Bernhard Weigand

Direct numerical simulation of evaporating droplets

A model for the three-dimensional direct numerical simulation of evaporating, deforming droplets in incompressible flow is presented. It is based on the volume-of-fluid method and is therefore capable of capturing very strong deformations. The evaporation rate is computed based on the vapour mass fraction and the PLIC reconstruction of the surface. Emphasis is put on the correct calculation of the velocities of the gaseous and liquid phase at the interface which is very important for cases with high mass transfer rates and thus high Stefan flow. It is accomplished by the use of an iterative algorithm that enforces a divergence constraint in cells containing the interface. Validation comprises a 1D test case for interfacial mass transfer, droplet collisions and oscillations as well as calculation of Sherwood numbers for two different cases of evaporating droplets where low and high mass transfer rates occur. Comparison with data from the literature shows good agreement of the obtained results. The simulation of a strongly deformed water droplet in a flow at a high Reynolds and Weber number is used to demonstrate the capabilities of the presented method. The emerging flow field in the wake of the droplet is very complex and three-dimensional.

The extended Graetz problem with piecewise constant wall temperature for pipe and channel flows

Heat transfer in the thermal entrance region of a pipe or a parallel plate channel has been analysed for laminar and turbulent internal flow taking into account axial heat conduction effects in the fluid. The present paper shows an analytical solution for the problem of a piecewise uniform wall heat flux. The obtained exact analytical solutions for the extended Graetz problem are as simple and efficient to compute as the related solutions of the parabolic problem. The obtained results show the effect of axial heat conduction in the fluid for a semi-infinite as well as for a finite length of the heated sections.

An extended Kays and Crawford turbulent Prandtl number model

For theoretical predictions of turbulent heat transfer in boundary layers and in duct flows, the knowledge of the turbulent Prandtl number is crucial. This is especially true for fluids with low molecular Prandtl numbers (liquid metals). The present formulation, which is an extended Kays and Crawford (Convective Heat and Mass Transfer, 3rd edn. McGraw-Hill, New York, 1993) turbulent Prandtl number model, can be used for accurately predicting the heat transfer for liquid metal flows. The Nusselt numbers calculated with the modified model for Prt are found to be in good agreement with experimental data for fully-developed pipe flows as well as for thermally developing pipe flows for various wall boundary conditions. The present model reduces to the one given in the above reference for liquids and gases with higher molecular Prandtl numbers.

Effect of viscosity on droplet-droplet collision outcome: Experimental study and numerical comparison

The influence of viscosity on droplet-droplet collision behavior at ambient conditions was studied experimentally and numerically. N-decane, monoethyleneglycol (MEG), diethyleneglycol (DEG), and triethyleneglycol were used as liquid phase providing viscosities in the range from 0.9to48mPas. Collision Weber numbers ranged approximately from 10 to 420. A direct numerical simulation code, based on the volume-of-fluid concept, was used for the simulations. Experimentally, observations of two droplet streams using a modified stroboscopic technique (aliasing method) were used to investigate the whole range of impact parameters during one experimental run. The experimental method has previously been verified for the water/air system [C. Gotaas et al., Phys. Fluids 19, 102105 (2007)]. In the present work, it was tested and validated for the n-decane/air system. Measured data agree well with those published in the literature. Well-defined regions of stretching separation and coalescence were identified, while refl...

Experimental and Numerical Investigation of Heat Transfer Characteristics of Inline and Staggered Arrays of Impinging Jets

A combined experimental and numerical investigation of the heat transfer characteristics within an array of impinging jets has been conducted. The experiments were carried out in a perspex model using a transient liquid crystal method. Local jet temperatures were measured at several positions on the impingement plate to account for an exact evaluation of the heat transfer coefficient. The effects of the variation in different impingement patterns, jet-to-plate spacing, crossflow schemes, and jet Reynolds number on the distribution of the local Nusselt number and the related pressure loss were investigated experimentally. In addition to the measurements, a numerical investigation was conducted. The motivation was to evaluate whether computational fluid dynamics (CFD) can be used as an engineering design tool in the optimization of multijet impingement configurations. This required, as a first step, a validation of the numerical results. For the present configuration, this was achieved assessing the degree of accuracy to which the measured heat transfer rates could be computed. The overall agreement was very good and even local heat transfer coefficients were predicted at high accuracy. The numerical investigation showed that state-of-the-art CFD codes can be used as suitable means in the thermal design process of such configurations.

An Extract Analytical Solution for the Extended Turbulent Graetz Problem with Dirichlet Wall Boundary Conditions for Pipe and Channel Flows

For turbulent flows in ducts axial heat conduction effects within the fluid can be important for low Prandtl number fluids (liquid metals). The paper presents an entirely analytical solution to the extended turbulent Graetz problem with Dirichlet wall boundary conditions. The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation for turbulent flow into a pair of first-order partial differential equations. The present approach, which is based on the solution method of Papoutsakis et al. for laminar pipe flow, is not plagued by any uncertainties arising from expansions in terms of eigenfunctions belonging to a nonselfadjoint operator. The obtained analytical results are compared with measurements of Gilliland et al. and Sleicher et al. showing good agreement between measured and predicted values.

Direct numerical simulation and analysis of instability enhancing parameters in liquid sheets at moderate Reynolds numbers

Direct numerical simulations based on the volume-of-fluid method have been performed in order to identify the influence of the inflow velocity conditions on the sensitivity of primary breakup phenomena. A liquid sheet ejected into a gaseous environment at moderate Reynolds numbers ranging from Re=3000 to 7000 was considered. The numerical setup allows to vary the influencing parameters individually such that numerical simulations can be performed as “numerical experiments” by varying each of the possible parameters separately. The focus of the present study was directed to the identification of those parameters that most strongly enhance primary breakup phenomena. These key parameters are the flow quantities such as the range of the inflow velocity and the inherent character of the mean velocity profile as well as the corresponding dimensionless groups and turbulence quantities of the nozzle flow. The present results show that in addition to these well known quantities the kinetic energy flux, which depen...

Film cooling on a convex surface with zero pressure gradient flow

Abstract The adiabatic film cooling effectiveness and heat transfer increase due to film injection was investigated on a convex surface at zero pressure gradient flow. Film cooling results were obtained using thermochromic liquid crystals to measure the local wall temperature distribution. Five different injection configurations, three with cylindrical and two with shaped holes were examined. Coolant injection with cylindrical holes indicates decreased film cooling effectiveness and increased heat transfer at moderate and high blowing rates. Significant higher film cooling effectiveness values and lower heat transfer increase due to film injection were achieved by shaped hole injection compared to cylindrical hole injection.

The transient liquid crystal technique: Influence of surface curvature and finite wall thickness

The transient liquid crystal technique is nowadays widely used for measuring the heat transfer characteristics in gas turbine applications. Usually, the assumption is made that the wall of the test model can be treated as a flat and semi-infinite solid. This assumption is correct as long as the penetration depth of the heat compared to the thickness of the wall and to the radius of curvature is small. However, those two assumptions are not always respected for measurements near the leading edge of a blade. This paper presents a rigorous treatment of the curvature and finite wall thickness effects. The unsteady heat transfer for a hollow cylinder has been investigated analytically and a data reduction method taking into account curvature and finite wall thickness effects has been developed. Experimental tests made on hollow cylinder models have been evaluated using the new reduction method as well as the traditional semi-infinite flat plate approach and a third method that approximately accounts for curvature effects. It has been found that curvature and finite thickness of the wall have in some cases a significant influence on the obtained heat transfer coefficient. The parameters influencing the accuracy of the semi-infinite flat plate model and the approximate curvature correction are determined and the domains of validity are represented.

Experimental Study on Combustion Mode Transition in a Scramjet with Parallel Injection

Mode transition from weak combustion to strong combustion or vice versa in a scramjet engine is a critical phenomenon in designing such engines, because the thrust of each mode varies considerably. The mode transition is supposed to interact strongly with a so-called pseudo-shock wave or shock train. In order to control vehicles with scramjet engines, it is, therefore, essential to understand mode transition. Several studies concerning this phenomenon have been conducted and most of them used the wall fuel injection method, where the disturbance of the boundary layer due to the wall injection could not be avoided. In order to prevent this disturbance, a parallel injection method was used in this study. The experiments were conducted using the supersonic combustion facilities of