An Introduction to Accurate HVAC System Modeling

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.

Controlling Temperature

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.

Illustration of dependency of house load and heating capacity on outside temperature
Figure 1 Illustration of dependency of house load and heating capacity on outside temperature

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Turbojets – Basics and Off-design Simulation

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.

Figure 1 T-S diagram for ideal and real Brayton cycle

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

Turbine Blade Cooling – An Integrated Approach

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.

Increase in net power output of a gas turbine over a one percentage point rise in turbine inlet temperature
Figure 1 Increase in net power output of a gas turbine over a one percentage point rise in turbine inlet temperature

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.

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Computational Fluid Dynamics for Centrifugal Compressors

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.

Parameterized Impeller Geometry
Figure 1. Parameterized Impeller Geometry

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.

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Flexible, Fast and High Fidelity Approach to Gas Turbine Unit Part-Load and Off-Design Performance Predictions

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:

  1. Different modes of aircrafts:
    1. Ground idle mode
    2. Take off
    3. Maximum continuous mode
    4. Cruising mode
  2. Different ambient conditions
  3. 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.

Compressor and Turbine Maps
Compressor and Turbine Maps [1]
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 [2]. Despite this, less 1% of machines that are in use today are modeled with digital twin technology [3]. Utilization of digital twin leads to a significant decrease in time and cost for developing and optimization of an object.

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Torsional Transient Analysis of a Single Piston Engine

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.

Tangential forces acting on the crankpin
Figure 1 Example of tangential forces acting on the crankpin (Mendes, A., S.; Zampieri, D.E.; Siqueira Meirelles, P.: Analysis of torsional vibration in internal combustion engines: Modelling and experimental validation) and implementation in AxSTREAM RotorDynamics™ (orange curve)

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:
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Anti-Icing Systems for Land Based Gas Turbines

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 image

Gas Turbine Anti-Icing Systems (GT-AIS) can be categorized in two groups.

  1. Inlet heating systems
  2. 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.

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Torsional Analysis of a Four-Stroke Engine

Reciprocating machines fall into many categories. Despite different applications and designs, e.g. pumps or internal combustion engines with a varying number of pistons, a simple approach to determine torsional modes of regardless which crankshaft assembly can be investigated. The resulting natural frequencies are required by ISO 3046 for rotor dynamic analysis.

Internal Combustion Engine with piston and flywheel geometry
Figure 1 Internal Combustion Engine with piston and flywheel geometry, (

Below, a common way to express a crankshaft assembly with massless shaft and mass-inertia elements is presented, whereas the reciprocating and revolving mass around the crack can be expressed as follows:
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Steam Turbine Seal Leakage Calculation in Design

Steam turbine seals are parts inserted between moving and stationary components, to reduce and prevent steam leakage and air leaking into the low pressure areas. The leakage can happen through vane, gland, and shaft, etc. To reduce leakage from those parts while guaranteeing smooth operation of a steam turbine, engineers have to design these seals, taking into account not only efficiency, but also mechanical strength, vibration and cost.

As an example, steam turbine flow path seals improve overall efficiency installing various types of shrouds, diaphragms, and end seals which prevent idle leaks of working steam in the cylinders. In steam turbines, labyrinth seals are widely used. Some labyrinth seals are also used with honeycomb inserts. It is believed that the use of such seals makes it possible to achieve a certain gain due to smaller leaks of working fluid and more reliable operation of the system under the conditions in which the rotor’s rotating parts may rub against the stator elements. However, we can only consider it as a successful design if the structures are compliant with the manufacturing capabilities and have good vibration stability. [1] Furthermore, seal leakage can significantly affect efficiencies. Better seals increase efficiencies but add extra cost to both manufacturing and maintenance, so the design needs to be done with the turbine flow path design. Although modeling the seals in 3D CFD is theoretically possible, the calculation resources and time are extremely demanding.

This important task can be completed very easily with AxSTREAM NETTM. AxSTREAM NETTM provides a flexible method to represent fluid path and solid structure as a set of 1D elements, which can be connected to each other to form a thermal-fluid network. For each fluid path section, the program calculates fluid flow parameters for inlet and outlet cross-sections, like velocity, density, temperature, mass flow rate, etc. Therefore, the leakage from the whole system can be modeled in this network, as shown in Figure 1.

Steam Turbine Seal Leakage Calculation with AxSTREAM NET
Figure 1. Steam Turbine Seal Leakage Calculation with AxSTREAM NET™

AxSTREAM NET™ is capable of doing:

  1. Choice of seal design at the stage of the steam/gas turbine preliminary design.
  2. Calculation of balances of pressures and mass flow rate to correctly account for the efficiency of the steam/gas turbine.
  3. Calculation of seals fluid flow parameters on the startup mode to estimate the thermal expansion of rotor and casing element.
  4. Calculation of thermal boundary conditions for thermo stresses estimation.

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Steam Turbine Aerodynamic Improvements for Significant Efficiency Gains

The steam turbine is one of the most important power generating equipment items in use. Around half of the electricity generated worldwide comes from steam turbines. Steam turbines can be fueled by coal, nuclear energy, petroleum or natural gas, alternatively by biomass, solar energy or geothermal energy. Thus a large amount of fuel can be saved and CO2 emissions significantly reduced by optimizing key components of these widely used machines.

An important goal in steam turbine technology is to improve efficiency. The continuous flow of steam conditions is one of the commonly accepted efficiency contributor for steam power plants. The chart below shows expected improvement in thermal efficiency for USC double-reheat fossil-fuel power units compared to common supercritical-pressure ones, according to Hitachi.

Expected Improvement in Thermal efficiency for USC power units
Figure 1: Expected improvement in thermal efficiency for USC power units.

Besides steam condition elevation, other areas help the development and refinement of innovative aerodynamic flow path design approaches and the improvement of design procedures for nozzle and blades design and analysis. Continuous growth of steam conditions since the mid-1990s and some advanced steam path design for large steam turbines have brought about 5% of efficiency gain. This effect is almost the same as the transition from subcritical-pressure steam conditions to the supercritical-pressure ones with elevated steam temperatures illustrated in the figure above. Here are some practical examples of steam turbines high efficiency, achieved during the last decade by advanced aerodynamic design (source: Leizerovich, A. Sh. Steam turbines for modern fossil-fuel power plants, ©2008 by The Fairmont Press).
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