Macromodels are dependencies of the “black box” type with a reduced number of internal relations. This is most convenient to create such dependence in the form of power polynomials. Obtaining formal macromodels (FMM) as a power polynomial based on the analysis of the results of numerical experiments conducted with the help of the original mathematical models (OMM).
Therefore, the problem of formal macro modelling includes two subtasks:
1. The FMM structure determining.
2. The numerical values of the FMM parameters (polynomial coefficients) finding.
As is known, the accuracy of the polynomial and the region of its adequacy greatly depend on its structure and order. At the same time, obtaining polynomials of high degrees requires analysis of many variants of the investigated flow path elements, which leads to significant computer resources cost and complicates the process of calculating the coefficients of the polynomial.
Microsatellites have been carried to space as secondary payloads aboard larger launchers for many years. However, this secondary payload method does not offer the specificity required for modern day demands of increasingly sophisticated small satellites which have unique orbital and launch-time requirements. Furthermore, to remain competitive the launch cost must be as low as $7000/kg. The question of paramount importance today is how to design both the liquid rocket engine turbopump and the entire engine to reduce the duration and cost of development.
The system design approach applied to rocket engine design is one of the potential ways for development duration reduction. The development of the design system which reduces the duration of development along with performance optimization is described herein.
The engineering system for preliminary engine design needs to integrate a variety of tools for design/simulation of each specific component or subsystem of the turbopump including thermodynamic simulation of the engine in a single iterative process.
The process flowchart, developed by SoftInWay, Inc., integrates all design and analysis processes and is presented in the picture below.
The preliminary layout of the turbopump was automatically generated in CAD tool (Block 11). The developed sketch was utilized in the algorithm for mass/inertia parameters determination, secondary flow system dimensions generations, and for the visualization of the turbopump configuration. The layout was automatically refined at every iteration. Read More
This is an excerpt from a technical paper, presented at the ASME Turbo Expo 2018 Conference in Oslo, Norway and written by Leonid Moroz, Leonid Romanenko, Roman Kochurov, and Evgen Kashtanov. Follow the link at the end of the post to read the full study!
High-performance rotating machines usually operate at a high rotational speed and produce significant static and dynamic loads that act on the bearings. Fluid film journal bearings play a significant role in machine overall reliability and rotor-bearing system vibration and performance characteristics. The increase of bearings complexity along with their applications severity make it challenging for the engineers to develop a reliable design. Bearing modeling should be based on accurate physical effects simulation. To ensure bearing reliable operation, the design should be performed based not only on simulation results for the hydrodynamic bearing itself but also, taking into the account rotor dynamics results for the particular rotor-bearing system, because bearing characteristics significantly influence the rotor vibration response.
Numbers of scientists and engineers have been involved in a journal bearing optimal design generation. A brief review of works dedicated to various aspects of bearing optimization is presented in . Based on the review it can be concluded, that the performance of isolated hydrodynamic bearing can be optimized by proper selection of the length, clearance, and lubricant viscosity. Another conclusion is that the genetic algorithms and particle swarm optimization can be successfully applied to optimize the bearing design. Journal bearings optimizations based on genetic algorithms are also considered in [2-5]. The studies show the effectiveness of the genetic algorithms. At the same time, the disadvantages of the approach are high complexity and a greater number of function evaluations in comparison with numerical methods, which require significantly higher computational efforts and time for the optimization. A numerical evolutionary strategy and an experimental optimization on a lab test rig were applied to get the optimal design of a tilting pad journal bearing for an integrally geared compressor in . The final result of numerical and experimental optimizations was tested in the field and showed that the bearing pad temperature could be significantly decreased. Optimal journal bearing design selection procedure for a large turbocharger is described in . In this study power loss, rotor dynamics instability, manufacturing, and economic restrictions are analyzed. To optimize the oil film thickness by satisfying the condition of maximizing the pressure in a three lobe bearing, the multi-objective genetic algorithm was used in . In the reviewed studies the optimization has been performed for ‘isolated’ bearing and influence on rotor dynamics response was not considered.
For higher reliability and longer life of rotating mechanical equipment, the vibration of the rotor-bearing system and of the entire drivetrain should be as low as possible. A good practice
for safe rotor design typically involves the avoidance of any resonance situation at operating speeds with some margins. One common method of designing low vibration equipment is to have a separation margin between the critical natural frequencies and operating speed, as required by API standard . The bearing design and parameters significantly influence rotor-bearing system critical speeds. Thus, to guarantee low rotor vibrations, the critical speeds separation margins should be ensured at rotor-bearing system design/optimization stage
Conjugated optimization for the entire rotor-bearing system is a challenging task due to various conflicting design requirements, which should be fulfilled. In  parameters of
rotor-bearing systems are optimized simultaneously. The design objective was the minimization of power loss in bearings with constraints on system stability, unbalance sensitivities, and
bearing temperatures. Two heuristic optimization algorithms, genetic and particle-swarm optimizations were employed in the automatic design process.
There are several objective functions that are considered by researchers to optimize bearing geometry, such as:
– Optimum load carrying capacity ;
– Minimum oil film thickness and bearing clearance optimization [1, 6, 8];
– Power losses minimization [6, 7];
– Rotor dynamics restrictions;
– Manufacturing, reliability and economics restrictions 
The most common design variables which are considered in reviewed works are clearance, bearing length, diameter, oil viscosity, and oil supply pressure.
Finding the minimum power loss or optimal load carrying capacity together with the entire rotor-bearing system dynamics restrictions, require to employ optimization techniques, because accounting the effects from all considered parameters significantly enlarge the analysis process. Several numerical methods, such as FDM and FEM are usually employed to solve this complex problem and calculation process can sometimes be time-consuming and takes a large amount of computing capacity. To leverage this optimization tasks, efficient algorithms are needed.
In the current study, the optimization approach, which is based on DOE and best sequences method (BSM) [11, 12] and allows to generate journal bearings with improved characteristics was developed and applied to 13.5 MW induction motor application. The approach is based on coupled analysis of bearing and entire rotor-bearing system dynamics to satisfy API standard requirements.
Problem Formulation and Analysis Methods Description
The goal of the work is to increase reliability and efficiency for the 13.5 MW induction motor prototype (Fig. 1) by oil hydrodynamic journal bearings optimization.
The motor operating parameters and rotor characteristics are presented below:
– Rated speed rpm: 1750
– Minimum operating speed rpm: 1750
– Maximum operating speed rpm: 1750
– Mass of the rotor kg: 6509
– Length of the rotor mm: 3500
Initially, for the motor application, plain cylindrical journal bearings were chosen to support the rotor. The scheme of the DE (drive end) and NDE (non-drive end) baseline bearings designs
is presented in Fig. 2. For baseline designs, bearing loads were 35 kN for DE and 28 kN for NDE bearing.
The methodology for the bearing characteristics simulation is based on the mass-conserving mathematical model, proposed by Elrod & Adams , which is by now well-established as the
accurate tool for simulation in hydrodynamic lubrication including cavitation.
HVAC (Heat, Ventilation and Air Conditioning) is all about comfort, and comfort is a subjective feeling associated with many parameters like air quality, air temperature, surrounding surface temperature, air flow and relative humidity. For example, while it is easy to understand how the temperature of the air in your living impacts how good you feel, the surfaces with which you are in contact also strongly affect your comfort. For example, last night I got out of bed to clean up after my dog who thought it would be a good idea to swallow (and give back) her chew toy. If I was wearing my slippers, it would have been much easier to go back to sleep between the warm bed sheets without the discomfort of waiting my cold feet warm up to normal temperature.
Speaking of sleep discomfort, many stem from HVAC imbalances. If you wake up in the middle of the night quite thirsty, then you should probably check how dry your bedroom is. The recommended range is 40-60% relative humidity. A higher humidity puts you at risk for mold while lower humidity can lead to respiratory infections, asthma, etc.
Now that we know how HVAC contributes to our comfort, let’s look at the HVAC unit as a system and see its role, functioning and simulation at a high level. The following examples provided are for a house, but similar concepts apply to residential buildings, offices, and so on.
The easiest parameter to control is the air temperature. It can be set by a thermostat and regulated according to a heating or cooling flow distributed from the HVAC unit to the different rooms through ducting. Without the introduction of thermally-different-than-ambient air, the house will heat or cool itself based on a combination of outside conditions and how well the building is insulated. Therefore, to keep a constant temperature a certain amount of energy must be used to provide heating (or cooling) at the same rate the house is losing (or gaining) heat. This is a match of the house load and heating/cooling capacity. Figure 1 provides a graph of the energy needed.
The Brayton cycle is the fundamental constant pressure gas heating cycle used by all air-breathing jet engines. The Brayton cycle can be portrayed by a diagram of temperature vs. specific entropy, or T–S diagram, to visualize changes to temperature and specific entropy during a thermodynamic process or cycle. Figure 1 shows this ideal cycle as a black line. However, in the real world, the compression and expansion processes are never isentropic, and there is always a certain pressure loss in the combustor. The real Brayton cycle looks more like the blue line in Figure 1.
The four stages of this cycle are described as:
1-2: isentropic compression
2-3: constant pressure heating
3-4: isentropic expansion
4-0: constant pressure cooling (absent in open cycle gas turbines)
The most basic form of a jet engine is a turbojet engine. Figures 2a and 2b provide the basic design of a turbojet engine. It consists of a gas turbine that produces hot, high-pressure gas, but has zero net shaft power output. A nozzle converts the thermal energy of the hot, high-pressure gas at the outlet of the turbine into a high-kinetic-energy exhaust stream. The high momentum and high exit pressure of the exhaust stream result in a forward thrust on the engine. Read More
It is a well-known fact in the turbomachinery community that the highest temperature achievable at the inlet of the turbine is a critical performance parameter for the turbine. For any given pressure ratio and adiabatic efficiency, the turbine specific work is proportional to the inlet stagnation temperature. Typically, a 1% increase in the turbine inlet temperature can cause a 2-3% increase in the engine output.
The major limitation for the maximum achievable value of the turbine inlet temperature comes from the material used for the turbine. The maximum material temperature has to be kept in check for multiple reasons, from the physical integrity to the structural reliability, and resulting temperature needs to be less than the turbine blade material’s maximum temperature.
In today’s world where “time is money,” each and every industry involving turbomachinery wants to deliver their high performance products in the quickest time possible. Computational fluid dynamics (CFD) replaces the huge number of testing requirements thus not only shortening the design cycle time, but also reducing development costs.
Today with advancements in computational resources, numerical methods, and the availability of commercial tools, CFD has become a major tool for the design phase of a project. With a large number of validations and bench markings available on the applicability of CFD for centrifugal compressors, it has become an indispensable tool for the aerodynamic designer to verify the design and understand the flow physics inside a compressor’s flow path. However, CFD is still computationally expensive and requires a high level of user-knowledge and experience to get meaningful results. CFD analysis can be performed with and without considering viscous effects of the flow. The inclusion of viscosity into the flow introduces additional complexities for choosing the most appropriate turbulence closure model. CFD however, has some limitations due to:
– Errors created during modeling where the true physics are not well-known and are very complex to model.
– Multiple approximation and model errors created during the calculation process (such as mesh resolution, steady flow assumption, turbulence closure, geometric approximation, unknown boundary profile etc.). These approximations impact the calculations of local values of vital parameters.
In CFD for example, if the 1D design is not accurate, (stage loading and blade diffusion factors etc.), then CFD cannot turn out a good design. It is critical to use a design tool such as AxSTREAM® which can generate optimized designs with less time and effort starting from the specification.
The preliminary design modules of AxSTREAM® uses inverse design tasks to generate the initial flow path for the centrifugal compressor. By choosing the right combination of geometrical and design parameters from the start, AxSTREAM® reduces the number of design cycle iterations required in generating an accurate design.
This initial design obtained is further analyzed and optimized using throughflow solvers in AxSTREAM® which considers various operating conditions. The throughflow solvers in AxSTREAM® predict the performance parameters at different sections and stations, and presents the blade loading, flow distribution along the flow path, etc.
The generation of 3D geometry for the impeller and diffuser is another complex activity which is greatly simplified by using the radial profiler and 3D blade design module in AxSTREAM®. The geometry generated in AxSTREAM® is fully parameterized with complete control for the user to modify as and when required. Figure 1 shows a parameterized impeller geometry generated using seven spanwise sections with contours of the curvature.
In CFD analysis of turbomachines, grid generation becomes a very challenging task due to the geometries of complicated, twisted blades. To achieve reliable CFD results, the grid must resolve the topology accurately to preserve this geometric information. The quality of the grid should be in an acceptable range especially the angle, aspect ratio, and skewness of the grid elements. Automatic mesh generation tools are employed to reduce the turbomachines meshing complications. The AxSTREAM® platform uses AxCFD™ to generate a high quality mesh in considerably short time which captures the accurate flow features.
Gas turbine (GT) engines are the primary engines of modern aviation. They are also widely used as power propulsion engines for power stations. The specificity of these engines implies they frequently work at off-design/part load modes that occur with:
Different modes of aircrafts:
Ground idle mode
Maximum continuous mode
Different ambient conditions
Grid demands (for power generation engines and gas pumping (compressor) stations)
Due to the off-design/part load operating conditions, the parameters of the engines might change significantly, which influences not only the engine efficiency, but also the reliable work of the turbine (high temperature at turbine inlet) and compressor (surge zone) at joint operational points. This is why accurate predictions of the gas generator parameters are crucial at every off-design mode.
To define the joint operational point, the compressor and turbine maps which are created for specified ambient conditions can be used. For example, pressure equal 101.3kPa, temperature – 288.15K. Maps method is widely used, relatively simple and allows you to find the needed engine parameters in the shortest time. However, when cooling is present, engine operation at low power modes (ground idle) impede the accurate determination of joint operational conditions based on maps. The significant drawback to the maps based approach is that it does not give the full picture of the physical processes in turbomachine flow paths which is critical for off-design calculations.
Utilization of the digital twin concept allows significant increase of the off-design performance calculation accuracy. Use of the digital equivalent of object was introduced in 2003 . Despite this, less 1% of machines that are in use today are modeled with digital twin technology . Utilization of digital twin leads to a significant decrease in time and cost for developing and optimization of an object.
In reciprocating engines, the reciprocating motion of pistons is transformed into a rotating motion of the crankshaft, which is responsible for the drive of a whole engine system. Instantaneous torque excitation due to gas forces after firing on the shaft system have to be investigated to ensure proper functioning. A typical torque function over the crankshaft angle can be seen in Figure 1.
Such a 720°-periodic function can be created in AxSTREAM RotorDynamics™, which provides a transient approach to determine the response torque in the shaft after a respective torque excitation. In this example, a rotor speed of 3000 rpm is considered. With this information, the total time for two crankshaft-revolutions (720°) reads: Read More
It is very important to have Anti-Icing Systems for ground-based gas turbines located in humid climates (where air relative humidity can be more than 80% and dense fog can cause air temperatures to drop below 5 0C). Such climatic conditions lead to ice formation. This ice can plug the inlet filtration system causing a significant drop in pressure in the inlet system, which in turn leads to performance loss. In extreme cases, there is even a possibility that the ice pieces get ingested into the compressor (first blade stage) which may cause foreign object damage. Ice may also cause the disruption of compressor work because of excessive vibration, or surging by decreasing the inlet flow. The major factors that lead to the ice formation in gas turbines are ambient temperature, humidity and droplet size. So, under the climatic conditions which are prone to ice formation, an anti-icing system is employed which heats the inlet air before entering the compressor. Let us discuss some important aspects of Anti-Icing Systems.
The objective of an Anti-Icing System is to prevent or limit the ice formation in the gas turbine inlet path.
Gas Turbine Anti-Icing Systems (GT-AIS) can be categorized in two groups.
Inlet heating systems
Component heating systems
Inlet heating systems operate by transferring heat from a heat source (exhaust gases can be used) to the cold ambient air at the entrance of the gas turbine. If the temperature of inlet air raises sufficiently by this heat transfer, icing cannot form in the gas turbine intake.
AxCYCLE™ is a tool, which provides the flexibility and convenience to study various parameters and understand the performance of thermodynamic cycles.