exit Reynolds numbers by factors of 2.3 and 1.8, respectively. Heat release significantly reduces the dissipation layer curvature in the reaction zone and in the low-temperature periphery of the jet flames. These results suggest that the reaction zone shields the outer regions of the jet flame from the highly turbulent flow closer to the jet axis.     

Hall effects on MHD flow in a rotating system with heat transfer characteristics

Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse uniform magnetic field. A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow rate distributions, for a wide range of the governing parameters. Asymptotic behavior of the solution is analyzed for large M ² (Hartmann number squared) and K ² (rotation parameter). The heat transfer aspect is considered also with Joule and viscous heating effects present. Boundary layers arise close to the channel walls for large K ², i.e. strong rotation of the channel. For slowly rotating systems (small K ²), Hall current parameter (m) reduces primary mass flow rate (Q _x /R ρ v). Heat transfer rate at the upper plate (d θ/d η) _η=1 decreases, while at the lower plate (d θ/d η) _η=−1 increases, with increase in either K ² or m. For constant values of the rotation parameter, K ², heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m. The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field components to the control parameters is also studied graphically. Applications of the study arise in rotating MHD induction machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing systems, hybrid magnetic propulsion systems for space travel etc.     

Advantages of using a power law in a low Rθ turbulent boundary layer

 At low values of the momentum thickness Reynolds number, R _θ, a relatively accurate estimate of the friction velocity U _r can be obtained by assuming a power law velocity distribution. Received: 13 October 1995/Accepted: 22 October 1996