P. F. Pelz

Upper Limit for Hydropower in an Open-Channel Flow

It is proved on the basis of the axiomatic energy equation that the theoretical upper limit for the hydropower gained by a water wheel or turbine per unit width in a rectangular open channel cannot exceed (2/5)5/2ρg3/2Heff5/2 by any means in which Heff = effective water head, which is the sum of specific energy E1=h1+u12/2g and the drop of ground level Δz; ρ = density; and g = gravity body force. As a dimensionless measure, a coefficient of performance or harvesting factor is introduced that is an analogue to the one introduced by Albert Betz for wind turbines.

The Influence of Reynolds Number and Roughness on the Efficiency of Axial and Centrifugal Fans—A Physically Based Scaling Method

There is a technical and economical need for a correction method to scale model test data, which fulfills five tasks: It should be (i) physically based, (ii) understandable and easy to apply, and (iii) universal, i. e., applicable to centrifugal as well as to axial machines of different specific speed. Moreover, the method should (iv) account for the aerodynamic quality of the machine and should (v) be reliable not only at peak efficiency, but also at off-design condition. Up to now, no method meets all five tasks. To fill that gap, a method developed at Technical University Darmstadt together with Forschungsvereinigung fur Luft- und Trocknungstechnik e. V. (FLT) is introduced in this work. The method consists of three steps: Assuming the so-called master curve, scaling the efficiency itself and shifting the best efficiency point to a higher flow coefficient. For each step, a simple physical explanation is given. The validation of the method is done with test data of two axial fans with four different stagger angles and two centrifugal fans. In spite of its simplicity, the method shows a good agreement to test data compared with traditional and most recent scaling methods. A short overview about the advantages and disadvantages of compared methods and a conclusion is given at the end of this work.

On the Transition from Sheet to Cloud Cavitation

Hydraulic components failures due to cavitation erosion are mostly a common cause of false or unfavorable operating parameters. In a parameter study with a convergent divergent nozzle, we found a flow change from sheet cavitation to a more aggressive cloud cavitation. This transition occurs at a critical Reynolds number. The critical Reynolds number was found to be the same for water and a glycol water mixture (increased cinematic viscosity by a factor of 1.16) as one would expect on the grounds of the Bridgman postulate. The critical Reynolds number, hence the transition point, is predicted by a physical model developed on first principles: The transition point is reached, when the time for sheet growth is the same than the time needed for the reentrant jet to reach the sheet leading edge. If this is the case, the reentrant jets cut of the sheet and detach closed clouds. To predict the critical Reynolds number is of great value for the industry, since harm full operation points can be identified already in the design process.

Experimental Validation of an Enhanced System Synthesis Approach

Planning the layout and operation of a technical system is a common task for an engineer. Typically, the workflow is divided into consecutive stages: First, the engineer designs the layout of the system, with the help of his experience or of heuristic methods. Secondly, he finds a control strategy which is often optimized by simulation. This usually results in a good operating of an unquestioned system topology. In contrast, we apply Operations Research (OR) methods to find a cost-optimal solution for both stages simultaneously via mixed integer programming (MILP). Technical Operations Research (TOR) allows one to find a provable global optimal solution within the model formulation. However, the modeling error due to the abstraction of physical reality remains unknown. We address this ubiquitous problem of OR methods by comparing our computational results with measurements in a test rig. For a practical test case we compute a topology and control strategy via MILP and verify that the objectives are met up to a deviation of 8.7 %.

Optimal Energy Systems Design Applied To An Innovative Ocean–wind Energy Converter

System level optimization is used to design an innovative ocean–wind energy converter to meet the “as good as it can be done” design objective. This general design procedure is then applied to the design of a 20 kW energy system and it is demonstrated that a combined energetic and economical design procedure is required for an optimal solution.

Physical Modeling of Automotive Turbocharger Compressor: Analytical Approach and Validation

Global warming is a climate phenomenon with world-wide ecological, economic and social impact which calls for strong measures in reducing automotive fuel consumption and thus CO2 emissions. In this regard, turbocharging and the associated designing of the air path of the engine are key technologies in elaborating more efficient and downsized engines. Engine performance simulation or development, parameterization and testing of model-based air path control strategies require adequate performance maps characterizing the working behavior of turbochargers. The working behavior is typically identified on test rig which is expensive in terms of costs and time required. Hence, the objective of the research project “virtual Exhaust Gas Turbocharger” (vEGTC) is an alternative approach which considers a physical modeled vEGTC to allow a founded prediction of efficiency, pressure rise as well as pressure losses of an arbitrary turbocharger with known geometry. The model is conceived to use smallest possible number of geometry as well as material parameters. Thus, conventional expensive and time-consuming application processes can be countered and test rig as well as in vehicle measurements can be reduced. Furthermore, the vEGTC model enables the prediction of different turbocharger behavior caused by geometry variations. Within this paper it is shown in which way the radial compressor as a representative modeling component can be described by zero-dimensional equations: in order to simulate the working behavior of the compressor the geometry, the thermodynamic state of the inlet-air and the turbocharger speed are assumed to be known. The loss mechanisms are devised using analytical and semi-empirical loss correlations. In order to validate the compressor efficiency the heat transfer from the turbine to the compressor is considered. Finally, the simulation output is compared to manufacturer maps of three different turbochargers pointing out the reliability of the model. Thus, a comprehensive validation of the vEGTC model is yielded. The object-oriented language Modelica is used for modeling and the simulations are provided by the Dymola solver.

On Reliable Performance Prediction of Axial Turbomachines

There is a need to reliably predict the performance (efficiency and total pressure rise) of axial turbomachines from model tests for different load ranges. The commonly used scale-up formulas are not able to reliably predict the performance, especially beyond the design point. Furthermore these formulas do not regard changes in relative roughness as they usually occur in practice. An improved scale-up formula is proposed which achieves not only the reliable scale-up of efficiency, but also the scale-up of the pressure coefficient. It is motivated from measurements on two geometric similar axial model fans with a diameter of 1000 mm respectively 250 mm at different rotational speeds, hence Reynolds numbers. By bonding grains of sand to the impeller the influence of relative roughness was investigated. For applying the formula to different load ranges a factor V is introduced that depends on the quotient of effective flow coefficient to optimal flow coefficient.Copyright

THE INFLUENCE OF TIP CLEARANCE ON THE ACOUSTIC AND AERODYNAMIC CHARACTERISTICS OF FANS

In addition to developing fans as aerodynamically efficient as possible, acoustic optimization gains more and more importance for the purpose of reducing fan noise exposure. In order to combine good aerodynamic properties with a silent fan, this experimental research investigates the acoustic and aerodynamic characteristics of an axial fan. In this case, a fan with skewed blades is tested in view of its aerodynamic efficiency and noise exposure in dependence on its tip clearance and stagger angle. For this purpose, six different stagger angles and five tip clearance gaps per angle were measured in a fan test rig (according to ISO 5136). Interpretation of the recorded data shows a clear trend toward higher aerodynamic efficiency and less noise with a down-sizing of the tip clearance gap. As the cost of manufacture rises with the decrease of the tip clearance, the efficiency of these measures can be calculated with the results of this study under consideration of aerodynamic and acoustic aspects.Copyright

On the Kinematics of Sheet and Cloud Cavitation and Related Erosion

The influence of flow parameters such as cavitation number and Reynolds number on the cavitating cloud behavior and aggressiveness is analysed in an experimental work. The focused geometry is a convergent-divergent nozzle with a given radius of curvature at the minimum cross section. By means of a high-speed camera the kinematics of cloud cavitation is visualized. The shape of the cloud is a horse shoe (U-shaped) with two legs ending at the material surface which is in agreement with the Helmholtz vortex theorem. Indeed it is worthwhile to look at the cavitation cloud as a ring vortex whose second half is a mirror vortex within the material. Due to the convection flow, the legs of the vortex are elongated and hence the rotational speed of the vortex core will increase. Thus cavitation bubbles will concentrate within the legs of the vortex and that behavior is observed in the cavitation experiments. The aggressiveness of the cloud is quantified by using soft metal inserts adapted on the nozzle geometry. The interpretation of the plastic deformation, called pits, is done with a 2-dimensional optical measurement system, which is developed to scan large and curved surfaces. In this way damage maps are obtained. Consequently dimensional analysis is used to analyse and generalize the experimental results. Thus a critical Reynolds number is found for the transition from sheet to cloud cavitation. Further an upper limit for the Strouhal number exists for the given geometry. A physical model for the critical Reynolds number is given elsewhere [1]. Also a model for the dynamics of the observed stretched cloud with circulation is published by Buttenbender and Pelz [2].

Validated biomechanical model for efficiency and speed of rowing

The speed of a competitive rowing crew depends on the number of crew members, their body mass, sex and the type of rowing-sweep rowing or sculling. The time-averaged speed is proportional to the rowers body mass to the 1/36th power, to the number of crew members to the 1/9th power and to the physiological efficiency (accounted for by the rowers sex) to the 1/3rd power. The quality of the rowing shell and propulsion system is captured by one dimensionless parameter that takes the mechanical efficiency, the shape and drag coefficient of the shell and the Froude propulsion efficiency into account. We derive the biomechanical equation for the speed of rowing by two independent methods and further validate it by successfully predicting race times. We derive the theoretical upper limit of the Froude propulsion efficiency for low viscous flows. This upper limit is shown to be a function solely of the velocity ratio of blade to boat speed (i.e., it is completely independent of the blade shape), a result that may also be of interest for other repetitive propulsion systems.