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Open Access
Potentials and limitations of the a priori data-augmentation of turbulence closure models
(2026) Mandler, Hannes; Weigand, Bernhard (Prof. Dr.-Ing. habil.)
Turbulent flows occur in numerous technical applications. In some applications, turbulence is deliberately exploited to increase their efficiency. In others, the efficiency can be increased by suppressing turbulence to the greatest extent possible. The ability to accurately predict turbulent flows is, therefore, of immense importance. Nowadays, mainly numerical simulation methods are used for this purpose. As solving the Navier-Stokes equations would be far too costly for most applications of practical interest, the Reynolds-averaged Navier-Stokes equations are typically considered instead. However, their solution requires closure models to describe the influence of the turbulence on the mean flow. As a result of structural and parametric deficiencies of existing models, especially the popular eddy viscosity models, the accuracy of the predicted flow fields often no longer meets the current quality requirements. One way to address these deficiencies is to replace the empirical but often constant model coefficients by functions of the local mean flow field. Unlike the classical modeling approach, which seeks to derive such functional dependencies from theory and physical reasoning, leveraging machine learning instead allows for extracting the desired coefficient functions from publicly available DNS data. The models could, therefore, be calibrated for applications that are still simple but exceed the complexity of the traditional calibration cases, e.g., applications governed flow separation and reattachment. This thesis investigates the merits of this approach with respect to the accuracy of the flow field predictions and the possibility of developing more universal closure models. To this end, an a priori augmentation method for existing closure models was developed. A two-stage procedure was proposed to find appropriate functions for the closure coefficients. First, using the DNS data, the extended closure model is inverted to obtain the spatial distribution of the optimal coefficients for a particular training case. These allow the optimal structure of the constitutive equation to be determined in order to prevent any structural deficiencies. By subsequently solving a regression problem, functions represented by neural networks can be inferred that predict those optimal values of the coefficients as a function of the local mean flow state. Based on three examples, namely the flows through a plane channel, a plane channel with periodic hills, and a square duct, the data-augmented development of such model corrections was demonstrated. The errors in the prediction of the velocity field for the respective training cases could be reduced by up to 65%. The accuracy achieved with this method is typically unmatched even for significantly more complex existing closure models. In addition, it was proven that the extended models provide at least equivalent, but often more accurate predictions than the baseline model for a wide range of Reynolds numbers. The same applies to applications that differ geometrically, but not phenomenologically from the training case. However, if the test case was characterized by different flow phenomena than the training case, a sometimes considerable decrease in the predictive accuracy compared to the baseline model was observed. The obvious strategy of dealing with this loss of universality, i.e., deriving the coefficient functions from a more diverse training data set, proved to be ineffective. This is considered to be due to the complexity of the structure of the coefficient functions, which is limited for stability reasons and, hence, usually not sufficient to actually reflect the diversity of the training data. The method developed in this work for the data-driven augmentation of existing closure models is representative of a number of similar approaches that seek to improve flow field predictions via a more accurate description of the Reynolds stress tensor. In summary, such methods are suitable for developing highly specialized models that achieve the desired accuracy gains for a class of not too complex and phenomenologically similar flows. These two limitations could probably be remedied by CFD-integrated training and well-designed combinations of many such expert models.
Open Access
Numerical simulation of wake interactions on a tandem wing configuration in high-speed stall conditions
(2023) Kleinert, Johannes; Stober, Jonathan; Lutz, Thorsten
In this work, the interaction of the separated wake of the front wing with the rear wing of a tandem configuration is investigated for high-speed stall conditions by means of hybrid RANS/LES simulations, using the zonal AZDES method. After a characterization of the transonic buffet on the front wing, the development of the separated turbulent wake behind the wing is investigated. The interaction of the separated wake with the rear wing is then analyzed in detail. The results reveal that there is a strong variation in the wake characteristics over the buffet cycle, caused by the varying amount of separation on the front wing. During the upstream movement of the shock, the flow is largely separated, resulting in a thick wake with strong, high-frequent fluctuations that can be attributed to large turbulent vortices. On the contrary, when the shock travels downstream, there is only a small amount of separation present, resulting in a thin wake with comparatively low fluctuations that are caused by corresponding smaller turbulent vortices. The impact of the wake of the front wing causes a strong variation in the rear wing loading. An oscillation with a comparatively low frequency can be distinguished from high-frequent fluctuations. The low-frequent oscillation is caused by the variation in the downwash behind the front wing as its lift changes during the buffet cycle. The high-frequent fluctuations are due to the impingement of the turbulent structures onto the rear wing. Because both size and frequency of those vortices vary significantly within the buffet cycle, the amplitude and frequency of the lift and surface pressure fluctuations also change accordingly.
Open Access
Coupled flow field and heat transfer in an advanced internal cooling scheme
(2010) Coletti, Filippo; Weigand, Bernhard (Prof. Dr.-Ing. habil.)
State-of-the-art gas turbines are designed to operate at turbine inlet temperatures in excess of 1850 K. Such temperature levels are sustainable only by means of an aggressive and efficient cooling of the components exposed to the hot gas path. Not only the maximum metal temperature needs to be kept below the safety limits, but the thermal field must be reasonably uniform, in order to limit the thermal stresses. This requires from the designer the most accurate knowledge of the local heat transfer rate. The need for such detailed information is in conflict with some common practices in the cooling system design: numerical simulations are often compared against area-averaged experimental data; the link between coolant flow field and heat transfer rates is scarcely analyzed; moreover, the coupling between convection and conduction is hardly taken into account. The present thesis aims at the aero-thermal characterization of a trailing edge cooling channel geometry. Cooling the trailing edge, one of the life-limiting parts of the airfoil, represents an especially challenging task since the aerodynamic requirement of high slenderness is conflicting with the need of integrating internal passages. The focus of the study is on three main aspects of the internal cooling technology: (i) the details of the coolant flow field; (ii) the contribution of the obstacles’ surface to the heat transfer; and (iii) the effect of the conduction through the cooling channel walls. The investigated cooling channel geometry is characterized by a trapezoidal cross-section. It has one rib-roughened wall and slots along two opposite walls. The coolant passes through a smooth inlet channel upstream of the investigated cavity; it crosses the divider wall through a first row of inclined slots, producing crossing-jets; the latter impinge on the rib-roughened wall, and the jet-rib interaction results in a complex flow pattern, rebounding the coolant towards the opposite smooth wall; finally the air exits through a second row of slots along the trailing edge. Such a scheme represents a combination of internal forced convection cooling and impingement cooling. An engine-representative Reynolds number equal to 67500 is defined at the entrance of the inlet channel. A comprehensive experimental investigation is carried out on a magnified model of the channel, at a scale of 25 : 1 with respect to engine size (applied to both the cavity volume and the walls thickness). The main flow structures are identified and characterized by means of particle image velocimetry, allowing to deduce a model of the highly three-dimensional mean flow. Each jet is shown to impinge on the three ribs in front of the slot, and the jet-rib interaction produces two upward deflections in each inter-rib domain. Distributions of heat transfer coefficient are obtained by means of liquid crystals thermography on the rib-roughened surface as well as on the opposite smooth wall in a purely convective regime, with a uniform heat flux imposed at the solid-fluid interface. The thermal patterns on the channel walls show the footprints of the flow features detected by the velocity measurements. Globally, the top side of the rib shows the highest Nusselt number among the investigated surfaces. The presence of the ribs enhances the global heat transfer level (averaged on all surfaces) by 14%. The aero-thermal results suggest a definite margin for improvement of the heat transfer performance by varying one or more geometrical parameters. In this perspective, the ribs have been tapered and shifted with respect to the slots position. Both expedients have proven to be useful in reducing the extent and intensity of the aforementioned hot spots in the vicinity of the ribs: an enhancement of about 20% in area-averaged heat transfer rate is achieved with respect to the standard configuration. The thermal behavior of the ribbed wall has also been investigated in conjugate heat transfer regime, in order to study the effect of the wall conduction on the thermal levels. By matching the solid-to-fluid thermal conductivity ratio found in an engine, the correct thermal boundary conditions for the convective problem are attained, which guarantees full similarity between laboratory model and engine reality. Infra-red thermography coupled to a finite element analysis is used to retrieve the whole thermal pattern through the considered rib-roughened wall. Nusselt number levels in conjugate regime differ by up to 30% locally and 25% globally with respect to the purely convective results. Neglecting wall conduction when evaluating the heat transfer coefficient leads to underestimating the maximum surface temperature by 26 to 33 K at engine conditions. Decreasing the wall thermal conductivity increases the overall heat transfer coefficient on the ribbed surface. However lower conductivities amplify local temperature gradients and hot spots.
Open Access
Stability of swirl tube flow
(2019) Novotny, Pavel; Weigand, Bernhard (Prof. Dr.-Ing. habil.)
This work focuses on detailed investigation of the flow phenomena and flow stability in swirl tubes. In general, a swirl tube is a tube with one or more tangential inlets generating complex swirling flow. This leads to large tangential velocities near the wall and to enhanced turbulent mixing in the tube, which results in a positive influence on the convective heat transfer in the tube. In the present work, a formulation of a condition to investigate stability of a flow is provided. This formulation reflects the definition of the second law of thermodynamics, i.e. the balance of entropy, and also the balance of the total enthalpy. So, the derived condition may serve as a criterion to investigate processes in general flows, for which an incompressible fluid via the Cauchy stress tensor is approximated. The experimental and numerical analysis of flow fields conducted for different Reynolds numbers show an axial backflow region in the tube centre determining possible vortex breakdown. For the lowest Reynolds number, an axial backflow region, in contrast to the higher Reynolds numbers, is observable up to the middle of the tube length. Thus, there is a region where the flow is characterised by no vortex breakdown. Moreover, similar behaviour is observed for the intermediate Reynolds number near the tube outlet. Nevertheless, for strong swirling flows, a possible vortex breakdown may be expected for a Rossby number lower than 0.65. Furthermore, the ratio between the local tangential and axial Reynolds numbers reveals that a vortex breakdown may occur in regions where this ratio is greater than 1. In addition, a connection between the derived stability criterion and the vortex breakdown confirms that the redistribution of flow fields is, due to the highest swirl strength, dominant at the beginning of the tube. Moreover, it is shown that vortex breakdown is accompanied by processes causing flow stabilisation.
Open Access
Experimental and numerical investigations of convective cooling configurations for gas turbine combustors
(2008) Maurer, Michael; von Wolfersdorf, Jens (Prof. Dr.)
Within the present study, experiments and numerical computations are conducted to analyze the cooling performance of different convective cooling techniques for backside cooled combustor walls. For all investigated configurations, the pressure loss and the heat transfer enhancement is observed. As possible candidates for a convective cooling scheme, rib turbulators, channels with dimples and channels with hemispheres are considered. The data bases for such convective cooling techniques, which have already been reported in literature, arise from the experience in internal blade cooling. Compared to the typical conditions found for backside cooled combustor walls, the Reynolds number and the mass flow rates are lower in the case of internal blade cooling. Additionally, the ribs or other convective cooling techniques are applied to two opposite channel walls within the blade. For backside cooled combustor walls, the heat transfer on only one channel wall needs to be enhanced. For the experimental setup, several measurement techniques are applied. The heat transfer coefficient between two successive ribs is obtained with a steady and a transient measurement technique. A comparison of the two measurement techniques is also provided. Averaged heat transfer coefficients on the rib itself are measured by using the lumped heat capacitance method. For the numerical setup, the commercial solver FLUENTTM is applied together with two different turbulence models. In the case of rib turbulators, a standard k-e turbulence model is used. It could be demonstrated that for dimpled surfaces or surfaces with hemispheres, a Reynolds Stress Model performs better. In general, the experimental results are underpredicted, whereas the trends are predicted correctly. It is concluded, that the present numerical approach is applicable to preliminary design studies. One result of this study is to extend the Reynolds number range of typical rib turbulators to Reynolds number levels found in backside cooled combustor walls. In contrast to internal blade cooling, the design requirements of a backside cooled combustor wall are a moderate pressure loss at higher Reynolds numbers and at the same time a good heat transfer enhancement. It could be demonstrated, that the geometry of rib turbulators need to be adjusted to satisfy the mentioned design requirements. The investigations on V shaped, W shaped and WW shaped ribs revealed the following fact. The existence of a second ribbed wall has an influence on the heat transfer of the opposite wall. It is therefore suggested not to directly use heat transfer correlations, which are derived from experimental data of two sided ribbed channels, for the design of one sided ribbed channels. Additionally, it could be demonstrated, that for higher Reynolds numbers the rib height has to be reduced to obtain lower levels of pressure losses. As the rib geometry is changed from V shaped to W shaped rib, the pressure losses are increased for an equal rib spacing and rib height. WW shaped ribs resulted in even higher pressure losses. For V shaped and W shaped ribs, a reduction of the rib spacing leads to a lower pressure loss. For WW shaped ribs, an opposite trend is observed. In the case of W shaped ribs, the heat transfer enhancement on the rib itself is obtained. It could be demonstrated that a reduction of the rib spacing has no impact on the heat transfer enhancement on the rib. A combination of the heat transfer data between two successive ribs and the data on the rib reveals, that heat transfer levels of around three times higher than the heat transfer of a smooth channel wall are realized for the investigated Reynolds number range. The possibility to replace the commonly used rib turbulators with dimples or hemispheres is also addressed in this study. For channels with hemispheres or dimples on one channel wall, a lower pressure loss and at the same time only moderate heat transfer enhancement levels are observed. For the design of a convective cooling technique for convectively cooled combustor walls, W shaped ribs should be preferred. This configuration shows the best thermal performance for the typical Reynolds numbers found in backside cooled combustor walls. In cases, where the convective cooling has to be achieved with very low pressure losses, dimpled channels represent an interesting alternative to ribbed configurations.
Open Access
Laser-induced thermal acoustics : simultaneous velocimetry and thermometry for the study of compressible flows
(2016) Förster, Felix Johannes; Weigand, Bernhard (Prof. Dr.-Ing. habil.)
Air-breathing propulsion concepts, such as scramjets, provide a promising alternative to conventional systems for a faster and economically as well as ecologically more efficient transportation of passengers and cargo to any destination on the globe. Furthermore, scramjets are an important supplement to existing rocket-based systems to increase the payload and reduce operational costs of space transportation systems. The development of a scramjet engine is, however, challenging and involves the knowledge of many disciplines. One of the most critical problems is a stable and reliable combustion. The flows relevant to this thesis are therefore characterized by high speeds, high temperatures and chemical reactions. Obtaining quantitative data of such a flow field, sufficiently resolved in time and space, is a difficult task for any measurement technique. However, the continuous study of the occurring flow phenomena as well as the requirement to validate advanced numerical simulations demand the development of new diagnostic methods to provide more sophisticated experimental data sets. The focus of this thesis is the development, evaluation and application of Laser-Induced Thermal Acoustics (LITA) as a promising diagnostic tool for the study of compressible flows. LITA allows non-intrusive and remote measurements of speed of sound, flow velocity, Mach number and temperature – resolved both spatially and temporally. A thorough validation of the setup was conducted for reference cases at flow conditions comparable to the intended application verifying that very accurate and detailed data sets can be obtained with LITA. Three different applications are investigated in this thesis. In the first case, time-resolved speed of sound, flow velocity and Mach number measurements were conducted in a hydrogen/air free jet flame. Flow profiles were obtained at different axial positions showing the evolution of the combustion zone. The second application is dedicated to the flow field inside scramjet combustor models. Detailed experimental data sets were provided for the validation of complementary CFD simulations. In addition, a precise reconstruction of the flow field and the shock system resulting from a jet injected into the supersonic cross flow was possible. These results motivated to use LITA in a shock tube facility. Measurements were successfully conducted behind the incident and reflected shock wave proving the technique’s potential for shock-heated flows.
Open Access
Concept of composite folded core skin heat exchanger with experimental investigation of surface temperatures using temperature-sensitive paints
(2026) Larschow, Marvin Tigre; Thissen, Simon; Gugliuzza, Jakob; Zistler, Stefan; Carosella, Stefan; Middendorf, Peter; Poser, Rico
With the increasing integration of low-temperature waste heat systems in aviation, large areas are needed for heat dissipation without causing significant pressure losses. Large-area skin heat exchangers (SHXs) are coming into focus as a possible solution. SHXs based on composite materials offer a promising approach due to their weight-saving potential. This article presents a structure-integrated SHX with a folded core using modern materials and design strategies. An analytical 1D heat transfer model, validated by measurements with temperature-sensitive paints (TSPs), was derived to efficiently identify the optimal parameter set in the design process of an SHX. The model focuses on transverse heat conduction effects in the facesheet for lateral heat distribution and uses these specifically for the overall mass-optimized configuration of the SHX. It is shown that with an optimally selected distance between the cooling channels in the case considered here, up to 12% more energy can be dissipated in relation to the total mass of the SHX. This article concludes with a sensitivity analysis of the analytical model. The influence of heat transfer, thermal conductivity in two spatial directions, and facesheet thickness on the optimal channel spacing is examined.
Open Access
The effect of patterned micro-structure on the apparent contact angle and three-dimensional contact line
(2021) Foltyn, Patrick; Restle, Ferdinand; Wissmann, Markus; Hengsbach, Stefan; Weigand, Bernhard
The measurement of the apparent contact angle on structured surfaces is much more difficult to obtain than on smooth surfaces because the pinning of liquid to the roughness has a tremendous influence on the three phase contact line. The results presented here clearly show an apparent contact angle variation along the three phase contact line. Accordingly, not only one value for the apparent contact angle can be provided, but a contact angle distribution or an interval has to be given to characterize the wetting behavior. For measuring the apparent contact angle distribution on regularly structured surfaces, namely micrometric pillars and grooves, an experimental approach is presented and the results are provided. A short introduction into the manufacturing process of such structured surfaces, which is a combination of Direct LASER Writing (DLW) lithography, electroforming and hot embossing shows the high quality standard of the used surfaces.
Open Access
Turbulence modeling of complex flows in CFD
(2008) Uddin, Naseem; Weigand, Bernhard (Prof. Dr.-Ing. habil.)
In the last two decades of the 20th century, the world had witnessed the enormous increase in the computational resources. This has brought in the tremendous increase in human knowledge and understanding of complex phenomenon, like turbulence and its modeling among others. The technical development has brought new challenges in engineering design. Whether we limit ourselves to the earthly matters or indulge in space exploration, the simulation of turbulence has become a routine task. Turbulence is a phenomenon in nature comprising of complex eddy structures which can greatly improve heat and mass transfer. The simplistic approach for the computation of turbulent flows is to compute them by Reynolds Averaged Navier-Stokes (RANS) equations based models. But due to the averaging procedure, the inherent unsteadiness of the flow is compromised. On the other hand, Direct Numerical Simulation (DNS) is the best approach for turbulent flow computations, in which no modeling assumptions are invoked and turbulent eddies as small as of the order of Kolmogorov scale are computed. The middle approach between these extremes is the Large Eddy Simulation (LES), in which part of the turbulence is modeled and rest is computed. However, the computational costs and memory requirement are still too large to take it as a general purpose engineering design tool. In this thesis, the effect of changes in inflow conditions on the heat transfer by an impinging jet is investigated using LES. The Dynamic Smagorinsky model proposed by Germano et al. has been used as a subgrid model. Results of several Large Eddy Simulations are reported in the thesis, which are conducted with use of total 244 processors on high performance computing clusters. The inflow conditions explored are: - The fully developed turbulent jet - Swirling jet - Velocity field active excitation - Velocity field passive excitation - Temperature field excitation An ERCOFTAC recommended benchmark test case of an orthogonally impinging round jet at Reynolds number of 23000 is simulated first. The agreement between the experiments and the LES gives encouragement for further investigations. Therefore in a next step, the effect of inlet velocity and temperature fields excitations of an orthogonally impinging round jet, on the heat transfer are explored. In case of the active control of the impinging jet’s inlet velocity field, it is found that the selection of excitational frequencies is important for heat transfer enhancement. The excitation at the subharmonic frequencies of the preferred mode is found to be a promising approach for heat transfer enhancement. A passively excited inlet velocity field is also investigated. It is found that this approach gives a better heat transfer than an active excitation case. The novel idea of heat transfer enhancement through jet’s inlet temperature field excitation is presented. The LES shows that the excitation at the preferred mode can give surface averaged Nusselt number higher than the non-excited jet impingement case. However the frequencies higher than the preferred mode should be taken with care, as they might cause thermal fatigue. The effect of the addition of the swirl to the impinging jet on the heat transfer is investigated. Also, it is found that the swirl does not give appreciable enhancement in heat transfer for H=D=2 case. The knowledge of flow and passive scalar flux dynamics gained through the simulation has helped in understanding the functional relationship between different turbulence quantities and heat transfer. It is found that the assumption of a constant turbulent Prandtl number (often used in RANS based models) is not a realistic approach. Alternative is to use scalarflux models, which allow the prediction of scalar-fluxes in non-isotropic turbulent state. The knowledge gained through the LES is then used to investigate coefficients in some explicit scalar-flux models (RANS based models). The investigation gives insight in the impingement phenomenon, which could help in the development of advanced turbulence models for heat transfer prediction.
Open Access
Experimental and numerical investigations of transient conjugate heat transfer processes
(2025) Hartmann, Christopher; Weigand, Bernhard (Prof. Dr.-Ing. habil.)
Effective cooling of components exposed to high thermal loads is a key challenge in aircraft engine development. Analyzing thermal loads during flight missions is critical, as they fluctuate with varying operating conditions. Accurate assessment requires considering coupled heat transfer processes and transient effects. The calculation of slow, transient phenomena was optimized by enhancing a coupling environment between a finite element and a finite volume solver. A wide range of boundary conditions and geometries were experimentally investigated. An existing ITLR test rig was adapted, and four geometries were examined. The rig enables independent, reproducible control of inlet velocity and temperature, allowing the study of various test cycles. Wall temperatures were measured with high resolution using infrared thermography, and wall heat fluxes were calculated. Numerical simulations complemented the experiments. The data support validation of the coupling environment and showed good agreement with simulations. A variable, adaptive, experiment-specific coupling step size reduced computation time while preserving accuracy. A method was developed to enhance prediction accuracy and account for local dissipation, targeting heat transfer coefficients and friction factors in complex flows. Experimental data were analyzed using heat transfer correlations. A close relationship between two local parameters was observed, which enabled the development of a simplified correlation. The resulting model included coefficients that could be linked to established laws for turbulent boundary layer flows. One parameter correlates with local pressure gradients, near wall streamlines and friction factor distributions, while the other yields a Reynolds analogy factor that was used to estimate wall shear stresses. The model agreed well with simulations and proved universally applicable.

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