Simulations and different test procedures can lead to greater efficiency of machines. Turbomachinery, especially turbochargers, are very complex with transient flow processes, for example, heat and flow transfers. There are correlations between the turbocharger and the combustion engine, like the pulsating air flow of the exhaust gases. This section specifies the test beds for turbomachinery at the Ostfalia University.
2.1. Friction Test Bed-FTB
Friction itself is omnipresent everywhere. Friction causes energy losses, wear and tear, friction-induced vibrations and therefore noise, vibration and harshness (NVH). In relation to the subject of turbomachinery, there are studies about friction pairs and tribological behavior of material pairings. The frictional coefficient is described as the quotient of tangential and the specific normal force, it has a crucial effect on the stability of a system. Under real conditions, this coefficient is highly transient and does not reach a steady state. Therefore, the friction test bed takes measurements of the turbomachinery under close to real boundary conditions, without the transient flow losses.
Only a select few state of the art bearing solutions are applied for modern turbomachinery applications. Turbochargers and similar turbomachinery predominantly apply oil bearings, the most common are radial fully floating bearings or single piece fixed floating bearings. For reference measurements, the Ostfalia uses a turbocharger by BorgWarner of the type BV35, which has a radial fully floating bearing, see
Figure 1.
The market shows a slow shift towards alternative bearing systems, such as rolling bearings or air bearings. The fluid of oil and air bearings is not only lubricating but also has a dampening effect, which is very useful for stabilization and alignment of the rotor shaft. In comparison, the viscosity of air is around 17 µPas, which is about 500 times less than oil at 100 °C with a viscosity-class of SAE30. To get an impression of the three mentioned bearing systems,
Figure 2 shows the friction power in contrast to a simulated start up procedure at different rotor speeds [
3].
Air bearings are commonly used where contamination with other lubricants is not desired, like in an FCS. To achieve the dampening effect, air bearings have characteristically narrow rotor dynamic requirements due to the very tight tolerances.
To get a better understanding of the interferences and influences of bending and torsion modes, it is necessary to investigate the rotor dynamics. Grouped under this headline are the vibrations, resonance/critical frequencies and movements of the shaft or rather the whole system. A rotor shaft is not infinitely rigid, under circumstances it is able to bend or move independently. The bearings of a flexible rotor can be assumed as dampers and springs of the system. Certain frequencies of rotation contribute to critical vibrations [
13]. CAD/CAE and FEA software can analyze these complex systems during the design process, although mostly under simplified assumptions and boundary conditions, this approach is taken to avoid damage to the system.
Figure 3 shows scaled, exemplary critical frequencies of the BW BV35 used on the FTB. The Ostfalia uses this method to check for potential influences for evaluation with the FTB and HGTB, at the stage of designing the dummy masses. The first critical resonance frequency of this shaft is at 623 Hz which equals 37,000 min
−1, where the compressor side bends slightly. At 1413 Hz which equals 85,000 min
−1, the compressor mass expands. These analyses are used to design the turbine/compressor dummy masses (TDM/CDM) and to detect and verify critical vibrations.
Special attention needs to be taken to the start-up behavior, lift off, stabilization and the alignment of the shaft when considering measurements of turbomachinery. Besides this, the differences and best operating conditions of a bearing system can be measured by the FTB. The setup and adaptations of the friction test bed are explained in the next section.
2.1.1. FTB Setup and Adaptations
The friction test bed consists of five major parts. First an electric motor is used to drive the shaft assembly and to eliminate the transient flow influences, that normally occur when hot gas is used to propel the shaft with a turbine. The electric motor has a nominal rotational speed of 100,000 min−1 and 0.04 Nm of torque.
Second, there is a coupling between the electric motor and shaft. This is a mandatory part of the test bed. The evaluation results of different coupling solutions are discussed in
Section 3.
Next there is the housing of the turbomachinery for the bearing system and the shaft assembly, with dummy masses for compressor and turbine wheels. To reduce influences of the turbine and/or compressor wheel, dummy masses with similar characteristics, such as weight, center of gravity and moment of inertia are essential.
Figure 4 shows exemplary dummy masses for a compressor and a turbine wheel, with integrated holes to insert balancing masses.
In addition, there are two integrated systems for water cooling the electric motor and, if necessary, the turbomachinery, as well as an oil conditioning system integrated into the test bed with indirect heating and circulation systems to provide pressurized and temperature-controlled oil for machines with oil bearings.
Sensors are applied to measure temperatures and mass flow of the liquids. Furthermore, strain gauges for torque and axial forces as well as acceleration sensors for vibrations and displacement sensors for two dimensions are used to measure shaft dynamics. This enables the FTB to measure not only orbital movements and shaft dynamics at high rotor speeds, but also frictional losses under real conditions, regardless of the bearing systems used. The measurements are performed with minimal losses of heat flow and other flow phenomena. The schematics of the friction test bed are shown in
Figure 5.
With the FTB it is possible to measure applied axial forces in operation. There are a variety of different application methods of axial force, ranging from manually applying the force though the coupling by pushing the electric motor, up to specifically designed pressure housings for the dummy masses and electromagnetic solutions. At the time of writing these methods are in their final phases of evaluation and depend on turbomachinery and bearing system. The axial force solution influences the design of the dummy masses. In the next section follow the mathematical basics for the FTB.
2.1.2. Mathematical Methods of FTB
Due to the utilization of machined and unbalanced dummy masses for the compressor and turbine wheels, it is of importance to balance the new shaft assembly, so that an acceptable level of balancing quality can be achieved. The balancing quality
G is determined according to the DIN ISO 21940-11: 2017 with the following equation, by dividing the imbalance
U by the mass of the rotating assembly
m and multiplying with the angular frequency
[
14]:
For turbochargers, the balancing quality should be below , for other fast rotating machines like turbo blowers or compressors (with air bearing for instance) it should be below .
The initial balancing is conducted with rotational speeds below 20,000 min−1 on the friction test bed. This is required to realize higher speeds without causing damage to the bearings of the machine.
The final balancing of the full assembly at high rotational speeds is also conducted on the friction test bed. The process for balancing the assembly is based on the numerical balancing approach introduced by MacDuff and Curreri for operational balancing of rotating assemblies. Which based on polar multiplication and addition of complex numbers.
For balancing the rotating assembly, the shaft displacement and the acceleration is measured in two planes, these planes are the balancing planes on the turbine and compressor dummy masses.
The balancing procedure consists of three steps and can be repeated multiple times until a satisfactory balancing quality is obtained. In the first step the angle and amplitudes of the displacement or the acceleration of the rotating assembly are being measured. These measurements for the turbine dummy mass
and for the compressor dummy mass
are the basis for calculating the imbalance of the rotating assembly. After the initial run there are measurements conducted for the second and third run with trial weights. These trial weights are additional imbalances that are added to the rotating assembly. The first imbalance
is added to the turbine dummy mass for the second run, which results in the measurements
and
. Afterwards the first imbalance is removed and the second imbalance
is added to the compressor dummy mass. The third run results in the measurements for
and
, the total imbalance in each plane can be calculated with the following equations:
For the primary purpose of the FTB, the friction power is calculated based on the measured reactionary torque of the electric motor used to propel the shaft assembly. The following equation is used to calculate the friction power
:
The reactionary torque of the electric motor is measured by a torque sensor, which is equipped with four strain gauges. The resistances of these strain gauges are connected as a Wheatstone bridge by the measuring equipment, the corresponding torque values are calculated. The rotational speed of the electric motor is measured by the control electronics.
Additionally, the effective power of the electric motor is used in comparison with the friction power to ensure plausibility. In the next section follows the explanation of the hot gas test bed.
2.2. Hot Gas Test Bed-HGTB
To determine and categorize compressor or turbine wheels of turbomachinery and their overall efficiency, maps are used to describe their functionality, mostly with mass flow, pressure (ratio) and in relation to efficiency. For turbines, these maps are not normed or fully standardized. There are guidelines such as SAE J922 [
15] or SAE J1826 [
5], but these do not describe the exact setup of the test bench or the precise locations for sensors. This leaves them only as recommendations [
4].
In practice, turbomachinery is subject to various and very complex influences that impact efficiency during the generation of maps. Thermodynamic and aerodynamic phenomena cause transient flow processes, that include heat and flow transfers and correlate within the used system [
6]. Therefore, the general set up of the system, the boundary conditions, automation and instrumentation can influence the measurements, see
Figure 6. The influencing factors include but are not limited to the ambient conditions, the adjustment and control mechanisms, the system boundaries and the geometric properties of the measuring tubes, the properties of the turbomachinery, the external influence of measurements methods and equipment and general measuring uncertainties [
7].
Due to changing ambient influences and boundary conditions it is difficult to compare different turbine wheels and their maps. To counteract these uncertainties and to evaluate performance, it is crucial that in front and behind the turbine, the mass flow, pressure and humidity are in a steady state. To simplify these calculation, compressor and turbine wheels are commonly declared as adiabatic. Measurements are taken by applying mass flow to the turbine wheel at different boundary conditions. There are different methods to determine turbine maps. The so-called “adiabatic” method simulates load by the compressor wheel. To achieve this, the turbine is slowed down, by reducing the mass flow towards the wheel. Only at high rotational speeds (less than 30% of maximum rotational speed) this is a reliable method [
16]. At lower speeds, so called “extended turbine maps” are used, due to the requirement of special measuring methods to characterize the turbine wheel at low rotational speeds. Therefore, the load is simulated by slowing down the shaft with the electric motor generator unit (MGU). With this method the operating points can be measured and extrapolated to indicate the behavior of the turbine within the entire range of rotational speeds. The HGTB is set up specifically for these types of measurements, see the next section. To get a more in-depth explanation of these both measuring methods for turbine maps, see following scientific paper about the HGTB [
7]. In the next section follows the mathematical methods and the test set up.
2.2.1. HGTB Setup and Adaptations
The hot gas test bench of the Ostfalia University bears similarity to the FTB with some modifications and other components carried over, for reference see
Section 2.1.1. In contrast to the FTB the HGTB uses an electrical motor only as drive component to balance the rotary shaft before the actual measurements. After that, the motor acts as a generator and retards the shaft. The shaft is driven by the hot gas with the (adapted) turbine wheel components of the FCAS in this case, or with the original turbocharger and turbine wheel attached to the shaft. The air is compressed by an electrical compressor, heated with a filament heating and afterwards humidified by a water injection system. This allows the boundary conditions to be set up to simulate a FCS or an internal combustion engine. The schematics are shown in
Figure 7.
To determine the thermodynamics of the fluid, sensors measure the temperature, pressure, mass flow and humidity in front, behind and in between air tube sections. Additionally, the rotor speeds and the torque of the shaft are measured, to calculate the efficiency of the turbine wheel by evaluating the inducted power of the electrical generator. The mathematical basics of the hot gas test bed are described in the next section.
2.2.2. Mathematical Methods of HGTB
For all measurements of the HGTB discussed in this paper, the fluid is assumed to be dry air. For all calculations the recorded quantities are used as mean values over the time of the measurement. Furthermore, all calculations of the HGTB use the total pressure. Therefore the measured static pressure needs to be converted. The following equation is used to determine the total pressure [
17].
The Equation (
5) shows that the total pressure
is dependent on the turbine mass flow
, the flow cross section
A, the static pressure
and the temperature
. As already mentioned, the flow medium is dry air, thus a value of
is applied for the specific gas constant [
17].
The pipes adjacent to the turbine have an inner diameter of 60 mm with a cross section of 0.0028 m 2.
To calculate the isotropic turbine output, the total turbine pressure ratio and the isobaric heat capacity are calculated. The total turbine pressure ration
is formed as the total pressure
before the turbine divided by the total pressure
after the turbine.
The isobaric heat capacity is described as a function of pressure and temperature using the mass fraction of the dry air components. The following
Table 1 shows the used values of the mass distribution of nitrogen
, oxygen
and other trace gases
.
To calculate the isobaric heat capacity
, the fraction of trace gases is completely attributed to carbon dioxide. This gas has the highest influence on the heat capacity of all trace gases. The isobaric heat capacity is calculated as shown in Equation (
7).
With the total turbine pressure ratio and the isobaric heat capacity the isentropic turbine output is calculated. Thereby the isentropic turbine output
is formed as the product of the turbine mass flow, the isobaric heat capacity
on the turbine entrance, the temperature
on the turbine entrance and the total turbine pressure ratio. For the isentropic exponent
, the value
is assumed [
18].
The compressor wheel is replaced by a motor generator unit (MGU) on the Ostfalia HGTB. The MGU is slowing the rotor shaft down by generating electric power
. The generated power is calculated by the measured torque
and rotational speed of the shaft
.
To determine the isentropic turbine efficiency
, the generated power is divided by the isentropic turbine power.
For the creation of the turbine map the velocity ratio
is calculated based on [
16].
The velocity ratio is described as the peripheral speed of the turbine wheel
(tip speed) divided by the flow velocity
. The flow velocity is calculated with the isentropic turbine power and the turbine air mass flow.
The tip speed is calculated by the diameter of the turbine wheel and the rotational speed of the turbine wheel. The used turbine wheel has a diameter of 40 mm.