Search

This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental representation of a reaction-diffusion system with both simplicity and significance. The focus lies specifically in investigating Fisher's equation under conditions of large reaction rate coefficients, wherein solutions manifest as traveling waves, posing a challenge for numerical methods due to the occurring steepness of the wave front. To address optimization challenges associated with the standard PINN approach, a residual weighting scheme is introduced. This scheme is designed to enhance the tracking of propagating wave fronts by considering the reaction term in the reaction-diffusion equation. Furthermore, a specific network architecture is studied which is tailored for solutions in the form of traveling waves. Lastly, the capacity of PINNs to approximate an entire family of solutions is assessed by incorporating the reaction rate coefficient as an additional input to the network architecture. This modification enables the approximation of the solution across a broad and continuous range of reaction rate coefficients, thus solving a class of reaction-diffusion systems using a single PINN instance., Comment: 14 pages, 7 figures

Flamelet models are widely used in computational fluid dynamics to simulate thermochemical processes in turbulent combustion. These models typically employ memory-expensive lookup tables that are predetermined and represent the combustion process to be simulated. Artificial neural networks (ANNs) offer a deep learning approach that can store this tabular data using a small number of network weights, potentially reducing the memory demands of complex simulations by orders of magnitude. However, ANNs with standard training losses often struggle with underrepresented targets in multivariate regression tasks, e.g., when learning minor species mass fractions as part of lookup tables. This paper seeks to improve the accuracy of an ANN when learning multiple species mass fractions of a hydrogen (\ce{H2}) combustion lookup table. We assess a simple, yet effective loss weight adjustment that outperforms the standard mean-squared error optimization and enables accurate learning of all species mass fractions, even of minor species where the standard optimization completely fails. Furthermore, we find that the loss weight adjustment leads to more balanced gradients in the network training, which explains its effectiveness., Comment: 8 pages. Part of Scientific Computing 2023 Conference Proceedings (ISBN e-Book: 978-3-903318-20-5)

The turbulent jet ignition concept using prechambers is a promising solution to achieve stable combustion at lean conditions in large gas engines, leading to high efficiency at low emission levels. Due to the wide range of design and operating parameters for large gas engine prechambers, the preferred method for evaluating different designs is computational fluid dynamics (CFD), as testing in test bed measurement campaigns is time-consuming and expensive. However, the significant computational time required for detailed CFD simulations due to the complexity of solving the underlying physics also limits its applicability. In optimization settings similar to the present case, i.e., where the evaluation of the objective function(s) is computationally costly, Bayesian optimization has largely replaced classical design-of-experiment. Thus, the present study deals with the computationally efficient Bayesian optimization of large gas engine prechambers design using CFD simulation. Reynolds-averaged-Navier-Stokes simulations are used to determine the target values as a function of the selected prechamber design parameters. The results indicate that the chosen strategy is effective to find a prechamber design that achieves the desired target values., Comment: 9 pages. Part of Scientific Computing 2023 Conference Proceedings (ISBN e-Book: 978-3-903318-20-5)

This paper empirically studies commonly observed training difficulties of Physics-Informed Neural Networks (PINNs) on dynamical systems. Our results indicate that fixed points which are inherent to these systems play a key role in the optimization of the in PINNs embedded physics loss function. We observe that the loss landscape exhibits local optima that are shaped by the presence of fixed points. We find that these local optima contribute to the complexity of the physics loss optimization which can explain common training difficulties and resulting nonphysical predictions. Under certain settings, e.g., initial conditions close to fixed points or long simulations times, we show that those optima can even become better than that of the desired solution., Comment: 22 pages

This paper introduces a method for the detection of knock occurrences in an internal combustion engine (ICE) using a 1D convolutional neural network trained on in-cylinder pressure data. The model architecture was based on considerations regarding the expected frequency characteristics of knocking combustion. To aid the feature extraction, all cycles were reduced to 60{\deg} CA long windows, with no further processing applied to the pressure traces. The neural networks were trained exclusively on in-cylinder pressure traces from multiple conditions and labels provided by human experts. The best-performing model architecture achieves an accuracy of above 92% on all test sets in a tenfold cross-validation when distinguishing between knocking and non-knocking cycles. In a multi-class problem where each cycle was labeled by the number of experts who rated it as knocking, 78% of cycles were labeled perfectly, while 90% of cycles were classified at most one class from ground truth. They thus considerably outperform the broadly applied MAPO (Maximum Amplitude of Pressure Oscillation) detection method, as well as other references reconstructed from previous works. Our analysis indicates that the neural network learned physically meaningful features connected to engine-characteristic resonance frequencies, thus verifying the intended theory-guided data science approach. Deeper performance investigation further shows remarkable generalization ability to unseen operating points. In addition, the model proved to classify knocking cycles in unseen engines with increased accuracy of 89% after adapting to their features via training on a small number of exclusively non-knocking cycles. The algorithm takes below 1 ms (on CPU) to classify individual cycles, effectively making it suitable for real-time engine control., Comment: accepted for publication in IEEE/ASME Transactions on Mechatronics. (c) IEEE 2022

Recently a new type of deep learning method has emerged, called physics-informed neural networks. Despite their success in solving problems that are governed by partial differential equations, physics-informed neural networks are often difficult to train. Frequently reported convergence issues are still poorly understood and complicate the inference of correct system dynamics. In this paper, we shed light on the training process of physics-informed neural networks. By trading between data- and physics-based constraints in the network training, we study the Pareto front in multi-objective optimization problems. We use the diffusion equation and Navier-Stokes equations in various test environments to analyze the effects of system parameters on the shape of the Pareto front. Additionally, we assess the effectiveness of state-of-the-art adaptive activation functions and adaptive loss weighting methods. Our results demonstrate the prominent role of system parameters in the multi-objective optimization and contribute to understanding convergence properties of physics-informed neural networks., Comment: 17 pages, 11 figures

In addition to the electrical and the thermodynamic losses in hermetic compressors, mechanical losses have a significant influence on the performance of the compressor. In the present paper the friction losses in the journal bearings of a hermetic reciprocating compressor are investigated using numerical methods. A dynamic model is set up to solve the Reynolds equation using a finite volume approach to calculate the pressure field in each journal bearing. The calculation of the fluid film thickness is accomplished with the formulas of the parallel gap. The resulting hydrodynamic forces are equated with forces obtained by a dynamic multibody model of the compressor crank drive to calculate the transient orbit movement of the bearing. Based on the movement of the crankshaft at steady-state conditions, the shear stresses in the gap between crankshaft and housing can be calculated. Thus the cycle averaged friction power loss can be determined. To consider effect such as surface roughness of the bearings or possible contacts between the solids, correlations found in the literature are implemented. The present method is used to assess the friction power loss of the journal bearings during the operation with different oil viscosities. The simulated data is verified with simple analytical friction loss calculations based on shear stresses in the Couette flow between bearing and housing.

Generally, domestic refrigerators and freezers are running in non-continuous operation mode most of the time, which is a necessity to match cooling capacity to thermal loads. In currently available domestic appliances it can be observed, that this matching is mainly realized in two different ways: On the one hand, a simple on/off control of the hermetic compressor is installed in lower priced appliances with limited energy efficiency for the mass market. On the other hand, modern top efficiency class appliances have a variable frequency controlled compressor installed. Both control strategies have a repetitive and transient change of thermodynamic states of the refrigerant in common. For better understanding of these cyclic patterns in terms of internal temperature distribution, a state of the art domestic refrigeration compressor with a displacement of approximately 6 cubic centimeters is integrated in a commercial freezer. The compressor which has an on/off control is equipped with extensive measurement instrumentation. Several temperature probes are inserted and temperatures on surfaces inside and outside the compressor as well as refrigerant temperatures are logged for both cyclic and steady state behavior. Finally, a comparison between transient experimental data and steady-state data from a standardized calorimeter test bench is done.

Comprehensive knowledge about the heat transfer mechanisms and the temperature field inside hermetic compressors is very important for the thermal management and thus their performance. A numerical model to predict the temperature field in a hermetic reciprocating compressor for household refrigeration appliances is presented in this work. The model combines a high resolution three-dimensional heat conduction formulation of the compressor’s solid parts, a three-dimensional computational fluid dynamics (CFD) approach for the gas line domain and lumped formulations of the shell gas and the lubrication oil. Heat transfer coefficients are determined by applying CFD to the gas line side and correlations from the literature on the shell gas and oil side, respectively. The valve in the gas line simulation is modelled as a parallel moving flat plate. By means of an iterative loop the temperature field of the solid parts acts as boundary condition for the CFD calculation of the gas line which returns a cycle averaged quantity of heat to the solid parts. Using an iteration method which is based on the temperature deviation between two iteration steps, the total number of iterations and consequently the computational time can be reduced. The loop is continued until a steady-state temperature field is obtained. Calculated temperatures of the solid parts are verified against temperature measurements of a calorimeter test bench. The numerical results show reasonable agreement with the measured data.

In addition to the adequate lubrication of the moving parts, the oil flow in a hermetic reciprocating compressor has a significant influence on the thermal characteristics of a compressor. The present work is concerned with the investigation of the oil pump system of a reciprocating hermetic compressor used in household refrigeration appliances. The considered oil pump system consists of a centrifugal pump immersed in the oil sump of the hermetic compressor and a helical groove machined on the crankshaft. The focus of this work lies on the immersed part of the centrifugal oil pump and its interaction with the oil in the oil sump. To analyse the flow in the immersed area of the oil pump, the commercial computational fluid dynamics (CFD) software ANSYS Fluent is used. The free surface of the oil flow is modelled with the volume of fluid (VOF) method. A numerical investigation is used to study the influence of the immersion depth and the oil pump design on oil mass flow rate and flow field at the oil pump intake. To evaluate the oil pump regarding the applicability in variable speed compressors, the influence of the rotational speed on the oil mass flow is also explored.

In addition to the adequate lubrication of the moving parts, the oil flow in a hermetic reciprocating compressor has a significant influence on the thermal characteristics of a compressor. The present work is concerned with the investigation of the oil pump system of a reciprocating hermetic compressor used in household refrigeration appliances. The considered oil pump system consists of a centrifugal pump immersed in the oil sump of the hermetic compressor and a helical groove machined on the crankshaft. The focus of this work lies on the immersed part of the centrifugal oil pump and its interaction with the oil in the oil sump. To analyse the flow in the immersed area of the oil pump, the commercial computational fluid dynamics (CFD) software ANSYS Fluent is used. The free surface of the oil flow is modelled with the volume of fluid (VOF) method. A numerical investigation is used to study the influence of the immersion depth and the oil pump design on oil mass flow rate and flow field at the oil pump intake. To evaluate the oil pump regarding the applicability in variable speed compressors, the influence of the rotational speed on the oil mass flow is also explored.

Comprehensive knowledge about the heat transfer mechanisms and the temperature field inside hermetic compressors is very important for the thermal management and thus their performance. A numerical model to predict the temperature field in a hermetic reciprocating compressor for household refrigeration appliances is presented in this work. The model combines a high resolution three-dimensional heat conduction formulation of the compressor’s solid parts, a three-dimensional computational fluid dynamics (CFD) approach for the gas line domain and lumped formulations of the shell gas and the lubrication oil. Heat transfer coefficients are determined by applying CFD to the gas line side and correlations from the literature on the shell gas and oil side, respectively. The valve in the gas line simulation is modelled as a parallel moving flat plate. By means of an iterative loop the temperature field of the solid parts acts as boundary condition for the CFD calculation of the gas line which returns a cycle averaged quantity of heat to the solid parts. Using an iteration method which is based on the temperature deviation between two iteration steps, the total number of iterations and consequently the computational time can be reduced. The loop is continued until a steady-state temperature field is obtained. Calculated temperatures of the solid parts are verified against temperature measurements of a calorimeter test bench. The numerical results show reasonable agreement with the measured data.

In addition to the electrical and the thermodynamic losses in hermetic compressors, mechanical losses have a significant influence on the performance of the compressor. In the present paper the friction losses in the journal bearings of a hermetic reciprocating compressor are investigated using numerical methods. A dynamic model is set up to solve the Reynolds equation using a finite volume approach to calculate the pressure field in each journal bearing. The calculation of the fluid film thickness is accomplished with the formulas of the parallel gap. The resulting hydrodynamic forces are equated with forces obtained by a dynamic multibody model of the compressor crank drive to calculate the transient orbit movement of the bearing. Based on the movement of the crankshaft at steady-state conditions, the shear stresses in the gap between crankshaft and housing can be calculated. Thus the cycle averaged friction power loss can be determined. To consider effect such as surface roughness of the bearings or possible contacts between the solids, correlations found in the literature are implemented. The present method is used to assess the friction power loss of the journal bearings during the operation with different oil viscosities. The simulated data is verified with simple analytical friction loss calculations based on shear stresses in the Couette flow between bearing and housing.

Generally, domestic refrigerators and freezers are running in non-continuous operation mode most of the time, which is a necessity to match cooling capacity to thermal loads. In currently available domestic appliances it can be observed, that this matching is mainly realized in two different ways: On the one hand, a simple on/off control of the hermetic compressor is installed in lower priced appliances with limited energy efficiency for the mass market. On the other hand, modern top efficiency class appliances have a variable frequency controlled compressor installed. Both control strategies have a repetitive and transient change of thermodynamic states of the refrigerant in common. For better understanding of these cyclic patterns in terms of internal temperature distribution, a state of the art domestic refrigeration compressor with a displacement of approximately 6 cubic centimeters is integrated in a commercial freezer. The compressor which has an on/off control is equipped with extensive measurement instrumentation. Several temperature probes are inserted and temperatures on surfaces inside and outside the compressor as well as refrigerant temperatures are logged for both cyclic and steady state behavior. Finally, a comparison between transient experimental data and steady-state data from a standardized calorimeter test bench is done.

During development of refrigeration cycle simulations, the modelling of the compressor requires a trade-off between computational speed and level of detail. In that case, the use of semi-empirical models makes sense instead of complex 1-dimensional models which are common in the development phase of a compressor. Also the very low measuring effort for the adaption of these models favours their use. The present work contains a comparison of different semi-empirical models found in the literature which simulate the dynamic performance of reciprocating compressors. These models calculate the refrigerant mass flow rate and the compressor power based on polytropic compression and the formulation of a volumetric efficiency. The model parameters are determined by fitting calorimeter data of several compressors. To validate the transient prediction-capability of compressors by these models, start-up and cycling measurements were carried out and compared with the computed data. Due to the common requirements in cycle simulation tools, a model for the discharge temperature was developed and validated additionally. The goal of the present study is to find a combination of accurate models of mass flow rate, compressor power and discharge temperature which can be applied to cycle simulations of the whole refrigeration system.

During development of refrigeration cycle simulations, the modelling of the compressor requires a trade-off between computational speed and level of detail. In that case, the use of semi-empirical models makes sense instead of complex 1-dimensional models which are common in the development phase of a compressor. Also the very low measuring effort for the adaption of these models favours their use. The present work contains a comparison of different semi-empirical models found in the literature which simulate the dynamic performance of reciprocating compressors. These models calculate the refrigerant mass flow rate and the compressor power based on polytropic compression and the formulation of a volumetric efficiency. The model parameters are determined by fitting calorimeter data of several compressors. To validate the transient prediction-capability of compressors by these models, start-up and cycling measurements were carried out and compared with the computed data. Due to the common requirements in cycle simulation tools, a model for the discharge temperature was developed and validated additionally. The goal of the present study is to find a combination of accurate models of mass flow rate, compressor power and discharge temperature which can be applied to cycle simulations of the whole refrigeration system.