Laboratory on Cascade Losses /HPT/KTH/NW 10/20/20181

laboratory on cascade losses /HPT/KTH/NW 10/20/20181

CONTENTS

NOMENCLATURE...... 2

1. INTRODUCTION AND OBJECTIVES...... 3

2. EXPERIMENTAL FACILITY...... 4

2.1. Introduction...... 4

2.2. Air Supply...... 4

2.3. Cascade Facility...... 7

3. MEASURING EQUIPMENT...... 9

3.1. Introduction...... 9

3.2. Side Wall Instrumentation (not existing presently)...... 9

3.3. Aerodynamic Probes...... 9

3.4. Temperature...... 13

3.5. Blade Surface Pressures (not existing presently)...... 13

3.6. Measurement Accuracy...... 13

4. HOW TO DETERMINE LOSSES...... 15

4.1. Equations for Determining the Loss Coefficient...... 15

4.2. To Obtain Average Values...... 17

5. HOW TO DO IN THE LABORATORY...... 19

5.1. Start the Test System...... 19

5.2. Measurements...... 19

5.3. Evaluation and Report...... 22

6. REFERENCES...... 23

Appendix 1:Coordinates of a Blade

Appendix 2:The General Requirements for Writing a Laboratory Exercise Report at The Chair of Heat and Power Technology

NOMENCLATURE

cabsolute velocity m/s

cheat exchange rate kJ/(kg oC)

cblade chordmm

Hspan of blademm

henthalpykJ/kg

hdifference of enthalpykJ/kg

ppressurePa

sdistance on pitch wise of cascademm

TtemperatureK

tblade pitchmm

utangential velocitym/s

flow angle between absolute velocity and o

axial direction of cascade

1,Rreading of probe angle down stream o

blades reference to vertical direction

ratio of heat exchange, cp/cv

stagger angleo

densitykg/m3

efficiency

difference of efficiency

coefficient of losses

index

0upstream of the cascade

1downstream of the cascade

cstagnation values in absolute frame of reference

cistagnation value at the cross section i, i=0, 1

ininlet

outoutlet

pprocess at the condition of the constant pressure

sisentropic

vprocess at the condition of the constant specific volume

1. INTRODUCTION AND OBJECTIVES

This laboratory exercise is incorporated in the lectures given as part of the curriculum "Thermal Turbomachines" in the Chair of Heat and Power Technology at KTH. Through this exercise, it is expected that participants will acquire some understanding about losses in turbomachines and know how to determine losses in a linear cascade measurement.

The exercise will be done at the linear test cascade which is fixed at the open subsonic wind tunnel system at the laboratory of the Chair of Heat and Power Technology, KTH. The main measurement equipment for this exercise are two aerodynamic probes and manometers. The flow through the cascade is air.

With the aerodynamic probes, total pressures at upstream and the downstream of the cascade will be measured for determining the losses.

Some details of the test facility, the exercise procedure and principle of determining the losses will be described in following chapters.

2. EXPERIMENTAL FACILITY

2.1. Introduction

The exercise will be done at the laboratory of Chair of Heat and Power Technology. The experiment facility for the laboratory consists of a air supply system and a test cascade.

Fig. 2.1 shows the plan of the testing room where the laboratory exercise will be done. It is situated at the entrance level in the Laboratory.

Fig. 2.1: Plan of the testing room

2.2. Air Supply

A flow scheme for the experiment facility is shown in Fig. 2.2. There is a compressor for supplying air flow at the basement of the Lab. Air is taken in the basement and flow along a horizontal pipe into a stagnation chamber. The flow changes direction to upstairs after the stagnation chamber, goes through a test section where a test cascade is located, and blows out after the test section.

Fig. 2.2: Flow scheme of the test facility

The technical data of the compressor is shown in table 2.1.

Table 2.1: Technical data of the compressor

2.3. Cascade Facility

Fig. 2.3 shows the scheme of the test section and cascade facility.

Fig. 2.3: The cascade facility.

The side walls of cascade facility, 3 in Fig. 2.3, are moveable, and the grid holder, 2 in Fig. 2.3, can be adjusted, thereby the inlet flow angle can be varied by changing the position of the side walls and the lean angle of the grid holder.

The cascade blades are shown in Fig. 2.4

Fig. 2.4: The cascade blades

Geometry of the cascade is shown in Table 2.2.

Table 2.2: geometry of test cascade

3. MEASURING EQUIPMENT

3.1. Introduction

Following measurements will be made, when the laboratory exercise is done

Upstream: pc0, total pressure

p0, static pressure (not existing presently)

Tc0, stagnation temperature (not existing presently)

Downstream:pc1, total pressure

p, difference of pressure measured by the probe

p1, static pressure, same value as atmosphere pressure patm

T1, temperature, same as environment temperature

On blade:static pressure distribution on the blade surfaces (not existing presently)

All pressure data are measured by manometers which are on the wall of the testing room. The resolution of these manometers is 9.8 Pa.

3.2. Side Wall Instrumentation (not existing presently)

The static pressure upstream of cascade will be measured by pressure taps on the side wall of the cascade facility. The taps will be connected to the manometer by a tube. The reading of the data can be taken from the manometer.

3.3. Aerodynamic Probes

Two aerodynamic probes are utilised for measuring total pressure and flow angle at upstream and downstream respectively. Probe HPT.00, a 4-holes probe, is at upstream of the cascade, and probe HPT.01, 5-holes probe is downstream of the cascade.

Fig. 3.1 shows the head part of the probe HPT.01. In Fig. 3.1, the middle hole is for measuring total pressure of flow, and the holes at the two sides are used for measuring a pair differential pressures which is for determining the pitch-wise angles of flow. There are two other holes, one at the cross section A-A in Fig. 3.1, the other one at the cross section B-B (same as the cross section A-A but in opposite direction), these two holes are for determining the span-wise angle of the flow.

Fig. 3.1: The head of the probe HPT.01

Fig. 3.2 shows the drawing of entire probe HPT.01.

Fig. 3.2.: Drawing of the probe HPT.01

Probe HPT.00 is shown in Fig. 3.3 and 3.4. In Fig. 3.3, the two holes at top and bottom are for measurement of the total pressure of the flow, and the other two holes at middle are used for measuring the pair differential pressures which determines the pitch-wise angles of flow.

Fig. 3.3: The head of the probe HPT.00.

Fig. 3.4.: Photo of the entire probe HPT.00.

The length of the probe HPT.00 shown in Fig. 3.4. is 500 mm.

In principle, pitch-wise angle and total pressure of the flow can be measured with these probes .

Fig. 3.5 shows the principle of measuring the pitch-wise flow angle with 3 holes on a probe.

Fig. 3.5: Principle of measuring the pitch-wise flow angle with a 3- holes probe

There is the relationship between the angle  and difference of pressurep=p1-p2, in Fig. 3.5. General speaking, the relationship can be expressed as:

=f(p)(2.1)

For each probe, the exact expression of the formula would be obtained after calibration of the probe.

For a good-manufactured probe, =0, when p=0.

It would be mentioned that the measurement with aerodynamic probes is concerning a wide field of aerodynamic knowledge which is not supposed to be introduced very much in this document. An interesting introducing about the probes could be obtained from many papers such as [Fransson & Sari, 1981] and [Dominy & Hodson, 1992].

In the exercise we will do, only the downstream flow angles will be measured with probe HPT.01. The upstream flow angle will be not measured since the probe HPT.00 is not satisfactory for measuring flow angles.

The probes are installed on the frame of the test cascade and are moveable along the pitch direction and span direction. Probes can be moved together in the pitchwise direction by the micrometer as shown in Fig. 2.3.

The total pressures at upstream and downstream of the cascade can be measured by probe HPT.00 and probe HPT.01 respectively. The pressure is read on the manometer which is connected to the probe.

By turning the downstream screw on the grid holder, the angle between probe HPT.01 and the downstream flow can be changed. When this angle is changed, the difference pressure p, which is measured by the two side holes on probe, is also varied. Until p is equal to zero, the angle between the probe and the flow (in Fig, 3.5) is zero. The angle of probe turned can be read on the scale on grid holder, thereby the flow angle at the outlet of the cascade can be obtained.

3.4. Temperature

The stagnation temperature at the inlet of the cascade is measured by a thermocouple which is installed ahead of the cascade (This measurement is not existing presently).

The downstream temperature is considered to be the same as the environment temperature which is measured with a normal temperature meter in the room.

3.5. Blade Surface Pressures (not existing presently)

In order to measure the static pressure distribution on the blade surfaces, some pressure taps will be manufactured on the blade. One row of the pressure taps will be on the middle span of the pressure surface of the blade, and another row will be on the middle span of the suction surface of the blade. Each tap is connected to a manometer on which the reading of the static pressure could be taken.

3.6. Measurement Accuracy

In the experimental studies, there are always measurement errors. General speaking, measurement accuracy could be affected by following aspects:

construction of measurement equipment

calibration of measurement equipment

installation of measurement equipment

conditions of measurements

human errors

In this laboratory exercise, the aerodynamic probes are the main measurement equipment. Comparing with others the construction and conditions of the probes will influence very much the measurement accuracy. For example, the diameter of the probes will influence the flow angle measurements. The smaller diameter the probes have, the better accuracy we get. It is difficult to estimate the accuracy of the probes. More information about the measurement accuracy of aerodynamic probes can be read from [Fransson & Sari, 1981] and [Dominy & Hodson, 1992].

The leakage from the tubes which connect the probes and manometers is another factor influencing the measurement accuracy, it is also difficult to estimate this error.

Resolution of the manometers can be estimated as 9.8 Pa.

Other errors could happen when you take the readings from the manometers, probe angle indicator, temperature meter and atmosphere pressure meter. So take readings correctly and try to avoid this kind of human error.

4. HOW TO DETERMINE LOSSES

4.1. Equations for Determining the Loss Coefficient

The efficiency of flow through a stator of turbine was defined by Söderberg [1989, p. 7.2.1] as:

(4.1)

and the coefficient of losses is as:

(4.2)

Fig. 4.1 shows enthalpy-entropy diagram for the flow in a turbine stage. The quantities in the equation 4.1 are shown in Fig. 4.1.

Let (4.3)

Substitute equation 4.3 into equation 4.1, we get:

(4.4)

from Fig. 4.1, we get:

(4.5)

(4.6)

(4.7)

For perfect and polytropic gas, there are basic thermodynamic relations as:

, ,

Substitute these thermodynamic relations and equation 4.6 into equation 4.5, we get:

(4.8)

In the same way, we can get:

(4.9)

Substitute equation (4.8) and (4.9) into equation (4.4) , and consider T00=T01, we get:

(4.10)

Then substitute equation (4.10) into equation (4.2), we finally get:

(4.11a)

Söderberg [1989] defined the stagnation values by "0". If we define the stagnation values by "c" (see the nomenclature in this note), equation (4.11a) will be changed to:

(4.11b)

In equation (4.11b) the losses coefficient  is determined by the upstream stagnation pressure pc0, downstream stagnation pressure pc1 and downstream static pressure p1.

At the test, pc0 and pc1 can be measured with the aerodynamic probes, p1 equal to atmosphere pressure. Thereby the losses coefficient  can be calculated with equation (4.11b).

4.2. To Obtain Average Values

With equation (4.11b), only the local loss coefficient at the measuring position will be determined. The average loss coefficient of the cascade must be calculated.

The averaged energy loss coefficient can be calculated on a mass-averaged basis [Mobarak et al, 1988].

According to mass-averaged basis, the general loss coefficient of the cascade with 3-D calculation is [Moore & Ransmayr, 1983]:

(4.12)

Here, c1n is the velocity component normal to the measuring plane downstream of the cascade, y and z are coordinates in pitch and span direction respectively.

In our exercise, the variation of the loss coefficient along the blade span direction is not concerned, so the above equation could be simplified as:

(4.13)

Here, s is the distance between every two measuring position in pitch direction, and subscript i represents different measuring positions.

From state equation,

1i=p1/RT1(4.14)

Since pressure p1 and temperature T1 are constant, the interval s is also constant we get:

(4.15)

In equation (4.15), the local loss coefficient i can be calculated by equation (4.11b), the normal velocity component c1ni can be calculated by:

c1n=c1 cos(1) (4.16)

and from Fig. 3.1:

c12=2(hc0-h1) (4.17)

From

(hc0-h1) =cp T1(Tc0/T1-1), and

Then, we get:

(4.18)

and

(4.19)

In this equation, pc0, p1 and 1 are measured by the aerodynamic probes, T1 is environment temperature and measured by the temperature meter. The c1n must be calculated at every measuring position with above measured values.

After local loss coefficient are calculated with equation (4.11b), the average loss coefficient of the cascade can be calculated from equation (4.19) and (4.15).

5. HOW TO DO IN THE LABORATORY

5.1. Start the Test System

The start of the test system is, in principle, taken care by an assistant. The process of this is (see Fig. 2.2):

1.Ensure that all of the equipment in the test section is fixed.

2.Make sure that the by-pass valve (3), which is for speed regulating, is opened.

3.Start the wind tunnel motor with the switch button (7) which is placed in the test room beside the pressure air manoeuvring bar (10). Wait until the motor has reached the right speed and the Y-D switch is ready. Then a lamp will be lighted on the manoeuvring device.

4.Open the inlet valve with the manoeuvring bar (10).

5.2. Measurements

At the test, the pc0 and pc1 are measured with the pneumatic probes. The value pc1 and (pc0-pc1) can be read from the manometers on the wall of testing room.

After the wind tunnel started, keep watching on the manometers to see if the pressure readings on it become stabilised. If the pressure is stable, make measurements as following:

1.Write down the flow inlet angle 0 in table 5.1.

2.Read the atmosphere pressure value from the atmosphere meter and write it down in table 5.1 as p1.

3.Read the environment temperature from the meter and write it down in table 5.1 as T1.

4.Check the spanwise position of downstream probe, then write down the position on table 5.1.

5. Check the angle of the downstream probe, make sure that the middle hole of probe point down and the half circle block on the end of the probe is horizontal. Remember this angle as the reference angle of the probe direction

6.Write the initial measurement position in table 5.1 as s=0.

7.Turn the downstream probe slowly and watch the manometer of the difference pressure of the probe until this difference pressure equal zero. Read the angle difference, 1,R, between the existing probe direction and the reference direction (vertical direction) on the scale. Write the reading in table 5.1.

8.Read the pc1 value from the manometer and write it down in table 5.1.

9.Read the value (pc0-pc1) from the manometer and write it down also in table 5.1.

10.Move the probes 2 mm along the pitch direction with the screw on the test grid, and write down the new measurement position, s, in table 5.1.

11.If the values on the manometers are stable, repeat to do as 7, 8, 9 and 10, and so on until measurements are made at all positions.

The test would be finished after measurements have been done over 2 pitch, 44 mm, of distance, i.e. probes will be moved 23 times along the pitch direction if the moving is with the step of 2 mm.

Table 5.1: Measured and calculated values

5.3. Evaluation and Report

After the measurements are finished, following evaluations are supported to be performed and reported:

1. Calculate the downstream flow angle, 1, by equation (5.1) : 1 = 1,R - 0 (5.1)

1. Calculate the upstream total pressure pc0 and the ratio (pc0-pc1)/pc0.

1. Calculate c1n, the normal component of downstream flow velocity, with equation (4.19), =1.4, and cp is chosen according to T1.

1. Calculate the local loss coefficient with equation (4.11b).

1. Calculate the total average loss coefficient with equation (4.15).

1. Calculate the cascade efficiency  with equation (4.2).

1. Construct the diagram with "(pc0-pc1)/pc0" as function f(s) on a millimeter paper.

1. Discus the results and write a report for this laboratory exercise including the measured data, evaluated results and discussions. The general requirements for writing a laboratory exercise report at The Chair of Heat and Power Technology are listed in Appendix 2.

The different groups will perform this laboratory with different test cases, i.e. with different inlet angles, Reynolds number or spanwise measurement positions of the downstream probe on the same cascade. When all the group finish their tests, the results will be put together in a suitable form, for example as diagram with the loss as the function of the inlet angle. Attached this should be commentaries with comparisons between the measurements and a possible computer calculation.