Universität Stuttgart
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Item Open Access DNS of multiple bubble growth and droplet formation in superheated liquids(2018) Loureiro, Daniel Dias; Reutzsch, Jonathan; Dietzel, Dirk; Kronenburg, Andreas; Weigand, Bernhard; Vogiatzaki, KonstantinaFlash boiling can occur in rocket thrusters used for orbital manoeuvring of spacecraft as the cryogenic propellants are injected into the vacuum of space. For reliable ignition, a precise control of the atomization process is required as atomization and mixing of fuel and oxidizer are crucial for the subsequent combustion process. This work focuses on the microscopic process leading to the primary break-up of a liquid oxygen jet, caused by homogeneous nucleation and growth of vapour bubbles in superheated liquid. Although large levels of superheat can be achieved, sub-critical injection conditions ensure distinct gas and liquid phases with a large density ratio. Direct numerical simulations (DNS) are performed using the multiphase solver FS3D. The code solves the incompressible Navier-Stokes equations using the Volume of Fluid (VOF) method and PLIC reconstruction for the phase interface treatment. The interfaces are tracked as multiple bubbles grow, deform and coalesce, leading to the formation of a spray. The evaporation rate at the interface and approximate vapour properties are based on pre-computed solutions resolving the thermal boundary layer surrounding isolated bubbles, while liquid inertia and surface tension effects are expected to play a major role in the final spray characteristics which can only be captured by DNS. Simulations with regular arrays of bubbles demonstrate how the initial bubble spacing and thermodynamic conditions lead to distinct spray characteristics and droplet size distributions.Item Open Access Particle image velocimetry measurements in accelerated, transonic wake flows(2022) Richter, Judith; Alexopoulos, Charalampos; Weigand, BernhardThis paper reports on particle image velocimetry (PIV) measurements in compressible accelerated wake flows generated by two different central injector types, which are mounted in a convergent-divergent nozzle. The injectors differ by the extent of their trailing edge located either in the subsonic (injector A) or supersonic flow region (injector B). In addition, the undisturbed nozzle flow without injector is studied as a reference case. The PIV results reveal typical wake flow structures expected in subsonic (injector A) and supersonic (injector B) wake flows. They further show that the Reynolds stresses Rexxand Reyysignificantly decay in all three cases due to the strong acceleration throughout the nozzle. Interestingly, in the case of injector A, the flow stays non-isotropic with Reyy>Rexxalso far downstream in the supersonic flow region. These measurements were motivated by the lack of velocity data needed to validate numerical simulations. That is why this paper additionally contains results from (unsteady) Reynolds-averaged Navier-Stokes ((U)RANS) simulations of the two wake flows investigated experimentally. The URANS simulation of the injector A case is able to accurately predict the entire flow field and periodic fluctuations at the wake centerline. However, in the case of injector B, the RANS simulation underestimates the far wake centerline velocity by about 4%.Item Open Access A theoretical and experimental investigation of smooth- and wavy ice layers in laminar and turbulent flow inside an asymmetrically cooled parallel-plate channel(1993) Weigand, Bernhard; Beer, HansThe present paper shows the adaption of the numerical model originally developed by Weigand and Beer [14] for calculating steady-state ice layers inside an asymmetrically cooled parallel-plate channel. The investigation shows the characteristics in ice formation behaviour due to asymmetrically cooled walls. Further, a simple analytical model is presented for calculating smooth ice layers in turbulent flow. The study is supported by own measurements of the freezing fronts inside an asymmetrically cooled channel. A comparison between theoretical calculations and measurements shows generally good agreement.Item Open Access An analytical study on the mechanism of grouping of droplets(2022) Vaikuntanathan, Visakh; Ibach, Matthias; Arad, Alumah; Chu, Xu; Katoshevski, David; Greenberg, Jerrold Barry; Weigand, BernhardThe condition for the formation of droplet groups in liquid sprays is poorly understood. This study looks at a simplified model system consisting of two iso-propanol droplets of equal diameter, Dd0, in tandem, separated initially by a center-to-center distance, a20, and moving in the direction of gravity with an initial velocity, Vd0>Vt, where Vt is the terminal velocity of an isolated droplet from Stokes flow analysis. A theoretical analysis based on Stokes flow around this double-droplet system is presented, including an inertial correction factor in terms of drag coefficient to account for large Reynolds numbers (≫1). From this analysis, it is observed that the drag force experienced by the leading droplet is higher than that experienced by the trailing droplet. The temporal evolutions of the velocity, Vd(t), of the droplets, as well as their separation distance, a2(t), are presented, and the time to at which the droplets come in contact with each other and their approach velocity at this time, ΔVd0, are calculated. The effects of the droplet diameter, Dd0, the initial droplet velocity, Vd0, and the initial separation, a20 on to and ΔVd0 are reported. The agreement between the theoretical predictions and experimental data in the literature is good.Item Open Access A numerical and experimental study of wavy ice-structure in an asymmetrically cooled parallel-plate channel(1992) Weigand, Bernhard; Beer, HansIce formation of flowing water in a pipe or a channel, whose wall is kept at a uniform temperature below the freezing temperature of the water, is a basic engineering problem. It Introduces many practical problems, such as pressure drop, diminution of flow rate and sometime, breakage of the pipe as a result of flow blockage by ice. The phenomenon of freezing of flowing water involves interactions between the turbulent flow, the shape of the ice layer and the heat transfer at the ice-water interface. Under certain conditions these interactions result in an instabilily of the ice layer. This instability is caused by the strong laminarization of the turbulent flow due to converging ice layers in the entrance region of the cooled channel and results in a wavy ice structure. Wavy ice layers with one wave, occuring in a parallel.plate channel subjected to symmetrically oooled walls were investigated experimentally by Seld et al. and by Weigand and Beer. More recently Weigand and Beer were able to predict numerically the shape of wavy ice layers with one wave occuring in a symmetrically cooled channel. Wavy ice layers in a parallel-plate channel with one wave in the case of asymmetrically cooled walls were investigated experimentally by Tago et al. and by Weigand and Beer. No numerical calculation of asymmetric wavy freezing fronts was done in the past. Therefore, the subject of this paper is the presentation of a numerical model for calculating steady state ice layers with one wave in the entrance region of an asymmetric cooled channel. The method is based on a work performed by Weigand and Beer. The given numerical study is supported by a detailed experimental investigation.Item Open Access Freezing in turbulent flow inside tubes and channels(1993) Weigand, Bernhard; Beer, HansA simple and quite flexible numerical model is presented to predict the steady state ice-layer formation inside a cooled two dimensional channel or a tube containing a turbulent flow. The effects of arbitrary entrance velocity distributions upon the shape of the ice-layers are examined. The presented numerical scheme is verified by comparing the predicted ice-layers with measurements and generally good agreement was found.Item Open Access Air entrapment and bubble formation during droplet impact onto a single cubic pillar(2021) Ren, Weibo; Foltyn, Patrick; Geppert, Anne; Weigand, BernhardWe study the vertical impact of a droplet onto a cubic pillar of comparable size placed on a flat surface, by means of numerical simulations and experiments. Strikingly, during the impact a large volume of air is trapped around the pillar side faces. Impingement upon different positions of the pillar top surface strongly influences the size and the position of the entrapped air. By comparing the droplet morphological changes during the impact from both computations and experiments, we show that the direct numerical simulations, based on the Volume of Fluid method, provide additional and new insight into the droplet dynamics. We elucidate, with the computational results, the three-dimensional air entrapment process as well as the evolution of the entrapped air into bubbles.Item Open Access Computations of a film cooled turbine rotor blade with non-uniform inlet temperature distribution using a three-dimensional viscous procedure(1994) Weigand, Bernhard; Harasgama, Sriwickrama P.A numerical investigation of film cooling on a turbine rotor blade has been carried out. The computations were performed with a 3D-Navier-Stokes code utilizing an unstructured solution adaptive grid methodology. The code uses a low Reynolds number k-epsilon model for prescribing the Reynolds stresses. The results show that there is a significant interaction between the coolant flow and the secondary flow near the hub and the tip of the turbine blade. It was observed that, by blowing on the pressure side of the blade some of the cooling air was transported through the tip gap of the blade to the suction side of the blade where the coolant flow interacts with the secondary flow field.Item Unknown A perturbation analysis of transient freezing of a laminar liquid flow in a cooled two-dimensional channel(1993) Weigand, Bernhard; Höhn, Werner; Beer, Hanshe paper shows the applicability of a regular perturbation method for predicting the transient development of the ice layer thickness inside a cooled planar channel subjected to laminar flow. Applying the perturbation expansion to the conservation equations, closed-form solutions for the velocity and temperature distributions in the fluid for an arbitrarily shaped channel could be derived under the assumption that the axial variation in solid layer thickness is small. The distributions obtained for the steady-state ice layer thickness and the velocity were checked by numerical calculations and generally good agreement was found.Item Open Access Ice-formation phenomena for water flow inside a cooled parallel plate channel : an experimental and theoretical investigation of wavy ice layers(1993) Weigand, Bernhard; Beer, HansA numerical model is developed for predicting steady-state ice formation inside a cooled two-dimensional channel. The study takes into account the strong interactions existing between the turbulent flow, the shape of the ice and the heat transfer at the ice-water interface which lead to the formation of wavy ice layers with one wave. The presented analysis is found to be able to predict realistic variations of the ice layer thickness for a wide range of Reynolds numbers and cooling parameters. The numerical results were verified by comparing the predicted ice layers with measurements and generally good agreement was found.