DNS of heat transfer in turbulent and transitional channel flow obstructed by rectangular prisms

Direct numerical simulation (DNS) of heat transfer in a channel flow obstructed by rectangular prisms has been performed for Re_τ = 80–20, where Re_τ is based on the friction velocity, the channel half width and the kinematic viscosity. The molecular Prandtl number is set to be 0.71. The flow remains unsteady down to Re_τ = 40 owing to the disturbance induced by the prism. For Re_τ = 30 and 20, the flow results in a steady laminar flow. In the vicinity of the prism, the three-dimensional complex vortices are generated and heat transfer is enhanced. The Reynolds number effect on the time-averaged vortex structure and the local Nusselt number are investigated. The mechanism of the heat transfer enhancement is discussed. In addition, the mean flow parameters such as the friction factor and the Nusselt number are examined in comparison with existing DNS and experimental data.     

Flow measurements inside a heated multiple rotating cavity with axial throughflow

This paper discusses experimental results from a multiple cavity test rig representative of a high pressure compressor internal air system. Measurements of the axial, tangential and radial velocity components are presented. These were made using a two component, laser doppler anemometry (LDA) system for a range of non-dimensional parameters representative of engine conditions (Re up to 4 × 10⁶ and Re_z up to 1.8 × 10⁵). Tests were carried out for two different sizes of annular gap between the (non-rotating) drive shaft and the disc bores.

The axial and radial velocities inside the cavities are virtually zero. The size of the annular gap between disc bore and shaft has a significant effect on the radial distribution of tangential velocity. For the narrow annular gap (d_h/b = 0.092), there is an increase of non-dimensional tangential velocity V/Ωr with radial location from V/Ωr < 1 at the lower radii to solid body rotation V/Ωr = 1 further into the cavity. For the wider annular gap (d_h/b = 0.164), there is a decrease from V/Ωr > 1 at the lower radii to solid body rotation further into the cavity. An analysis of the frequency spectrum obtained from the tangential velocity measurements is consistent with a flow structure in the r– plane consisting of pairs of contra rotating vortices.     

Impingement heat transfer at a circular cylinder due to a submerged slot jet of water

An experimental investigation was carried out on the heat transfer due to a submerged slot jet of water impinging on a circular cylinder in crossflow. The cylinder diameter and the slot width are of the same order of magnitude, specifically D_s = 2.0 and 3.0 mm and D_c = 2.5 and 3.0 mm. The experimental apparatus allowed variation of the slot width, the cylinder diameter, and the distance from nozxle exit to heater. Conditions of impingement from the bottom (ascending flow) were taken into consideration as well as impingement from above (descending flow). The Nusselt number was determined as a function of Reynolds and Prandtl numbers in the range 1.5 × 10³ < Re < 2.0 × 10⁴, 2.7 < Pr < 7.0, and 1.5 ≤ z/D_s ≤ 10. The experimental data were correlated with a simple equation that fits 90% of the data with a precision of 20%.     

Numerical and experimental study of turbulent impinging twin-jet flow

The two dimensional impinging circular twin-jet flow with no-cross flow is studied numerically and experimentally. The theoretical predications are carried out through numerical procedure based on finite volume method to solve the governing mass, momentum, turbulent kinetic energy and turbulent kinetic energy dissipation rate. The parameters studied were jet Reynolds number (9.5 × 10⁴  Re  22.4 × 10⁴), nozzle to plate spacing (3  h/d  12), nozzle to nozzle centerline spacing (l/d = 3, 5 and 8) and jet angle (0°  θ  20°). It is concluded that the stagnation primary point moves away in the radial main flow direction by increasing the jet angle. This shift becomes stronger by increasing the nozzle to nozzle centerline spacing (l/d). A secondary stagnation point is set up between two jets. The value of pressure at this point decreases by decreasing Reynolds number and/or increasing the jet angle.

The sub atmospheric region occurs on the impingement plate. It increases strongly by increasing Reynolds number and decreases as the jet angle and/or a nozzle to plate spacing increases. The spreading of jet decreases by increasing nozzle to plate spacing. The intensity of re-circulation zone between two jets decreases by increasing of h/d and jet angle. The increase of turbulence kinetic energy occurs within high gradient velocity.     

A general correlation for the local loss coefficient in Newtonian axisymmetric sudden expansions

Results from numerical simulations and guidance from an approximated corrected-theory, developed by Oliveira and Pinho (1997), (Oliveira, P.J. and Pinho, F.T. 1997. Pressure drop coefficient of laminar Newtonian flow in axisymmetric sudden expansions. Int. J. Heat and Fluid flow 18, 518–529) have been used to arrive at a correlation expressing the irreversible loss coefficient for laminar Newtonian flow in axisymmetric sudden expansions. The correlation is valid for the ranges 1.5 < D₂/D₁ < 4 and 0.5 < Re < 200 with errors of less than 5%, except for 25 < Re < 100 where the error could be as much as 7%. The recirculation bubble length is also presented for the same range of conditions and the pressure recovery coefficient was calculated for Reynolds numbers above 15.     

Flow and heat transfer in a rotating cavity with a radial inflow of fluid Part 1: The flow structure

Flow visualization has been conducted in a rotating cavity, comprising two steel discs and a peripheral polycarbonate shroud, for dimensionless flow rates of air up to |C_w|8000 and rotational Reynolds number up to Re_φ10⁶. For all the experiments, the ratio of the inner to outer radii of the discs was 0.1 and the ratio of the axial clearance between the discs to their outer radii was 0.133; five different shroud geometries were tested. The flow visualization has confirmed that the flow structure comprises a source region near the shroud, laminar or turbulent Ekman layers on the discs, a sink layer near the centre of the cavity, and an interior core of rotating fluid. Above a certain flow rate, this structure was found to be unstable; heating one disc tended to stabilize the flow. For isothermal flow, measurements of the size of the source region were in good agreement with values predicted from a simple theoretical model.     

Boundary layer receptivity measurements on compliant surfaces

This paper describes receptivity measurements in a pre-transitional boundary layer flowing over either a rigid or a compliant surface. Fluctuating velocities and frequency spectra were determined on one rigid and nine compliant surfaces. The results showed that the near wall receptivity grows linearly with Re_θ. An empirical correlation of the gain frequency spectrum for a rigid wall was also established. For the compliant surfaces, the near wall gain is increased markedly near the leading edge of the plate due to the amplification of high and mid-frequencies. These frequencies are dissipated though as the flow progresses over the compliant surface such that the receptivity is lower on all the compliant surfaces than on the rigid surface at the trailing edge. An empirical correlation for the ratio of the gains on compliant and rigid surfaces in terms of the compliant surface coefficient ζ²/Eρ_CSL² and Re_θ was established. This correlation indicates that compliant surfaces can suppress receptivity by up to 25% for a Re_θ = 400.     

The turbulent character and pressure loss produced by periodic symmetric ribs in a circular duct

The structural character and steady-state statistics of the turbulence inside a rib-wall circular duct is investigated by the large-eddy simulation (LES) methodology. The impetus of this study is to gain an understanding of the principle physics attributing to minimizing the pressure recovered (or maximizing the pressure loss) within the core flow. For a rib periodicity with height (h) to pitch (p) ratio p/h=5, the computational results show that the majority of turbulence produced due to the rib’s presence is concentrated near the rib crest leading edge. Pairs of counter-rotating streamwise vortices form soon after the leading edge that are quickly convected radially toward the core flow. The turbulent activity within the duct trough region is negligible compared to the turbulence levels of the core flow. At this rib periodicity, the separated shear layers from the trailing edge of each rib nearly reattach to the trough floor before reaching the next rib. The resultant irrecoverable pressure loss in the form a centerline frictional coefficient is verified by an ‘at-sea’ test on board a US Navy submarine. Based on the duct diameter, their Reynolds numbers are Re_D^LES=8×10³ and (Re_D^exp)_avg=4×10⁶, respectively.     

Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer

To investigate the relationship between characteristics of the coherent fine scale eddy and a laminar–turbulent transition, a direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer with Re_ω,0 = 700 was conducted. On the onset of the transition, strong coherent fine scale eddies appears in the mixing layer. The most expected value of maximum azimuthal velocity of the eddy is 2.0 times Kolmogorov velocity (u_k), and decreases to 1.2u_k, which is an asymptotic value in the fully-developed state, through the transition. The energy dissipation rate around the eddy is twice as high compared with that in the fully-developed state. However, the most expected diameter and eigenvalues ratio of strain rate acting on the coherent fine scale eddy are maintained to be 8 times Kolmogorov length (η) and :β:γ = −5:1:4 in the transition process. In addition to Kelvin–Helmholtz rollers, rib structures do not disappear in the transition process and are composed of lots of coherent fine scale eddies in the fully-developed state instead of a single eddy observed in early stage of the transition or in laminar flow.     

Fluid flow and heat transfer around circular cylinder – flat and curved plates combinations

Experimental studies were carried out to investigate the fluid flow and heat transfer around a heated circular cylinder which was placed at various distances of a wall boundary with different geometries (flat or curved plate) with subcritical Reynolds number ranging from 3.5×10³ to 10⁴. The effects of plate geometry (aspect ratio: W|H=1.0,1.5 and 2.0, and rim angle, φ=0°,60°,90°, and 120°) and gap ratio, (G|D=0.0,0.86,2.0,7.0,10.0) on the fluid flow and heat transfer characteristics (static pressure around cylinder surface, wake width, base pressure, pressure drag coefficients, velocity distribution, and both local and mean Nusselt numbers) were presented. Also flow visualization was carried out to illustrate the flow patterns around the cylinder at various gap ratios (G|D). It was found that the heat transfer and fluid flow characteristics are dependent on the plate geometry at all tested gap ratios, except for G|D=7.0 and 10.0, they are independent of the plate geometry.     

A complete and irreducible dynamic SGS heat-flux modelling based on the strain rate tensor for large-eddy simulation of thermal convection

In this paper, a general family of explicit algebraic tensor diffusivity functions based on the resolved temperature gradient vector and strain rate tensor is studied and applied to the construction of new constitutive relations for modelling the subgrid-scale (SGS) heat flux (HF). Based on Noll’s formulation, dynamic linear and nonlinear tensor diffusivity models are proposed for large-eddy simulation of thermal convection. The constitutive relations for these two proposed models are complete and irreducible. These two new models include several existing dynamic SGS HF models as special cases. It is shown that in contrast to the conventional modelling approach, the proposed models embody more degrees of freedom, permit non-alignment between the SGS HF and resolved temperature gradient vectors, reflect near-wall flow physics at the subgrid scale, and therefore, allow for a more realistic geometrical representation of the SGS heat flux for large-eddy simulation of thermal convection. Numerical simulations have been performed using a benchmark test case of a combined forced and natural convective flow in a vertical channel with a Reynolds number of and a Grashof number of Gr = 9.6 × 10⁵. The results obtained using the two proposed SGS HF models are compared with reported direct numerical simulation (DNS) data as well as predictions obtained using several conventional dynamic SGS HF models.     

Variational formulation of ideal fluid flows according to gauge principle

On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized by symmetries of translation and rotation. The rotational transformations are regarded as gauge transformations as well as the translational ones. In addition to the Lagrangians representing the translation symmetry, a structure of rotation symmetry is equipped with a Lagrangian Λ_A including the vorticity and a vector potential bilinearly. Euler's equation of motion is derived from variations according to the action principle. In addition, the equations of continuity and entropy are derived from the variations. Equations of conserved currents are deduced as the Noether theorem in the space of Lagrangian coordinate a. Without Λ_A, the action principle results in the Clebsch solution with vanishing helicity. The Lagrangian Λ_A yields non-vanishing vorticity and provides a source term of non-vanishing helicity. The vorticity equation is derived as an equation of the gauge field, and the Λ_A characterizes topology of the field. The present formulation is comprehensive and provides a consistent basis for a unique transformation between the Lagrangian a space and the Eulerian x space. In contrast, with translation symmetry alone, there is an arbitrariness in the transformation between these spaces.     

Open channel turbulent flow over hemispherical ribs

This paper reports an experimental investigation of open channel turbulent flow over hemispherical ribs. A row of ribs consists of hemispheres closely placed to one another in the spanwise direction and cover the entire span of the channel. The pitch-to-height ratio is varied to achieve the so-called d-type, intermediate and k-type roughness. The Reynolds numbers based on water depth, h, and momentum thickness, θ, of the approach flow are respectively, Re_h = 28,100 and Re_θ = 1800. A particle image velocimetry is used to obtain detailed velocity measurements in and above the cavity. Streamlines, mean velocity and time-averaged turbulent statistics are used to study the effects of pitch-to-height ratio on the flow characteristics and also to document similarities and differences between the present work and prior studies over two-dimensional transverse rods. It was observed that interaction between the outer flow and the shear layers generated by ribs is strongest for k-type and least for d-type ribs. The results also show that hemispherical ribs are less effective in augmenting flow resistance compared to two-dimensional transverse ribs. The levels of the Reynolds stresses and budget terms increase with increasing pitch-to-height ratio inside the roughness sublayer.     

Experimental characterization of non-premixed turbulent jet propane flames

This paper reports an experimental study conducted on turbulent jet propane flames aiming at further understanding of turbulent structure in non-premixed slow-chemistry combustion systems. Measurements of mean and fluctuating velocity and temperature fields, mean concentration of major chemical species, correlation between velocity and temperature fluctuations, and dissipation of temperature fluctuations are reported in a turbulent round jet non-premixed propane flame, Re=20 400 and 37 600, issuing vertically in still air. The experimental conditions were designed to provide a complete definition of the upstream boundary conditions in the measurement domain for the purpose of validating computational models. The measured data depicts useful flow field information for describing turbulent non-premixed slow-chemistry flames. Velocity–temperature correlation measurements show turbulent heat fluxes tended to be restricted to the mixing layer where large temperature gradients occurred. Observations of non-gradient diffusion of heat at x/D=10 were verified. Temperature fluctuation dissipation, χ, showed the highest values in the shear layer, where the variance of temperature fluctuations was maximum and combustion occurred. The isotropy between the temperature dissipation in the radial and tangential directions was confirmed. By contrast, the observed anisotropy between axial and radial directions of dissipation suggests the influence of large structures in the entrainment shear layer on the production of temperature fluctuations in the flame region. The value of the normalized scalar dissipation at the stoichiometric mixture fraction surface, χ_st, was calculated, and ranges between 2 and 4 s⁻¹. The measured data were used to estimate the budgets in the balance equations for turbulent kinetic energy, Reynolds shear stresses, turbulent heat flux and temperature variance, quantifying the mechanisms involved in the generation of turbulence as well as in the transport of the temperature.     

A survey of experimental heat transfer data for nucleate pool boiling of liquid metals and a new correlation

The experimental data for heat transfer during nucleate pool boiling of saturated liquid metals on plain surfaces are surveyed and a new correlation is presented. The correlation is h = Cq^0.7p_r^m, where C and m are, respectively, 13.7 and 0.22 p_r < 0.001 and 6.9 and 0.12 for p_r > 0.001 (h is in W/m² K and q in W/m²). This correlation has been verified with data for K, Na, Cs, Li, and Hg from 17 sources over the reduced pressure (p_r) range of 4.3 × 10⁻⁶ to 1.8 × 10⁻². The correlation of Subbotin et al. was found unsatisfactory, but a modified correlation was developed that also gives good agreement with most of the data.     

Conjugate natural convection from an array of discrete heat sources: part 2 — a numerical parametric study

Coupled conduction and natural convection transport within a discretely heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wall and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equations for the fluid and solid region are solved simultaneously using a control volume formulation, coupled with an additive correction multigrid procedure that increases the convergence rate of the solution. The fluid Prandtl number and heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modified Rayleigh number (10⁴ < Ra_Lz^* < 109), the cavity flow becomes more boundary layer-like along the vertical walls, and multiple fluid cells develop in the central region. Thermal spreading in the substrate increases with decreasing modified Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10⁻¹ <- R_s ≤ 10³). For large R_s, the discrete heat sources lose their thermal identity, and the streamlines and isotherms resemble those associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cavity and on maximum surface temperatures.     

On the flow in a uniformly porous pipe

This article considers fully laminar flow of an incompressible viscous fluid in a uniformly porous pipe with suction and injection. An exact solution of the Navier–Stokes equations is given. The velocity filed can be expressed in a series form in terms of the modified Bessel function of the first kind of order n. The volume flux across a plane normal to the flow, the vorticity and the stress on the boundary are presented. The flow properties depend on the cross-Reynolds number, Ua/ν, where U is the suction velocity, a is the radius of the pipe and ν is the kinematic viscosity of the fluid. It is found that for large values of the cross-Reynolds number, the flow near the region of the suction shows a boundary layer character. In this region the velocity and the vorticity vary sharply. Outside the boundary layer, the velocity and the vorticity do not show an appreciable change.     

On the influence of near-wall forces in particle-laden channel flows

Computation of a turbulent dilute gas–solid channel flow has been undertaken to study the influence of using wall-corrected drag coefficients and of the lift force on the dispersed phase characteristics. The incompressible Navier–Stokes equations governing the carrier flow were solved by using a direct numerical simulation approach and coupled with a Lagrangian particle tracking. Calculations were performed at Reynolds number based on the wall-shear velocity and channel half-width, Re_τ ≈ 184, and for three different sets of solid particles. For each particle set, two cases were examined, in the first one the particle motion was governed by both drag and lift wall-corrected forces, whereas in the other one, the standard drag force (not corrected) was solely acting. The lift force model used represents the most accurate available expression since it accounts for weak and strong shear as well as for wall effects. For this study, we considered elastic collisions for particles contacting the walls and that no external forces were acting. Present results indicate that the use of the lift force and of the drag corrections does not lead to significant changes in the statistical properties of the solid phase, at the exception of some statistics for the high inertia particles.     

Analysis for a screw dislocation accelerating through the shear-wave speed barrier

An analysis is performed for an accelerating screw dislocation through the shear-wave speed barrier. At this instant, the function that determines the interval of the path of the dislocation motion that contributes to the wave front has roots that change from a pair of complex conjugate to a double real, which subsequently splits into two real ones. The analysis is performed at this transition to supersonic that occurs at the double root maximum of the function that defines the interval of the dislocation path that contributes to the field points. It is found that the stress has a log|ξ-ξ^*|/|ξ-ξ^*|^1/2 singularity in the coefficient of the delta function of the forming Mach front, implying that for this phenomenon the Volterra dislocation model has too strong a discontinuity (step-function) in the displacement to be meaningful. A ramp-core displacement dislocation model analysis, which removes the singularity in the stress, is presented. These results can be useful in a multiscale dislocation dynamics modeling with inertia effects.     

An application of Nagumo''s lemma to some singularly perturbed systems

The existence and asymptotic behavior as ε → 0⁺ of periodic, almost periodic, and bounded solutions of the differential system x = f(t, x, y, ε), Ωy′ = g(t, x, y, ε), are considered where x, f; are n-vectors, y, g are m-vectors and Ω = diag{ε^h₁}…, ε^h_m for integral h_i, h₁ h₂ …, h_m. The principal tools are a lemma of Nagumo which allows the construction of appropriate upper and lower solutions and the asymptotic theory of singularly perturbed linear differential systems.