Prandtl number | EPFL Graph Search

The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as: : \mathrm{Pr} = \frac{\nu}{\alpha} = \frac{\mbox{momentum diffusivity}}{\mbox{thermal diffusivity}} = \frac{\mu / \rho}{k / (c_p \rho)} = \frac{c_p \mu}{k} where:

\nu : momentum diffusivity (kinematic viscosity), \nu = \mu/\rho, (SI units: m2/s)
\alpha : thermal diffusivity, \alpha = k/(\rho c_p), (SI units: m2/s)
\mu : dynamic viscosity, (SI units: Pa s = N s/m2)
k : thermal conductivity, (SI units: W/(m·K))
c_p : specific heat, (SI units: J/(kg·K))
\rho : density, (SI units: kg/m3).

Note that whereas the Reynolds number and Grashof number are subscripted with a scale variable, the Prandtl number contains no such length scale and is depen

Experimental investigation into localized instabilities of mixed Rayleigh-Benard-Poiseuille convection

Emeric Grandjean, Peter Monkewitz

The stability of the Rayleigh-Benard-Poiseuille flow in a channel with large transverse aspect ratio (ratio of width to vertical channel height) is studied experimentally. The onset of thermal convection in the form of 'transverse rolls' (rolls with axes perpendicular to the Poiscuille flow direction) is determined in the Reynolds-Rayleigh number plane for two different working fluids: water and mineral oil with Prandtl numbers of approximately 6.5 and 450, respectively. By analysing experimental realizations of the system Impulse response it is demonstrated that the observed onset of transverse rolls corresponds to their transition from convective to absolute instability. Finally, the system response to localized patches of supercriticality (in practice local 'hot spots') is observed and compared with analytical and numerical results of Martinand, Carriere & Monkewitz (J. Fluid Mech., vol. 502, 2004, p. 175 and vol. 551, 2006, p. 275). The experimentally observed two-dimensional saturated global modes associated with these patches appear to be of the 'steep' variety, analogous to the one-dimensional steep nonlinear modes of Pier, Huerre & Chomaz (Physica D, vol. 148, 2001, p. 49).

Cambridge University Press2009

Two-Phase Heat Transfer Mechanisms within Plate Heat Exchangers

Raffaele Luca Amalfi

Plate heat exchangers are adopted in many domestic and industrial applications, such as ventilation, air conditioning, evaporation or condensation process, heat pumps and cooling of hydrodynamic circuits in engines. In the present thesis, an extensive experimental study to characterize thermal and hydraulic performance of a compact plate heat exchanger has been carried out and then follow up with proposition of new prediction methods for single-phase and evaporating flows in the plate¿s channels, in the form of general correlations that include large additional databases culled from the literature. Specifically, upward single-phase flow and flow boiling heat transfer of low pressure liquid refrigerants were investigated within a plate heat exchanger prototype fabricated with 1 mm pressing depth and chevron angle of 65°. High spatial and temporal resolution infrared measurements were implemented to obtain local (pixel-by-pixel) heat transfer coefficients and frictional pressure drops. Single-phase experiments were carried out for Reynolds numbers ranging from 34 to 1615 and Prandtl numbers from 4.9 until 6.5, and the associated effect of the main involved parameters on the thermal and hydraulic performance was analyzed in detail. Several of the most quoted prediction methods available in the literature were statistically evaluated against the present heat transfer and pressure drop database and a new models were proposed to predict mean and local thermal and hydraulic performance of the present compact plate heat exchanger. Two-phase experiments were carried out for mass fluxes ranging from 10 kgm-2s-1 to 85 kgm-2s-1, imposed heat fluxes from 225 Wm-2 to 4100 Wm-2, saturation temperatures from 19°C to 35°C and vapor qualities from 0.05 to 0.90. The heat transfer coefficient increased with mass flux, heat flux and saturation temperature (system pressure) whilst the frictional pressure drop rose with mass flux and vapor quality but decreased with saturation temperature. Based on local infrared measurements, a new correlation for predicting local frictional pressure gradient through the test section was proposed. Next, a wide experimental databank was culled from thirteen literature research studies, which investigated flow boiling heat transfer and two-phase frictional pressure drop within chevron plate heat exchangers. The database was first adopted to validate the predicted capabilities of 29 literature models, and then utilized to provide the new prediction methods to evaluate local heat transfer coefficients and frictional pressure gradient. These new models were developed from 1903 heat transfer and 1513 frictional pressure drop data points (3416 total) and were proved to work better over a very wide range of operating conditions, plate designs and fluids (including ammonia). The general flow boiling prediction methods have been programmed into a simulation code to analyze local thermal and hydraulic performance of the plate heat exchangers over a large range of test conditions. The simulation results were then validated against independent experimental database from literature, resulting in very good agreement between each other. The present simulation code represents a powerful tool to be used for practical applications by the thermal engineers in order to design and rate commercial plate heat exchangers.

EPFL2016

DNS of buoyancy-driven flows and Lagrangian particle tracking in a square cavity at high Rayleigh numbers

Abdelouahab Dehbi, Michel Deville, Emmanuel Leriche, Riccardo Puragliesi, Alfredo Soldati

In this work we investigate numerically particle deposition in the buoyancy driven flow of the differentially heated cavity (DHC). We consider two values of the Rayleigh number (Ra = 10(9), 10(10)) and three values of the particle diameter (d(p) = 15, 25, 35 [mu m]). We consider the cavity filled with air and particles with the same density of water rho(w) = 1000 [kg/m(3)] (aerosol). We use direct numerical simulations (DNS) for the continuous phase, and we solve transient Navier-Stokes and energy transport equations written in an Eulerian framework, under the Boussinesq approximation, for the viscous incompressible Newtonian fluid with constant Prandtl number (Pr = 0.71). First- and second-order statistics are presented for the continuous phase as well as important quantities like turbulent kinetic energy (TKE) and temperature variance with the associated production and dissipation fields. The TKE production shows different behaviour at the two Rayleigh numbers.

2011

Two-Phase Heat Transfer Mechanisms within Plate Heat Exchangers

Raffaele Luca Amalfi

EPFL2016