The mass flow rate of a Couette flow in a long rectangular channel is calculated for constant or linear wall velocities in the whole range of the gas rarefaction and in a wide range of the width-to-height ratio. Analytical solutions for arbitrary width-to-height ratios are given for the hydrodynamic regime, the slip regime, and the free molecular regime. Therefore, both the velocity field and the mass flow rate can be calculated. In the transitional regime, simulations via direct simulation Monte Carlo method are performed. The results are provided as reduced flow rates in tabulated data, which can be used for any constant or linear increasing wall velocity (e.g., bounding walls of working chambers in positive displacement vacuum pumps). © 2022 Author(s).

MoS2 thin films for unsynchronized, dry-running screw machines. Unsynchronized, dry-running screw machines have great potential to provide a resource-saving alternative to conventional screw machine designs. By saving external synchronization and the absence of a liquid lubricant, there are economic and ecological advantages. The use of materials and energy are reduced and the purity of the process gas is increased, the impact on the environment is minimized. Vacuum coating processes are one of the key technologies for realizing an unsynchronized, dry-running screw machine. The synthesized thin films can be optimally conditioned thanks to the near-net-shape coating and the possibility of changing the structural properties of the coating in a targeted manner. MoS2 thin films as solid lubricant exhibit improved friction properties. As a result there is also a great potential to reduce friction and thus the use of energy. © 2021, John Wiley and Sons Inc. All rights reserved.

Modifying MoS2 thin films by additional elements shows great potential in order to adjust the property profile and to meet the increasing requirements regarding high wear resistance and low friction properties of industrial components. Within that context, MoSx:N:Mo thin films were deposited by a reactive hybrid dcMS/HiPIMS process. By systematically increasing the Mo target cathode power, an investigation of the structural and the mechanical properties was conducted to understand the evolution of the tribological behavior. A low Mo target cathode power of 1 kW is related to the formation of the preferential (002) MoS2 basal-plane and thus a low friction with µ = 0.2. With an increasing amount of Mo, the film loses its solid lubricant MoS2 properties and a nitride constitution of the thin film is developing due to the formation of crystalline Mo and MoN phases. Related to this transformation, the hardness and elastic modulus are increased, but the adhesion and the tribological properties are impaired. The film loses its plasticity and the generated film material is directly removed from the contact area during the sliding contact. © 2021, The Author(s).

Tribology, as the science and technology of interacting surfaces, typically relies on liquid lubricants which reduce friction and wear. For environmentally friendly tribological purposes and applications requiring a liquid-free performance, solid lubricants, such as MoS2 coatings, play an essential role. It is crucial to understand the interplay between the parameters of the coating synthesis and the characteristics of the coating. The impact of the deposition parameters on the structural, mechanical and frictional properties of MoSx thin films, which are synthesized by high-power impulse magnetron sputtering, are studied. The morphology, topography and stoichiometry (2.02 < x < 2.22) of the films are controlled by, in particular, the bias-voltage and heating power applied during the sputtering process. In combination with a low pulse frequency the hardness and elastic stiffness of the MoSx films are enhanced up to 2 and 90 GPa, respectively. This enhancement is assigned to a shortening of the Mo-S bonding lengths and a strengthening in the interatomic coupling as well as to a formation of small-sized crystallites at the surface. The friction coefficient reduces to μ = 0.10 for films with an initial (100) orientation and the mean roughness of the MoSx films decreases below 15 nm by shortening the cathode pulses. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. All right reserved.

Clearance mass flows are a major loss mechanism in dry running rotatory positive displacement vacuum pumps. Therefore, a detailed knowledge of the clearance mass flow is crucial to calculate the operation of those pumps. The small clearance heights and the large pressure range of such pumps require a wide range of gas rarefaction parameters to be taken into account. The flow in the clearance can be described as a combined Couette-Poiseuille flow with variable cross section. This is typically done by solving the Stokes equation, but especially at high gas rarefaction parameters, the inertia cannot be neglected any more, which can lead to choking of the flow. A one-dimensional approach for the compressible fluid flow was provided by Shapiro. It is shown that this approach can be carried over for the rarefied gas flow. The problem is solved in bounds for the constant total temperature and compared to experimental investigations by varying the pressure ratio and the circumferential speed of the clearance boundary in a wide range of gas rarefaction parameters. © 2020 Author(s).

During the operation of twin screw expanders with slightly superheated vapours or even two-phase fluids, surface condensation on machine parts occurs during the filling period and the expansion phase when the working fluid is in contact with cooler inner surfaces. This heat exchange from the working fluid to adjacent machine parts effects the working cycle and the efficiency of these machines. Short time scales and the periodicity of the process indicate the condensation process is best described by models for dropwise condensation. In this paper the effects of surface condensation on the operation of twin screw expanders are initially discussed in a simulation-based investigation. Chamber model simulation coupled with a thermal analysis is used for the thermodynamic simulation, whereby heat transfer coefficients are systematically varied. It is found that during the inlet phase condensate emerges on the inner surfaces of the machine being substantially cooler than the working fluid. This results in a higher mass being trapped within the working chamber and, thus, an increasing mass flow rate of the machine. An increase in power output is, however, not observed. The results obtained from chamber model simulations are finally compared against experimental data of a screw expander prototype. © Published under licence by IOP Publishing Ltd.

Understanding the generation of third body particles and their contribution to the formation of tribofilms of MoSx thin films is still challenging due to a large number of influencing factors. Besides the structure of the as-deposited MoSx films, the environment and the conditions during the Ball-on-disk tests affect tribofilms and thus the friction. Therefore, the influence of the surface pressure and sliding velocity in air, argon and nitrogen environments on the generation of the third body particles and the tribofilm formation of randomly oriented MoSx films is investigated. A high surface pressure is one major factor to achieve low friction, especially under humid conditions, which is important considering the use in industrial applications, for example dry-running screw machines. However, the mechanisms leading to that frictional behavior are still affected by the surrounding environment. While low friction is caused by a more extensive tribofilm formation in air, in argon and nitrogen, large size third body particles dispensed all over the contact area contribute to a lower friction. Raman scattering reveal a different chemistry of these particles reflected in the absence of laser- or temperature-induced surface oxidation compared to the as-deposited film and the wear track. The Raman scattering results are discussed with respect to the wear particle size, its chemical reactivity and strain-induced bonding changes. © 2019 by the authors.

Raman spectroscopy is used to investigate the structural and tribological properties of HiPIMS sputtered MoSx thin films which were post-growth-annealed at different temperatures. The Raman scattering combined with X-ray diffraction determines a reduction in the residual strain within the MoSx layers with increasing annealing temperature. In the high-temperature annealed coatings a Raman signature at 40 cm−1 emerges, which results from a strengthening of the inter-layer van-der-Waals interaction. This observation indicates that the thermally annealed MoSx thin films become more resistant against shear forces, which is manifested in an increase of the coefficient of friction measured with a ball-on-disc tribometer. The coefficient of friction moreover decreases with lowering the sulfur/molybdenum ratio which, in turn, depends on the substrate and annealing temperatures. Furthermore, a Raman forbidden mode may be exploited to detect stacking faults within the sputtered coatings. Its observation is realized through resonant excitation of an MoS2 exciton at about 633 nm. © 2019 Elsevier B.V.

Condensation and its effects on turbomachinery operation are well understood and have been widely investigated. However, only little scientific work on condensation in positive displacement machines has been published. Although, depending on machine type, high expansion rates and, as a consequence, significant supersaturation can be achieved for working fluids with a negative saturation vapour curve. In this paper, the effects of spontaneous steam condensation in screw expanders are discussed. Classical nucleation theory is used for the thermodynamic simulation of operational behaviour. The study shows at which point during the expansion phase spontaneous condensation can be expected and typical nucleation rates are determined. The impact of released latent heat during expansion on chamber states is depicted. Furthermore, a comparison of purely metastable expansion with equilibrium expansion is provided in order to show the full-range discrepancies. Additionally, the influence of internal leakage and throttling effects during the inlet phase on the course of spontaneous condensation and droplet growth is analysed. Typical operating parameters are widely varied in simulation so as to identify the impact of steam parameters and expander parameters on the condensation process. © IMechE 2019.

Subject of discussion are simulations and experimental investigations on the acoustic characterization of three single stage centrifugal pumps of different specific speed. In operation, these pump-types generate pressure pulsation at blade passing frequency, primarily due to rotor-volute-interaction. In order to determine the acoustic excitation it is necessary to know about the pumps' acoustic transmission parameters. In this paper, a one-dimensional numerical model for transient time-domain simulation is presented, which takes into account the pump geometry as well as the volutes' structural behaviour by means of the local effective speed of sound. Numerical results for the transmission characteristics of the three different pumps are shown in terms of scattering matrices and evaluated against parameters calculated from measurement results. The experimental analyses are carried out using dynamic pressure sensors in both the suction and the discharge pipe. Assuming solely plane wave propagation, the complex acoustic field on each side is evaluated independently. The so called "two source" method is then used to determine the transmission parameters of the pumps in standstill for a range of frequencies experimentally. Subsequently, the acoustic excitation at varying rotational speed is evaluated by means of measurements at the pumps in operation and presented as monopole and dipole source types for cavitation-free conditions. © 2019 by the authors.

Clearance flows are the main loss mechanism in dry running positive displacement vacuum pumps. In order to calculate the operation of those pumps, a detailed knowledge of the clearance mass flow rates is crucial. The dimensions of such pumps and the large pressure range of the operating points require a wide range of gas rarefaction to be taken into account. The clearance flow can be described by a combined Couette Poiseuille flow due to the pressure gradient between two chambers and the rotation of the rotary pistons. These clearance flows are studied experimentally and theoretically in the present work. Therefore, a suitable experimental setup is described together with the requirements of sensors and the necessity of a low leakage. A theoretical approach is presented, and the results are compared to experimental investigations varying the pressure ratio and the circumferential speed of a clearance boundary in a wide range of the gas rarefaction. © 2018 Author(s).

Condensation and its effects on turbo machinery operation are well understood and have been widely investigated. However, only little scientific work on condensation in positive displacement machines has been published. Although, depending on machine type, high expansion rates and, as a consequence, significant supersaturation can be achieved for working fluids with a negative saturation vapour curve. In this paper the effects of spontaneous steam condensation in screw expanders are discussed. Classical nucleation theory is used for the thermodynamic simulation of operational behaviour. The study shows at which point during the expansion phase spontaneous condensation can be expected, and typical nucleation rates are determined. Since the calculation of condensation requires a suitable fluid model providing consistent data for the metastable region, the advantages of Pollak's equation of state over the IAPWS property formulation are demonstrated. The impact of released latent heat during expansion on chamber states is depicted. Furthermore, a comparison of purely metastable expansion with equilibrium expansion is provided in order to show the full range discrepancies. © Published under licence by IOP Publishing Ltd.

The paper deals with a theoretical investigation into the ways in which fluid properties influence the optimal geometrical parameters of dry running twin screw compressors with uniform and dual lead rotors. Dual lead rotors possess two segments with different rotor leads in order to optimise the progression of chamber volume, clearance size and outlet area. Optimal geometry parameters are determined by means of a multi-chamber model simulation. Fluids are treated as an ideal gas and fluid properties are varied systematically in order to provide guidance on how the machine should be designed for a particular application. The optimal geometry parameters mainly depend on the speed of sound and isentropic exponent of the fluid, because they influence outlet throttling during discharge, and pressure progression due to volumetric compression. In particular, the values for the rotor wrap angle and the internal volume ratio need to be adjusted individually for each compressor application. The results reveal that dual lead compressors possess most potential for fluids with low speed of sound and isentropic exponent. © Published under licence by IOP Publishing Ltd.

Currently, the simulation of multi-phase rotary displacement machines in reasonable accordance with the experimental results is not possible. Clearance sealing, additional frictional losses, heat transfer and lubrication are among the various effects caused by the presence of a liquid, which would all have to be modelled. Moreover, complex processes, such as condensation and evaporation affecting the thermodynamic equilibrium, as well as expansion of the multi-phase gas-liquid-mixture would have to be included. With the purpose of achieving a better understanding of liquid-flooded screw expanders, this paper describes a theoretical evaluation of clearance sealing by means of a liquid, and the resulting frictional losses. The influence of different auxiliary liquids, namely water and oil, is examined. Thus, after introducing the expander geometry and the auxiliary liquids, the results of a thermodynamic analysis are presented. The multi-chamber model-based simulation tool KaSim, that has been developed at the Chair of Fluidics, is applied to analyze the maximum potential of clearance sealing. Subsequently, dry running and liquid-flooded screw expanders are compared, taking clearance sealing as well as frictional losses into account. On the one hand, the study demonstrates that the influence of liquid water on temperature is negligible. On the other hand, the results show that reasonable modelling of oil requires a consideration of temperature-dependent dynamic viscosity for this auxiliary liquid. Finally, an extension of the presented simulation approach is introduced. © IMechE 2016.

Screw-type expanders offer excellent prospects for energy conversion in lower and medium power ranges, for instance as expansion engines in Rankine cycles with regard to either waste or geothermal heat recovery. With the aim of identifying the potential in organic Rankine cycle (ORC) power systems, an oil-flooded twin-screw expander without timing gears was designed and experimentally investigated in an ORC with R245fa as working fluid. Here, the scope for the experimental determination of the expander characteristic map was limited by the test rig specifications. Based on the experimental results, a multi-chamber model of the test twin-screw expander was calibrated and theoretical approaches according to mechanical and hydraulic loss calculation were applied. Consequently, the expander's complete characteristic map could be calculated. Furthermore, relevant mechanisms influencing the operational behaviour of oil-flooded twin-screw expanders were identified and analysed in-depth. © 2017 by the authors.

In the present study flash vaporisation of liquid injection in a twin screw expander for a Trilateral Flash Cycle (TFC) is examined theoretically. The TFC process comprises a pressure increase in the working fluid, followed by heating the liquid close to boiling point. The hot liquid is injected into the working chamber of a screw expander. During this process the pressure of the liquid drops below the saturation pressure, while the temperature of the liquid remains virtually constant. Hence the liquid is superheated and in a metastable state. The liquid jet seeks to achieve a stable state in thermodynamic equilibrium and is therefore partially vaporised. This effect is referred to as flash vaporisation. Accordingly, a two-phase mixture, consisting of vapour and liquid, exists in the working chamber. Thermodynamic simulations were carried out using water as the working fluid for representative screw expander geometry. The simulations presented are performed from two different aspects during the filling process of a screw expander. The first case is the vaporisation of the injected liquid in a state of thermodynamic equilibrium, whereby the two-phase mixture is treated entirely as a compressible and homogeneous gas. The second case considers flashing efficiency. It describes the quantity of flashed vapour and consists of a liquid and vapour domain. Both models are compared and analysed with respect to the operational behaviour of a screw expander. © Published under licence by IOP Publishing Ltd.

By comparing the worn and untouched locations of a tungsten-carbide/carbon surface of a dry-running twin-screw rotor, we demonstrate that tungsten-oxide Raman modes become observable only at worn locations and the integral intensity of the Raman line at 680 cm-1, which is related to the incipient oxidation of the tungsten-carbide stretching mode, is enhanced. Its frequency and width moreover change significantly, thus indicating the mechanical distortion of the bonding that has been occurred during the wearing process. The shape of the tungsten-oxide Raman lines, resembling the Voigt function, hints at a surface morphology that is a characteristic for an amorphous solid environment. Our Raman scattering results may be exploited to characterize the degree of wear of coated surfaces and to identify signatures of a tribological layer. © 2016 Author(s).

For the compressible coupled simulation of piping systems including fluid machinery, an embedment of 3D finite volume schemes for active components such as pumps and compressors into 1D finite difference characteristic methods for passive components (e.g. pipes, valves) offers a sophisticated 3D investigation of the machinery with a moderate simulation effort for the entire system. While a 3D-1D coupling method for finite volume Godunov schemes is available from preliminary studies, in the present paper, a new non-reflecting coupling method for 1D finite volume Godunov and 1D finite difference characteristic methods is presented, and the mechanisms for spurious reflections at the coupling interface are revealed. The proposed methodology is based on spectral error analysis and is in general applicable to the coupling of any fundamentally different numerical schemes. It is demonstrated that by matching the numerical diffusion and speed of sound in both coupled domains, reflections can be minimized. © 2016 Elsevier Ltd

A lot of effort has been expended on understanding the influences of an injected auxiliary liquid on a twin screw expander's performance. Sealed clearances improve performance on the one hand, but involve considerable frictional losses on the other hand. This paper contributes to an evaluation of these opposing effects with regard to the efficiency of screw expanders. First, thermodynamic analyses using the multi-chamber model-based simulation tool KaSim, developed at the Chair of Fluidics, are presented for a test screw expander in order to show the maximum potential of clearance sealing. This analysis involves thermodynamic simulations for sealed and unsealed clearances and leads to an order of priorities for different clearance types. Second, hydraulic losses within front and housing clearances are calculated, applying an analytical model of incompressible one-phase clearance flow. Subsequently dry and wet screw expanders are evaluated while both clearance sealing and frictional losses are considered for the simulation of a liquid-injected machine. © Published under licence by IOP Publishing Ltd.

In natural gas flow metering and pressure regulation stations flowmeters, heat exchangers and control valves are usually connected in series. Especially in the case of two or more measuring bars sometimes at minor flow rates untypical pipe vibration together with flow metering faults are observed. Based on field investigations the dependencies between the pipe vibration level, the gas pulsation inside the pipe and the operating conditions of the heat exchanger are analysed. It turns out that with increasing heat flow rates into the natural gas the pulsation and hence the metering faults as well as the pipe vibrations are amplified.In order to understand the physical dependencies of this phenomenon besides experiment a theoretical study is performed. The origin of the vibration turns out to be a thermoacoustic instability. According to the Rayleigh criterion gas pulsations are amplified if heat is given to the gas at the moment of greatest condensation. Based on detailed theoretical investigations by means of the method of characteristics using a Rijke tube model the physical dependencies are analysed. Finally potential solutions to avoid this vibration problem at natural gas metering stations are introduced. © 2011 Elsevier Ltd.

The construction and development of different rotor profiles is an important area in connection with the development of screw compressors for specific applications. Geometrical performance figures (using criteria to describe interdependencies of geometrical parameters for screw compressors) for profile optimization are used in order to achieve specific improvements in performance. During this process, rotor profiles and spatial parameters are the main factors. Compared to data derived from the front section of rotor profiles, these figures which also take spatial parameters into account provide a better evaluation of gap conditions and operating efficiency of the compressors under examination. © Authors 2011.

Screw spindle vacuum pumps are characterised by a high suction performance and the ability to achieve high pressure ratios. Screw spindle vacuum pumps have varying progressions for the rotor pitch gradient, depending on the manufacturer. From a scientific point of view, the question arises which rotor gradient along the rotors has to be preferred for a particular set of operating conditions with reference to the machine characteristics. To answer this question a simulation of the compression process in the screw spindle vacuum pump is performed. The simulation program is used to calculate an energy-specific optimal rotor pitch applying an evolutionary optimization approach. It turns out that - in contrast to actually available rotor geometries - a continuous increase in rotor pitch from the pressure to the suction side is not ideal. An optimized rotor pitch curve is presented and the underlying physical dependencies are clarified by means of pressure and mass flow diagrams. © 2011 Elsevier Ltd. All rights reserved.