# Turbine Engine

## Objective

This laboratory introduces the measurement of gas temperature and explores the performance of a jet engine. First, the operation and proper use of thermocouples is explored. Then, thermocouples are used to measure gas temperatures at various locations in the jet engine. In addition, engine pressures are measured with piezoresistive transducers.

{% hint style="warning" %}
**NOTE: All combustion experiments are potentially hazardous. Please follow all precautions outlined in the safety section and given during the lab.**
{% endhint %}

## **Background**

### Temperature Measurements

There are a number of devices used for the measurement of temperature. Most rely on the effect temperature has on some other _measurable_ property of a substance. One of the oldest types is the expansion thermometer, which relies on the change in volume of a substance (usually a liquid) as the temperature varies. An example is the glass tube, mercury-filled thermometer, in which the height of the mercury column becomes a measure of temperature. While easy to manufacture, expansion thermometers are not easily implemented as small, compact electronic sensors.

Various electronic temperature sensors have been developed, including thermocouples, resistance thermometers and quartz resonance thermometers. In a quartz resonance thermometer, temperature is determined by its influence on the resonant frequency of a quartz crystal. Since frequency can be determined to great accuracy, these devices have potential for high resolution. Resistance temperature detectors (RTDs) rely on the change in resistance of a material with temperature; thus measurement of resistance is converted to a temperature measurement. There are two basic types of RTDs: metal based devices and semiconductor devices (also known as _thermistors_). While quite accurate temperature measurements can be obtained with RTDs and crystal thermometers,\* they are usually limited to “low temperature” operation. For example, platinum resistance thermometers can operate only up to \~1000°C, while thermistors are generally limited to a few hundred degrees Celsius. Thermocouples, on the other hand, can provide reasonably accurate measurements at temperatures up to at least 2600 K with proper choice of materials.

{% hint style="info" %}
\*Quartz resonance thermometers and RTDs can have precisions better than 10-4 °C.
{% endhint %}

#### **Thermocouple Principles**

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fae3610%2F-MMHuyGav47Xk9URWn6t%2F-MMI-aRliM3vzAx_LfHB%2F19.png?generation=1605562953809906\&alt=media)

> **Figure 1.** Simple (open) thermoelectric thermocouple circuit.

Thermocouples rely on the voltage produced by a temperature difference between two junctions formed between thermoelectrically dissimilar metals (see Fig. 1). In other words, a thermocouple is simply two different types of metals, usually in the form of wires, connected together. The voltage is produced because a temperature gradient in a metal conductor also induces a gradient in electron density in line with the temperature gradient. It can be shown that the voltage produced between the two junctions of the Fig. 1 circuit is given by:

$$
\large V=\int_{0}^{L}\varepsilon_A\frac{dT_A(x)}{dx}+\int_{L}^{0}\varepsilon_B\frac{dT_B(x)}{dx}dx
$$

(1)

where _T_(_x_) is the temperature distribution along each wire, and ε is called the thermoelectric power of the material.$$^†$$ Thus it can be seen that the **voltage difference is generated throughout the length of the wires**, and is due to the local temperature gradient.

{% hint style="info" %}
$$^†$$Equal to the sum of the Thomson coefficient and temperature derivative of the Peltier coefficient for the metal.
{% endhint %}

**When the wire is perfectly uniform in composition**, such that ε is not a function of position, and the two wires are connected between $$T_{cold}$$ and $$T_{hot}$$, the integrals in equation (1) become,

$$
\Large V=\int_{T_{cold}}^{T_{hot}}\varepsilon_adT+\int_{T_{hot}}^{T_{cold}}\varepsilon_BdT=\int_{T_{cold}}^{T_{hot}}(\varepsilon_A-\varepsilon_B)dT
$$

(2)

In this case, one can think of the voltage produced in a thermocouple as strictly due to the temperature difference between the junctions. It is important to remember that this holds only for the above **uniformity assumption**. In fact, some descriptions of thermocouples erroneously state that the voltage is produced “at the junction”, when in fact it is produced wherever there is a temperature gradient in the metal. The thermocouple circuit that will be considered the “ideal” circuit is shown in Fig. 2. The difference between it and the circuit of Fig. 1 is simply that the voltage is “measured” at the reference junction, instead of midway through one of the legs of the thermocouple. Note, both points in the reference junction must be at the same temperature (_isothermal_) to be equivalent to the circuit of Fig. 1.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2F9652027966841903ef1e5ceaf7fa2fd5fd49a057.png?generation=1610643643819000\&alt=media)

> **Figure 2.** Ideal thermoelectric circuit, with the thermocouple voltage measured across the _isothermal_ reference junction.

While any two metals with different ε can be used to produce a thermocouple,**\*\*** a small number of metals (both pure and alloys) have been identified for their stability, linearity, reproducibility, and high temperature capability. Table 1 lists some common pairs of thermocouple materials, including their approximate limiting operating temperature. Some of these are sufficiently common that they are considered standards and are denoted simply by a letter. For example, a chromel/alumel$$^{††}$$ device is called a “type K” thermocouple, and it has a nearly linear temperature sensitivity (see Fig. 3). The pairs of metals listed in Table 1 were also chosen for their good temperature sensitivity, which is normally achieved by picking materials that have ε with different signs. Figure 4 shows the voltage that would be generated along a single, homogeneous wire of various materials as a function of the temperature difference between its two ends. For the type K thermocouple, the chromel and alumel alloys produce voltages of opposite sign for the same temperature gradient.

{% hint style="info" %}
\*\*In fact, there have been a number of applications where the operating temperature of a machinery part has been measured using the machine structure itself as part of the thermoelectric circuit.

$$^{††}$$Chromel is a nickel-chromium alloy; alumel is a nickel-aluminum alloy
{% endhint %}

| **Material**                              | \*\*\*\*$$\bold{\textnormal{T}}_{\bold{\textnormal{max}}}$$  **°C (°F)** | **ANSI Type** | **Allowable atmosphere**                  | **Avg Output mV/100°C** |
| ----------------------------------------- | ------------------------------------------------------------------------ | ------------- | ----------------------------------------- | ----------------------- |
| Tungsten/ tungsten 26% rhenium            | 2320/4210                                                                | -             | inert,$$\textnormal{H}_2$$ (nonoxidizing) | 1.7                     |
| Tungsten 5% rhenium/ tungsten 26% rhenium | 2320/4210                                                                | -             | inert,$$\textnormal{H}_2$$ (nonoxidizing) | 1.6                     |
| Platinum 30% rhodium/ platinum 6% rhodium | 1820/3310                                                                | **B**         | oxidizing, inert                          | 0.76                    |
| Platinum 13% rhodium/ platinum            | 1770/3200                                                                | **R**         | oxidizing, inert                          | 1.2                     |
| Platinum 10% rhodium/ platinum            | 1770/3200                                                                | **S**         | oxidizing, inert                          | 1.0                     |
| Chromel/alumel                            | 1370/2500                                                                | **K**         | oxidizing, inert\*                        | 3.9                     |
| Chromel/constantan                        | 1000/1830                                                                | **E**         | oxidizing, inert\*                        | 6.8                     |
| Iron/constantan                           | 1200/2193                                                                | **J**         | reducing, inert, vacuum$$^†$$             | 5.5                     |
| Copper/constantan                         | 400/750                                                                  | **T**         | mild oxidizing, reducing vacuum, inert    | 4.0                     |

\*Limited use in vacuum or reducing environments\
$$^†$$Limited use in oxidizing at high temperature

> **Table 1**. Some standard thermocouple materials and their properties.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2F3860c17b72853679681a901bc21b7eb4fa86b52d.png?generation=1610643644463029\&alt=media)

> **Figure 3**. Sensitivity of a standard type-K thermocouple, based on ITS-90 inverse polynomial fit. The millivolt output is based on a reference temperature of 0°C.

The temperature behavior shown in Fig. 4 can be used to explain what happens in a thermocouple circuit like that of Fig. 2. Consider a type-J thermocouple connected between a reference junction at $$\textnormal{T}_{\textnormal{ref}}$$ and a junction at higher temperature, $$\textnormal{T}_{\textnormal{probe}}$$. As shown in Fig. 5, the voltage that would be produced is found by starting at the reference temperature, following a line with a slope equal to $$\varepsilon_{\textnormal{iron}}$$ up to $$\textnormal{T}_{\textnormal{probe}}$$, and then switching to a line with the slope of $$\varepsilon_{\textnormal{constantan}}$$ back to $$\textnormal{T}_{\textnormal{ref}}$$. Thus the constantan end of the reference junction will be at a higher voltage than the iron. If the temperature at the probe junction is raised, the thermocouple voltage increases. The reason that two dissimilar materials must be used is also evident in Fig. 5. If iron was used for both legs of the thermocouple, the voltage developed in the first leg of the circuit would be canceled as the temperature drops in the other leg, i.e., we would follow the iron curve upward to $$\textnormal{T}_{\textnormal{probe}}$$, and then back down to $$\textnormal{T}_{\textnormal{ref}}$$ with no net voltage induced.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2F627ed803200586112b5b05b420e5efee3220810f.png?generation=1610643644214886\&alt=media)

> **Figure 4.** Voltage−temperature response for several metals.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2F9a98b0c6470b00848e4b16661a0fd77498bc6020.png?generation=1610643643599203\&alt=media)

> **Figure 5**. Development of the voltage difference across the thermocouple, Vth, in a thermocouple circuit, like that of Fig. 2, formed by two metals.

While the circuit of Fig. 2 is ideal, it is usually not practical. First, thermocouple wire can be somewhat expensive. Thus it becomes costly if the measuring device needs to be located remotely from the experiment. Also, it is not uncommon to connect multiple thermocouples to a single measurement device through some sort of switching circuit. Finally, the measurement device may have wires and connectors of its own, which effectively become part of the thermocouple circuit. Therefore, it is important to consider modifications to the ideal circuit. For example, Fig. 6 shows a circuit in which the reference junction is connected to the measurement device through copper wires. As seen in Fig. 7, the voltage difference across the device junction ($$\textnormal{V}_{15}$$) is identical to the reference junction voltage ($$\textnormal{V}_{24}$$) **if the copper wires are identical**, and if the **device connections** (1 and 5) are both **at the same temperature**. In this case the voltage developed in leg 1-2 is counteracted by the voltage produced in leg 4-5.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fae3610%2F-MMHuyGav47Xk9URWn6t%2F-MMI-aRqJin-FS2eKGAx%2F24.png?generation=1605562953822978\&alt=media)

> **Figure 6**. Modified circuit; copper extension wires connect the thermocouple to the measuring device, and the device connections are at the same temperature.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2Fb5a74ef9235bbe809d7a224800c1961cf2de2205.png?generation=1610643643495177\&alt=media)

> **Figure 7**. Development of the thermocouple voltage difference for the thermocouple circuit shown in Fig. 6. If the wires connecting points 1 to 2, and 4 to 5 are identical, and the temperatures $$\textnormal{T}_{1}$$ and $$\textnormal{T}_{\textnormal{5}}$$ are the same, then the voltage measured across the device ($$\textnormal{V}_{15}$$) is equal to the voltage that would be produced by the ideal thermocouple circuit ($$\textnormal{V}_{\textnormal{th}}=\textnormal{V}_{24}$$).

#### **Thermocouple Referencing**

So far we have explored the thermocouple voltage that is produced between a junction at an unknown temperature $$\textnormal{T}_{\textnormal{hot}}$$ and another junction at $$\textnormal{T}_{\textnormal{ref}}$$. To convert the thermocouple voltage to the unknown $$\textnormal{T}_{\textnormal{hot}}$$ requires us to know two things: 1) the change in voltage associated a given temperature change, i.e., the temperature sensitivity of the thermocouple materials, and 2) $$\textnormal{T}_{\textnormal{ref}}$$.

First, consider ways to determine $$\textnormal{T}_{\textnormal{ref}}$$. There are two basic approaches: 1) create a situation where $$\textnormal{T}_{\textnormal{ref}}$$ is fixed by some physical condition, and 2) measure $$\textnormal{T}_{\textnormal{ref}}$$ with another device. A known temperature can be produced using a phase point of a material, for example 0°C can easily be produced to within 0.01°C accuracy by a bath of liquid water and ice, _if the ice and water are both present and allowed to come to equilibrium_ (this generally requires crushing the ice to small size and putting the mixture in an insulated container). If the reference junction (or points 2 and 4 in Fig. 6) are place in the ice bath, then $$\textnormal{T}_{\textnormal{ref}}$$ will essentially be 0°C. It many situations, however, it is impractical to require access to ice. Therefore, a popular approach is to measure the reference junction’s temperature with a thermistor or similar device that can provide accurate, absolute temperature measurements, _though_ _at low temperatures_.

With $$\textnormal{T}_{\textnormal{ref}}$$ known, all that remains is to convert the thermocouple voltage to temperature. Standard thermocouple materials have been extensively studied at the National Institute of Standards and Technology (NIST), and the voltage produced by a thermocouple at Thot is generally reported for $$\textnormal{T}_{\textnormal{ref}}=0\degree\textnormal{C}$$, and the values are available in tables, graphs (such as Fig. 3) or polynomial fits (see Table 2). If one is using a 0°C reference junction, then you simply look up the measured thermocouple voltage in the table (or graph or fit) and find the corresponding temperature. If you are using a different reference temperature, you must first add an offset voltage to your measured voltage. The offset is the voltage would be produced by a thermocouple at your measured $$\textnormal{T}_{\textnormal{ref}}$$ referenced to 0°C. Electronic ice reference circuits exist to do just this, the add the proper offset voltage to account for $$\textnormal{T}_{\textnormal{ref}}\neq 0\degree\textnormal{C}$$.

| **Temperature Range** | **0-500 °C**           | **500-1372 °C**        |
| --------------------- | ---------------------- | ---------------------- |
| **Voltage Range**     | **0-20,644 μV**        | **20,644-54,886 μV**   |
| $$\textnormal{a}_0$$  | 0.000000               | -1.318058×10$$^{2}$$   |
| $$\textnormal{a}_1$$  | 2.508355×10$$^{-2}$$   | 4.830222×10$$^{-2}$$   |
| $$\textnormal{a}_2$$  | 7.860106×10$$^{-8}$$   | -1.646031×10$$^{-06}$$ |
| $$\textnormal{a}_3$$  | -2.503131×10$$^{-10}$$ | 5.464731×10$$^{-11}$$  |
| $$\textnormal{a}_4$$  | 8.315270×10$$^{-14}$$  | -9.650715×10$$^{-16}$$ |
| $$\textnormal{a}_5$$  | -1.228034×10$$^{-17}$$ | 8.802193×10$$^{-21}$$  |
| $$\textnormal{a}_6$$  | 9.804036×10$$^{-22}$$  | -3.110810×10$$^{-26}$$ |
| $$\textnormal{a}_7$$  | -4.413030×10$$^{-26}$$ | -                      |
| $$\textnormal{a}_8$$  | 1.057734×10$$^{-30}$$  | -                      |
| $$\textnormal{a}_9$$  | -1.052755×10$$^{-35}$$ | -                      |

> **Table 2**. ITS-90 thermocouple inverse polynomials for type K thermocouples; two polynomial fits are listed, for separate temperature/voltage ranges. The reference junction is assumed to be at 0°C, and the polynomials are of the form, $$T=\Sigma a_i V^i$$, with _T_ in degrees Celsius and _V_ in microvolts.

#### **Gas Temperature**

Strictly speaking, a thermocouple sensor measures the temperature of the thermocouple junction itself, which of course is not what we usually want to know. Rather, we wish to determine the temperature of the body in which the thermocouple is embedded. For gas temperature measurements, the “body” of interest is the gas. As shown in Fig. 8, there are two basic thermocouple probe arrangements: one in which the thermocouple junction is immersed in the gas (_unshielded probe_); and one where the junction is inside some housing material (usually a metal), and the housing is immersed in the gas (_shielded probe_). The former provides a better measure of the gas temperature and a better time response; the latter approach protects the thermocouple from damage or exposure to incompatible gases (see Table 1). For high speed flows, there are also shielded _stagnation probes_, which are designed to slow the flow down to a very low velocity before it contacts the thermocouple junction (see Fig. 8 for a simple example).

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2Faa5d89432df8853a7612f42844bf9b9845e0c03d.png?generation=1610643645049774\&alt=media)

> **Figure 8**. Examples of unshielded, shielded and stagnation thermocouple probes.

In general, the thermocouple temperature can not exactly equal the gas temperature due to heat losses. Assuming the gas is the hotter material, it will heat up the initially colder thermocouple junction. If the thermocouple had no way of losing energy, then it would eventually heat up to the gas temperature. However, the thermocouple can lose heat; either by thermal conduction from the junction down through the thermocouple wires, or by radiation. Therefore even in steady-state operation, the thermocouple will tend to be at a lower temperature than the surrounding (hot) gas in low speed flows. For high speed flows, the thermocouple temperature will also be affected by the conversion of the flow’s kinetic energy to thermal energy in the region in front of the probe. Therefore in high speed flows, the thermocouple temperature will generally exceed the freestream static temperature.

### Pressure Measurements

You will also be making pressure measurements in this lab with a transducer that is something like the Barocel/Baratron type transducers used in a previous lab, i.e., a differential pressure is determined from the movement of a thin diaphragm exposed to the pressure difference. Instead of the capacitance based approach of the Barocel/Baratron devices, the sensors used in this lab consist of a miniature diaphragm and strain sensors composed of semiconductor material and manufactured using MEMS (Micromachined Electro-Mechanical Systems) technology. The sensors are described in more detail in a following lab.

### Turbine Engines

In most cases, with the exception of civil aviation, modern aircraft are powered by turbine engines (also called gas turbines). While piston engines are efficient for low power applications, their power (or thrust) to weight ratio drops significantly as engine power increases. This makes them unsuitable for large aircraft that require high power engines. Gas turbine engines are also used in a number of other applications including marine propulsion, operating gas pipeline compressors, and most notably, the generation of electric power.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2F49e563a215fcfbfbaffe8ecee276cfb5dfcad99d.png?generation=1610643644797737\&alt=media)

> **Figure 9**. Basic components of a gas turbine engine.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2Fc8dd0d650db0bd57a9af015c44656e4bd6a2edda.png?generation=1610643644138884\&alt=media)

> **Figure 10**. Basic components of a gas turbine engine.

The components of a basic gas turbine system are shown in Fig. 9. Air enters the engine (through an inlet not shown) and passes through a rotating compressor that raises the air pressure. Next, the high pressure air enters the combustor where it is mixed with fuel and burned without much change in pressure. The hot products then pass through a rotating turbine that extracts work from the flow and sends it to the compressor via a rotating shaft. The exhaust of the turbine is a hot, high pressure gas. In a **turbojet**, the exhaust is expanded through a nozzle (Fig. 10), which converts the thermal energy to kinetic energy, i.e., it accelerates the gas in order to produce thrust. On the other hand in a **turboshaft** engine, the hot, high pressure gas exiting the first turbine is expanded through a following power turbine that converts the thermal energy to shaft power, which can be used to run a rotor in a helicopter engine or to turn an electric generator in an aircraft’s auxiliary power unit (APU) or in a ground power station. In this lab, you will operate and perform measurements on an SR-30 turbojet manufactured by Turbine Technologies, Ltd. (Fig. 11), operating on Jet-A fuel.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fae3610%2F-MMHuyGav47Xk9URWn6t%2F-MMHyqSkQpo0_wUTUiWJ%2F29.jpeg?generation=1605562495353601\&alt=media)

> **Figure 11**. Schematic of the gas turbine system to be used in this lab.

#### **Thermodynamic Analysis**

The following is a brief description of the thermodynamic expressions used to analyze a jet engine.\*\*\* The processes that occur in a turbine engine can be modeled, _in the ideal case_,$$^{†††}$$ by a Brayton cycle. As shown in Fig. 12, the ideal compressor (2→3), turbine (4→5) and nozzle (5→e) can be modeled as isentropic processes (constant entropy, _s_). The ideal combustor (3→4) is modeled as a constant pressure heat addition, where the “heat” comes from burning the fuel, and the heat release rate is given by

$$
\large \dot{Q}=\dot{m}\times HV
$$

(3)

where $$\dot{m}_f$$ is the fuel mass flow rate and _HV_ is the heating value of the fuel (\~$$45\textnormal{MJ}/\textnormal{kg}_{\textnormal{fuel}}$$for most liquid jet fuels).

{% hint style="info" %}
\*\*\*A more detailed development can be found in the text for AE 4451, Hill and Peterson’s Mechanics and Thermodynamics of Propulsion.

$$^{†††}$$Meaning each component of the engine is reversible and has no heat losses
{% endhint %}

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2Fsync%2F5173e6a1f996ea596151387b761b2d33aa72aceb.png?generation=1610643644596541\&alt=media)

> **Figure 12**. Ideal Brayton cycle; stations 2-e correspond to the numbering scheme shown in Fig. 10.

For the three isentropic processes, we can find a relationship between the ratios of temperature (absolute, i.e., in Kelvin or Rankine units) and pressure (absolute, not gauge pressure) across each device from the entropy state equation for a perfect gas, i.e., for an isentropic process going from state a to state b,

$$
\Large 0=S_b-S_a=\int_{T_a}^{T_b}c_p\frac{dT}{T}-R\ln\frac{p_b}{p_a}\Rightarrow\frac{p_b}{p_a}=e^{\int_{T_a}^{T_b}\frac{c_p}{R}\frac{dT}{T}}
$$

(4)

Assuming that the gas is also calorically perfect ($$c_p$$=constant),

$$
\Large \frac{p_b}{p_a}=\left(  \frac{T_b}{T_a}\right)^{\frac{c_p}{R}}=\left(  \frac{T_b}{T_a}\right)^{\frac{\gamma}{\gamma-1}}
$$

(5a)

or equivalently for stagnation properties,

$$
\Large \frac{p_{ob}}{p_{oa}}=\left(  \frac{T_{ob}}{T_{oa}}\right)^{\frac{\gamma}{\gamma-1}}
$$

(5b)

where $$\gamma$$ is the ratio of specific heats ($$\gamma=c_p/c_v$$).

There is also a relationship between the stagnation temperature change across the compressor and turbine. Since the turbine is used to power the compressor, the output power of the turbine should equal the power input to the compressor (assuming steady operation and no shaft losses, which are typically less than 1% of the shaft power). Therefore from conservation of energy (_and for adiabatic conditions_),

$$
\large \dot{W_T}=(\dot{m_a}+\dot{m_f})c_{p,T}(T_{o4}-T_{o5})=\dot{m_a}c_{p,C}(T_{o3}-T_{o2})=\dot{W_c}
$$

(6)

where $$\dot{m_a}$$ is air mass flow rate entering the engine, and $$c_{p,T}$$ and $$c_{p,C}$$ are the (average) specific heats of the gases passing through the turbine and compressor. Similarly, the velocity at the nozzle exit can be found from

$$
\large u_e=\sqrt{2c_{p,N}(T_{oe}-T_e)}
$$

(7)

where $$c_{p,N}$$ is the (average) specific heat of the gas passing through the nozzle, and $$T_{oe}=T_{05}$$ (again _assuming the nozzle is adiabatic, i.e. no heat losses)_. For the combustor, again using energy conservation, we can calculate the expected change in temperature caused by burning the fuel:

$$
\large T_{o4}=(T_{o3}+f\space HV/c_{p,Combustor})/(1+f)
$$

(8)

where _f_ is the fuel-air ratio $$\dot{m_f}/\dot{m_a}$$.

If the compressor, turbine and nozzle are not ideal, i.e., they are not reversible (_but still adiabatic_), the temperature and pressure ratios across each component are related by the adiabatic component efficiencies:\*\*\*

$$
\Large \eta_{compressor}=\frac{(p_{o3}/p_{o2})^{\frac{\gamma-1}{\gamma}}-1}{(T_{o3}/T_{o2})-1}
$$

(9)

$$
\Large \eta_{turbine}=\frac{1-(T_{o5}/T_{o4})}{1-(p_{o5}/p_{o4})^{\frac{\gamma-1}{\gamma}}}
$$

(10)

$$
\Large \eta_{nozzle}=\frac{1-(T_{e}/T_{o5})}{1-(p_{e}/p_{o5})^{\frac{\gamma-1}{\gamma}}}
$$

(11)

Note, if the nozzle is truly adiabatic, then $$T_e/T_{o5}=T_e/T_{oe}=(p_e/p_{oe})^{\frac{\gamma-1}{\gamma}}$$.

We can also define an overall thermal efficiency of a static (stationary) turbojet engine, which is given by,

$$
\large \eta_{th}=\frac{\textnormal{Output Kinetic Power}}{\textnormal{Input Heat Rate}}=\frac{(\dot{m_f}+\dot{m_a})u_{e}^{2}/2}{\dot{m_f}HV}
$$

(12)

_If the turbojet is ideal_ (and $$c_p$$ is assumed constant throughout the engine), it can be shown that the thermal efficiency should solely be a function of the cycle pressure ratio:

$$
\Large \eta_{th}=1-\frac{1}{(p_3/p_2)}^{\frac{\gamma-1}{\gamma}}
$$

(13)

Thus as pressure ratio of the compressor increases, $$\eta_{th}$$ of the engine should increase.

## **Safety Considerations**

As with any combustion experiment **safety is a primary concern**. Improper operation of the jet engine can damage the engine, and pose a hazard to those nearby. Carefully follow all the safety instructions presented during the lab concerning startup, operation and shutdown of the engine. Do not operate the engine without direct supervision by the lab technician. Do not place any part of your body, or any objects in the inlet or exhaust regions. **All students working in the lab MUST WEAR safety glasses/goggles in the lab and hearing protection when the engine is operating** (both will be supplied to you).

## **Preliminary**

_The following items must be turned in at the start of your lab session._

1. Using the information supplied in Table 2, determine the thermocouple voltage you would expect to measure if the type-K thermocouple junction was at room temperature (\~74°F) and the reference junction was placed in an ice bath.
2. Bring a modified copy of the equation you developed in the earlier labs that relates dynamic pressure to velocity of a gas, and the ambient pressure and temperature. You need to **modify** the **equation** to use **dynamic pressure** in **psi** rather than mm H&#x67;**.**

## **Procedure**

### **Part A - Thermocouples**

**For this experiment you will need the items in the image below, where:**

* **A = Digital weather station** - used to measure atmospheric temperature and pressure
* **B = Anti-spill tumbler holder** - once you've filled the thermal tumblers, place them in here to prevent them tipping over and spilling
* **C = Thermal tumbler for iced water** - fill with ice and tap water from the combustion lab kitchen
* **D = Thermal tumbler for boiling water** - fill with boiling water from the combustion lab kitchen kettle
* **E = Thermocouple-to-multimeter adapter** (all copper wires)
* **F = Reference junction breakout cable** (copper wires between multimeter and terminal block, K-type thermocouple extension wire ([also known as KX wire](https://www.grainger.com/product/TEMPCO-Thermocouple-Extension-Wire-5ZY36))  between terminal block and thermocouple - this is a physical realization of the schematic in Figure 6 but with alumel and chromel)
* **G =** [**Cold junction compensator**](https://assets.omega.com/manuals/M0084.pdf) - an electronic device that acts as a surrogate ice bath reference
* **H = K-type shielded thermocouple**
* **J = Digital multimeter**

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2F2hZvpQGc62a5QMZnXwzM%2FTurbineEngineThermocouples.drawio.png?alt=media\&token=2d532441-d99b-46db-bbd1-9aa478030d65)

{% hint style="info" %}
Note that with all of these connectors and junctions, there is a reasonable chance that throughout the week at least one will loosen and allow a flaky electrical connection. If this occurs, check through the wiring and debug where any loose connections are, tightening any loose screws/connectors. The thermocouple connectors may be opened to reveal the screw terminals inside.

Also note that you should only record multimeter readings when the thermocouple output has stabilized. This can take a little time due to the thermal mass of the shielded thermocouple.
{% endhint %}

1. Locate the storage box containing all the items from the list above and prepare the iced and boiling water in the combustion lab kitchen. Be sure to keep the lids sealed tight to minimize temperature change, and to place the tumblers in the anti-spill tumbler holder.
2. Using the electronic weather station, record the ambient pressure and temperature.
3. Connect the thermocouple and the multimeter to the reference junction breakout cable (black cable to multimeter -COM port, red cable to +V.mA.Ω port).
4. With the multimeter set to read DC voltage ("°C/°F V" setting), record the voltage with the thermocouple exposed to:
   1. Ambient air
   2. Iced water
   3. Near-boiling water
5. With the thermocouple exposed to the ambient air, expose each of the terminal block junctions to the water baths. You should do this four times:&#x20;
   1. Where only the wires connected to the thermocouple are (reference junction)…
      1. In the ice water
      2. In the near-boiling water
   2. Where only the wires connected to the multimeter are (device junction)…
      1. In the ice water
      2. In the near-boiling water
6. Remove the multimeter and thermocouple from the reference junction breakout cable.
7. Connect the thermocouple directly to the cold junction compensator, and the cold junction compensator to the multimeter via the thermocouple-to-multimeter adapter.
8. _Having switched on the cold junction compensator_, record the voltage with the thermocouple probe exposed to:
   1. ambient air
   2. iced water
   3. near-boiling water
9. Close up the experiment:
   1. Turn off the cold junction compensator and multimeter.
   2. Disconnect all components.
   3. Pour out the tumblers and return to the holder with the lids off to air dry.
   4. Return everything to its storage box.
10. Proceed to the turbine engine experiment.

### Part B - Turbine Engine

{% hint style="danger" %}
The turbine engine can be extremely dangerous if not operated correctly. Follow the TAs instructions at every step, wear your ear and eye PPE, and never stand in front of the inlet port when running
{% endhint %}

1. Take a tour of the turboshaft engine cutaway in the Combustion Lab foyer.
2. Return to the lab turbojet engine, the [Turbine Technologies SR-30](https://www.turbinetechnologies.com/educational-lab-products/turbojet-engine-lab), and have the TAs help open the blast hood. You will need to un-brake the cabinet wheels, move it slightly so the extraction duct is clear, and then reapply the brakes.
3. Familiarize yourself with the flow path through the engine (the poster on the engine inlet and the LabView VI, as well as[ documentation from the manufacturer](https://www.turbinetechnologies.com/Portals/0/CAD%20Model%20Specs.pdf), may help also). Also observe how the throttle handle on the control panel varies engine throttle.
4. **With the electrical power and compressed air switched off, and with no one stood next to the control panel to accidentally switch something on:**
   1. Rotate the compressor by hand to check that it freely rotates. Have anyone who wants to do this also have a turn.
   2. Break your group into 2 sub-groups at random. Using the measuring tools provided, each person in the first sub-group will take turns measuring the outer diameter of the shaft, with each person in the other group measuring the inner diameter of the inlet. With the guidance of the TAs, compare individual results and select a final measurement for each dimension. These will be used to determine the cross-sectional area of the inlet.
5. Remove any foreign objects, replace the blast hood, and move back into place with the extractor slightly inside the hood and the wheel brakes applied.
6. Review the engine startup and shutdown procedure with the TAs (embedded below this list, and printed out on the engine control panel and by the PC). Familiarize yourself with the emergency exit routes, fire extinguisher locations, and emergency shutdown procedure.
7. Open the LabView VI and prepare it for recording:
   1. Hit run and choose a save location.
   2. Input the room temperature and pressure as read from the electronic weather station _(beware of units!)._
   3. Sanity check that the live readings make sense (the TAs will help):
      1. RPM will not be valid until running.
      2. Temperatures should be similar to room temperature.
      3. Pressures should be close to zero.
      4. Fuel flow rate should be around 0.5V.
   4. Hit "Record Data" to save a data point in non-running conditions.
8. Familiarize yourselves with Step 13 below for what will need to happen by way of data gathering when the engine is running.
9. Have everyone stand around the _**sides of the engine**_ so that they are both protected by the polycarbonate shields of the enclosure, and can see either the large monitor or the control panel. _**No one should stand beyond upstream of the inlet!!!**_
10. Designate one person to press the "RECORD DATA" button at each data point. Have them stand near the engine operator to co-ordinate timing.
11. Do all the steps in the startup procedure (taped to the engine control panel, and shown here below) right up to starting the engine.
12. Having put on your PPE and got your video camera ready _(for fun, not for a deliverable!)_, have the TA start the engine.
13. Once the engine is warmed up, acquire data as follows:
    * Capture data at _**roughly**_ the following RPMs:&#x20;
      1. Idle
      2. 35,000
      3. 40,000
      4. 45,000
      5. 50,000
      6. 55,000
      7. 60,000
      8. Full throttle
    * RPM lags throttle so allow the RPM to settle before taking a reading.
    * To minimize running time and thus fuel consumption, don't worry about hitting the above RPM targets perfectly... just get it within 1000 RPM or so and capture data.
    * DO NOT EXCEED 82,000 RPM.&#x20;
14. When you are finished, have the TA shutdown the engine according to the "Initial shutdown sequence".
15. Click "Done" in the LabView VI. Check the data is saved successfully by having the TA import it into MS Excel and compare the approximate order of magnitude of results with known good data.
16. If the data is not satisfactory, re-start the engine and repeat Step 13 onwards. If it is satisfactory, email the data to yourself or upload it to Canvas, then help the TA follow the "Full closedown sequence" procedure to turn off the compressed air, exhaust, etc.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2F1rqG1ZRZgkDWdXFLmzWA%2FAE3610%20Turbine%20Engine%20Operating%20Procedure%20January%202022.PNG?alt=media\&token=74d2b67c-4e00-4c34-8bb3-8c2e93d0c026)

## **Data to be Taken**

1. Ambient pressure and temperature.
2. Voltages from the type-K thermocouple probe connected to the voltmeter under the different connection and temperature cases described above.
3. Cross-sectional area of the compressor inlet.
4. Values of:
   1. dynamic pressure and $$T_{2}$$ at the compressor inlet
   2. $$T_{o3}$$ and $$p_{o3}$$ (gauge) at the compressor exit
   3. $$p_{o4}$$ (gauge) and $$T_{o4}$$ at the turbine inlet
   4. $$p_{o5}$$ (gauge) and $$T_{o5}$$ at the turbine exit
   5. $$p_{o6}$$ (gauge) and \~$$T_{o6}$$ at the nozzle exit
   6. pressure drop (a voltage signal) in the fuel system at various RPM settings.

## **Data Reduction**

1. Thermocouple probe temperatures reduced from the measured voltages (without heating or cooling the strip terminal junctions).
2. Air mass flowrate (from dynamic pressure at the compressor inlet).
3. Fuel mass flowrate (from fuel pressure reading and calibration, see Table 3).

| **Voltage (Volts)** | **Flowrate (cc/min)** |
| ------------------- | --------------------- |
| 1.7                 | 175                   |
| 2.2                 | 227                   |
| 2.8                 | 255                   |
| 3.0                 | 300                   |

> **Table 3**. Calibration data for fuel flowrate

1. Compressor efficiency.
2. Exit static temperature determined from the nozzle exit $$p_{o6}$$ (which is measured as a gauge pressure here) and the exit stagnation temperature $$T_{oe}$$.
3. Nozzle exit velocity.
4. An estimate of the heat loss rate from gas to the nozzle (based on the difference in stagnation temperature across the nozzle).
5. Compressor and turbine powers (assuming adiabatic operation).
6. The actual engine thermal efficiency.

## Results Needed for Report

1. Tables of the thermocouple voltages and reduced temperatures for the different cases.
2. Tables of the raw and reduced engine conditions at each operating RPM.
3. Plot of the compressor pressure ratio versus air mass flowrate.
4. Plot of the compressor efficiency versus air mass flowrate.
5. Plot of the heat loss in the nozzle rate versus air mass flowrate.
6. Plot of the engine thermal efficiency versus compressor pressure ratio.

## **Further Reading**

1. Philip Hill and Carl Peterson, _Mechanics and Thermodynamics of Propulsion_, 2nd edition, Prentice-Hall, 1992.
