Turbulent Prandtl Number Distribution Research Articles

Improvements in the prediction of heat transfer to supercritical pressure fluids by the use of algebraic heat flux models

The paper discusses the latest improvements obtained in performing heat transfer calculations by RANS turbulence models when dealing with fluids at supercritical pressure.An algebraic heat flux model (AHFM) is adopted as an advanced tool for calculating the turbulent Prandtl number distribution to be used in the energy equation. Though maintaining a simple gradient approach, the proposed model manages to obtain interesting results when dealing with temperatures spanning from low to supercritical values.This is due to the introduction of a correlation for defining one of the relevant AHFM parameters. As stated in previous works, in fact, single fixed constant values could not be sometimes sufficient for dealing with very different operating conditions such as the ones occurring with supercritical fluids. In order to make the relation suitable for different fluids, a dependence on a non-dimensional quantity which proved to be relevant by parallel work is assumed.Some sensitivity analyses are also performed, showing some interesting capabilities in reproducing a sort of threshold behaviour when working in transition regions.Buoyancy induced phenomena are much better captured than in past attempts, though incomplete accuracy is observed for some boundary conditions.

Direct numerical simulation of turbulent forced convection in a wavy channel at low and order one Prandtl number

Turbulent forced convection in a channel with one planar wall and one wall of sinusoidal shape is investigated by Direct Numerical Simulation. The flow is fully developed and the Reynolds number based on the mean bulk velocity and the average hydraulic diameter is Re ≈ 18,900; in this weakly turbulent flow regime three different Prandtl number values are investigated, Pr = 0.025, 0.20, 0.71. The fluid is in contact with the colder channel walls at an equal, uniform temperature. The main statistical quantities, like the root-mean-square of temperature fluctuations and the turbulent heat fluxes, the local heat transfer coefficient and turbulent Prandtl number values are reported. Effects of flow separation and reattachment on the local heat transfer rate and turbulent Prandtl number distribution are also presented and discussed.An a priori analysis of the behavior of the simple gradient diffusion model of turbulent heat fluxes is performed in the low Prandtl number, separated flow conditions of the present work. While the low Prandtl number effect can be accounted for by an appropriate selection of the turbulent Prandtl number value to be provided to the model, deviations form the expected behavior of turbulent heat fluxes are seen to occur in the flow separation region and downstream reattachment.

New development of the turbulent Prandtl number models for the computation of film cooling effectiveness

This paper presents the new development on the turbulent Prandtl number distribution models which are used to improve the computation accuracy of film cooling effectiveness distribution in the frame of the isotropic turbulence models. In the new developed turbulent Prandtl number distribution models, the turbulent Prandtl number varies with some characteristic quantity of the film cooling to make the models applicable for more film cooling cases effectively. A new VTG-Pr t model is developed for the computation of film cooling cases in which the wall is mainly influenced by the mixing layer region between the jet core and the mainstream. The Pr t value in this model varies with dimensionless temperature gradient which is suggested to be the characteristic quantity of the mixing layer region. The VTG-Pr t model has been used in the computations of long cylindrical hole film cooling, short cylindrical hole film cooling, compound angle cylindrical hole film cooling and expansion shaped hole film cooling in the present paper. And it is validated to be an effective and easy way to obtain accurate film cooling effectiveness distributions for this kind of film cooling. But for the kind of film cooling, in which the wall is mainly influenced by the jet core region and the influence of heat diffusion in the mixing layer region on the cooling effectiveness is very small, the VTG-Pr t model is disabled. Another turbulent Prandtl number distribution model, named VT-Pr t model, is developed for this kind of film cooling in the present paper. The Pr t value in this model varies with dimensionless temperature which is suggested to be the characteristic quantity of the jet core region. Good agreement between the computed and measured results is obtained through the use of VT-Pr t model in the computation of converging slot hole film cooling.

Turbulent Transport Coefficients with Allowance for Density Fluctuations

A model of turbulent transfer processes modified to take into account the effect of density fluctuations is proposed. The model is used for finding expressions for the turbulent transfer coefficients (viscosity, thermal conductivity, and diffusion of admixtures) in flows of the boundary-layer type in the presence of small density gradients. The turbulent Prandtl number distribution in the far wake behind a heated cylinder is compared with the results of measurements.

Isothermal and heated turbulent upflow in a vertical annular channel – Part I. Experimental measurements

The velocity and thermal fields were measured in isothermal and heated turbulent upflow of liquid Refrigerant-113 through a vertical annular channel of inner to outer radius ratio 0.415. A two-component laser Doppler velocimeter was used for the velocity measurements and, simultaneously, a cold-wire for the temperature measurements. The dimensions of the LDV measuring volume and the cold-wire, and their proximity to each other were important considerations. Also crucial to the measurements were the LDV coincidence time window and the temporal response of the cold-wire. Time-mean axial and radial velocities, axial and radial turbulent intensities, the single-point cross-correlation between axial and radial velocity fluctuations (∼axial Reynolds shear stress), and single-point cross-correlations between axial velocity and temperature fluctuations (∼axial turbulent heat flux) and radial velocity and temperature fluctuations (∼radial turbulent heat flux) were measured. Results are reported for Reynolds numbers at channel inlet of 22,800, 31,500, and 46,400 at annulus inner wall heat fluxes of 0, 9000 and 16,000 W m −2. The measured radial turbulent heat flux distribution is compared with that calculated from an approximate form of the thermal energy balance equation in which the measured mean velocity and temperature values are used. Also reported is the radial distribution of turbulent Prandtl number estimated from the measurements.

Turbulent Prandtl number within a near-wall flow

T HE turbulent Prandtl number variation within the nearwall region of fully developed boundary layers is obtained by using profile analysis. This is achieved by deriving expressions for the eddy diffusivities from Spalding's inner layer formula and its thermal analog. The analysis is performed over two orders of magnitude of the molecular Prandtl number, encompassing most of the common, nonmetallic fluids. The turbulent Prandtl number distribution is found to be complex and dependent on its molecular counterpart within the diffusive sublayer. This behavior has important consequences for the treatment of the near-wall region in numerical calculation methods for thin shear layers.

Influence of turbulent Prandtl number on heat transfer of a flat plate

In computations involving heat transfer in turbulent flow past bodies it is necessary to assume turbulent Prandtl number distribution across the boundary layer. A review and comparison of results obtained by different authors are given, e.g., in [1–5]. Unfortunately, the existing data are so contradictory that, at present, it does not appear to be possible to establish reliably a function that determines turbulent Prandtl number distribution across the boundary layer. The absence of sufficiently reliable and general results on the distribution of turbulent Prandtl number led to the result that in the majority of studies conducted in earlier years its value was assumed a constant and either close to or equal to one. The effect of turbulent Prandtl number on the intensity of heat transfer from a flat plate is numerically investigated in the present paper. The thermal, turbulent boundary layer equation is integrated for this purpose at different values of turbulent Prandtl number and results are compared with experimental data. Results from [6], where the thermal boundary layer was numerically integrated with Prt=1 and compared with experimental data, were used for comparison in the present paper. The same numerical integration procedure as in [6] was used here.

Temperature Distributions in Supersonic Turbulent Boundary Layers

Abstract : Experimental investigations of total temperature and Mach number distributions in turbulent boundary layers have been performed in the Mach number range from 1.75 to 4.5, using a newly developed combined temperature and pressure probe. The measurements carried out so far have been used to reanalyze the process of heat transport by calculating the turbulent Prandtl number distribution throughout the boundary layer. The results show an increase of the turbulent Prandtl number close to the surface, thus indicating that the turbulent transport of heat decreases more rapidly towards the wall than the turbulent transport of momentum. A simple relation, based on the Prndtl mixing length theory, is proposed for the variation of the turbulent Prandtl number within the viscous layer. This relation gives temperature distributions that are in good agreement with the experimental data in the region of constant shear stress. (Author)