HM284_e - V1.5

Experiment Instructions HM 284

Series and Parallel Connected Pumps

HM 284

3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

SERIES AND PARALLEL CONNECTED PUMPS

Experiment Instructions Dipl.-Ing. (FH) Dipl.-Ing.-Päd. Michael Schaller

This manual must be kept by the unit. Before operating the unit: - Read this manual. - All participants must be instructed on handling of the unit and, where appropriate, on the necessary safety precautions.

Version 1.4

Subject to technical alterations

i

HM 284

ii


HM 284


Table of Contents 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Didactic notes for teachers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2

Safety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Intended use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Structure of safety instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5


2.3 Safety instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Ambient conditions for the operating and storage location . . . . . . . . . 7 3

Description of the HM 284 device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1 Fluid energy machines range and introduction to HM284. . . . . . . . . . 9 3.2 Process schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Device design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Device function and components . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.5 Operation and measurement data acquisition. . . . . . . . . . . . . . . . . . 13 3.5.1

Program installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5.2

Program operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.6 Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.7 Operating modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.7.1

Pump in standalone operation . . . . . . . . . . . . . . . . . . . . . . . 18

3.7.2

Pumps in series operation . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.7.3

Pumps in parallel operation . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.8 Decommissioning, storage and disposal . . . . . . . . . . . . . . . . . . . . . . 21

iii

HM 284

4


Basic principles for GUNT Labline fluid energy machines . . . . . . . . . . . . . 23 4.1 Classification of fluid energy machines . . . . . . . . . . . . . . . . . . . . . . . 23 4.1.1

Power machines / work machines . . . . . . . . . . . . . . . . . . . . 24

4.1.2

Turbomachines / positive displacement machines . . . . . . . . 24

4.2 Fundamental physical principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2.1 4.2.1.1 4.2.1.2 4.2.1.3 4.2.1.4

Laws of conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Continuity equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Conservation of momentum . . . . . . . . . . . . . . . . . . . . . . . . . 28 Conservation of energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Bernoulli's principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2.2 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2.2.1 Specific work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5

4.2.3

Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.4

Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2.5

Energy conversion in the motion of fluid. . . . . . . . . . . . . . . . 41

Further basic principles for HM 284 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.1 Converting pressure energy into velocity . . . . . . . . . . . . . . . . . . . . . 45 5.1.1

Supply pressure and head of centrifugal pumps . . . . . . . . . 45

5.2 Pump characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.3 System characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.4 Operating point: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.5 Pumps in series and parallel connection . . . . . . . . . . . . . . . . . . . . . . 51

iv

5.5.1

Parallel connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.5.2

Series connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.5.3

Selecting the type of connection. . . . . . . . . . . . . . . . . . . . . . 55

HM 284

6


Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.1 Experiment 1: Recording a system characteristic curve . . . . . . . . . . 60 6.1.1

Objectives of the experiment . . . . . . . . . . . . . . . . . . . . . . . . 60

6.1.2

Conducting the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.1.3

Measured values with calculations of the analysis . . . . . . . . 61

6.1.4

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.1.5

Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.2 Experiment 2: Determining the reference speed . . . . . . . . . . . . . . . . 67 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

6.2.1

Objective of the experiment: . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.2.2


6.3 Experiment 3: Determining the pump characteristic curve . . . . . . . . 68 6.3.1


6.3.2


6.3.3

Measured values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.3.4.1 Pump characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.3.4.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.3.5

Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.4 Experiment 4: Pumps in series operation . . . . . . . . . . . . . . . . . . . . . 76 6.4.1


6.4.2


6.4.3

Measured values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.4.4

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.4.5

Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.5 Experiment 5: Pumps in parallel operation . . . . . . . . . . . . . . . . . . . . 81 6.5.1


6.5.2


6.5.3

Measured values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.5.4

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.5.5

Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

v


HM 284

6.6

7

Final analysis of the experiments and proposal for further experiments. . . . . . . . . . . . . . . . . . . . . . . . . 85

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.1 Technical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.2 List of formula symbols and units . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.3 Tables and graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

vi


HM 284

1

Introduction

The HM 284 "Series and Parallel Connected Pumps" device is part of the GUNT Labline fluid energy machines series. The GUNT Labline fluid energy machines allow experiments on power engines and machines such as pumps, fans and water turbines. All devices in the GUNT Labline fluid energy machines range are equipped with electronic sensors for PC-based measurement data acquisition and are operated from a PC. Measurements can be represented graphically and characteristics can be recorded using the measurement data acquisition software provided. The GUNT Labline series of devices puts the HSI "Hardware-Software Integration" product approach into effect.


The experimental unit is designed as a tabletop device. The measurement data acquisition software supplied and a PC provided by the customer are required to operate the HM 284 device. Centrifugal pumps belong to the group of dynamic pumps. They are the most widely used type of pump in the world. The advantages are mainly: – simple design – no oscillating masses – few parts – little wear – reliable – suitable for different media – direct coupling to electric motor without gearing.

1 Introduction

1

HM 284


If necessary, different operating ranges can be covered by connecting two or more pumps. The centrifugal pumps in HM 284 pump water. HM 284 essentially consists of the centrifugal pump with drive motor, the throttle valve, the flow meter and the water tank. These components are connected to the water circuit by pipes.

Characteristic curves and operating points can be recorded by: • Using the throttle valve to vary the flow resistance. • Variable speed at pump 1 and optionally switchable pump 2. • Varying the pump circuit (series and parallel connection).

Learning objectives for the centrifugal pump are:

• Principle of operation of a centrifugal pump • Recording a system characteristic curve • Recording a pump characteristic curve • Identifying characteristic data • Investigation of typical dependencies (flow rate and the supply pressure dependent on the speed).

2

1 Introduction


HM 284

1.1

Didactic notes for teachers HM 284 can be employed both in the training of skilled workers and in academic engineering education.

Areas where the HM 284 experimental unit can be employed include:  Demonstration experiments

The demonstrator operates the previously prepared experimental unit while a small group of five to eight students observe. Key effects can be demonstrated over an operating time of half an hour.


• Practical experiments

Small groups of two or three students can carry out experiments for themselves. The time required to record measurements and some characteristic curves can be estimated at about one hour. • Project work HM 284 is particularly well suited to carrying out project work. In addition to detailed studies using HM 284, it is possible to conduct a wide range of comparative experiments using the separate HM 283 centrifugal pump and comparisons to the HM 285 and HM 286 positive-displacement pumps .

In this case a single, experienced student can operate the experimental unit.

These materials are intended to be used to help you prepare your lessons. You can compose parts of the material as information for students and use it in class.

1 Introduction

3

HM 284


We also provide these experiment instructions in pdf format on a CD to support your lessons. We grant you unlimited reproduction rights for use within the context of your teaching duties.

We hope that you enjoy using this experimental unit from the GUNT Labline range and wish you success in your important task of introducing students to the fundamentals of technology. Should you have any comments about this device, please do not hesitate to contact us.

4

1 Introduction


HM 284

2

Safety

2.1

Intended use

The unit is to be used only for teaching purposes.

2.2

Structure of safety instructions

The signal words DANGER, WARNING or CAUTION indicate the probability and potential severity of injury.


An additional symbol indicates the nature of the hazard or a required action.

Signal word

DANGER

Indicates a situation which, if not avoided, will result in death or serious injury.

WARNING

Indicates a situation which, if not avoided, may result in death or serious injury.

CAUTION

Indicates a situation which, if not avoided, may result in minor or moderately serious injury.

NOTICE

2 Safety

Explanation

Indicates a situation which may result in damage to equipment, or provides instructions on operation of the equipment.

5

HM 284


Symbol

Explanation Electrical voltage

Hazard area (general)

Note

Wear ear defenders

6

2 Safety

HM 284

2.3


Safety instructions

WARNING Electrical connections are exposed when the switch cabinet is open.

Risk of electrical shock. • Disconnect the plug from the power supply before opening the switch cabinet. • All work must be performed by trained electricians only.


• Protect the switch cabinet from humidity.

WARNING Noise emission > 80dB(A).

Risk of hearing damage. • Wear ear defenders.

NOTICE

To prevent algae growth and sludge formation: • Only operate the device with water of potable quality.

2.4

Ambient conditions for the operating and storage location

• Enclosed space • Free from dust and humidity. • Tabletop. • Frost-free.

2 Safety

7

HM 284

8


2 Safety

HM 284


3

Description of the HM 284 device

3.1

Fluid energy machines range and introduction to HM284

The fluid energy machines range allows experiments on power engines and machines such as pumps, fans and water turbines. The HM 284 "Series and Parallel Connected Pumps" device is part of the fluid energy machines series. HM284 allows experiments on interconnected centrifugal pumps and is a fully functional stand-alone experimental unit.


The range of devices includes the other experimental unit that covers a similar topic: • HM 283, Experiments with a Centrifugal Pump

Comparative experiments across devices can be used to achieve additional learning goals. Comparative measurements across devices using the pumps and fan/compressor in this range are recommended and offer additional benefits.

The following chapters provide a detailed description of the HM284 supply unit.

3 Description of the HM 284 device

9


HM 284

3.2

Process schematic

Fig. 3.1 shows the process schematic of the experimental unit with all measuring points and essential components.

Measuring points Energy input Pel of pump 1 · Volume flow V Pressure p1 upstream of pump 1 Pressure p2 downstream of pump 1 Pressure p3 downstream of pump 2

Fig. 3.1

10

Components Pump 1 Pump 2 Three-way valve for selecting operating mode Valve for pump 2 Valve for volume flow quantity Outlet valve

HM284: Process schematic



HM 284

3.3

Device design

The practical implementation of the process schematic can be seen in Fig. 3.2. The measuring points and components listed above can be seen in the diagram. 8


7

6

9

5 4 3

10 11

12

1 2 3 4 5 6

Pump P2 Pump P1 Pressure p1 upstream of pump P1 Pressure p2 downstream of pump P1 Pressure p3 downstream of pump P2 Three-way valve for operating mode, V1

Fig. 3.2

1

2

7 Volume flow sensor, FI1 · 8 Valve for flow rate V , V3 9 Water tank 10 Shut-off valve for pump P2, V2 11 Outlet valve, V4 12 Housing

HM 284: Main components


11

HM 284

3.4


Device function and components

The experimental unit consists of the controllable pump P1 (2) and the optionally switchable constant-speed pump P2 (1). Water is sucked in from the water tank (9) and pumped through the piping in the circuit. The experimental unit can be operated in a variety of different operating modes using the 3-way valve for the operating mode (6) and the shut-off valve for pump P2 (10). The valve for flow rate (8) is used to adjust the system's flow resistance. In this way, it is possible to analyse the behaviour of the pressures p1, p2 and p3 (3, 4, 5) and the flow rate (7) of the system and the pumps. Relatively small cross-sections of the suction lines affect the system characteristics in operation and can be used to evaluate the flow configuration and to expand knowledge of fluid mechanics.

12



HM 284

3.5

Operation and measurement data acquisition 16

15

The main switch (16 in Fig. 3.3) is used to turn the power supply on and off. It uses a I/0 rocker switch design. The connection sockets are located next to the main switch (power supply no. 13, USB no. 14). The fuse holder (15) holds the two microfuses.


The integrated microcontroller board is used to control the device and for measurement data acquisition.

Fig. 3.3

The measurement data acquisition program provided is used both to operate the experimental 13 14 unit and to detect and display the measurement Rear of the device, with main switch and connection sockets data. The measurement data acquisition program (referred to simply as the program below) is installed on a PC provided by the customer (cf. Chapter 3.5.1, Page 15). The experimental unit and the PC are connected via the USB port. The program is used to operate the radial fan (switch on, change speed and switch off). The program offers the following options for displaying the current measured values and calculated values: • System diagram

Fig. 3.4

Rear of the device, with cables connected


• Graphical values.

presentation

of

the measured

• The available measured values and calculated values are recorded in measurements files. These measurements files can be imported into a spreadsheet program (e.g. MS Excel®) for further processing.

13

HM 284


The program's help feature explains how to use the program (see also Chapter 3.5.2, Page 16).

It should also be pointed out that the measured values and calculated values are measured continuously in rapid succession. These values are averaged before they are displayed and written to the data file. This mostly compensates for fluctuations. "Taring" the values at standstill sets the applied pressures to zero at the moment of taring. The effect of taring can be clearly seen while the program is running.

14


HM 284

3.5.1


Program installation

Required for installation: • A ready-to-use PC with USB port (for minimum requirements see Chapter 7, Page 87). • G.U.N.T. CD-ROM NOTICE! All components required to install and operate the program are included on the CDROM provided by GUNT with HM 284. No other tools are required.


Installation procedure NOTICE! The device must not be connected to the PC's USB port while the program is being installed. The device may only be connected after the software has been successfully installed.

• Start the PC. • Insert GUNT CD-ROM. • In the "Installer" folder, launch the "Setup.exe" installation program. • Follow the installation procedure on screen. • Installation will run automatically after starting it. The following program components are installed onto the PC: – LabVIEW® - Runtime software for PCbased data acquisition. – Driver routines for USB data acquisition. • After the installation has finished, restart the PC.


15

HM 284

3.5.2


Program operation

• Select the program and start via: Start / Programs / G.U.N.T. / HM 284 • When you start the software for the first time after installation you are prompted to select the desired language for the program operation. Notice! The language may be changed at any time in the " Language" menu. • Afterwards the system diagram for HM 284 appears on the screen. Fig. 3.5

Language selection

• Various pull-down menus are available for other functions. • For detailed instructions on use of the program refer to its Help function. You can get to the help function via the "?" pull-down menu and selecting "Help".

16


HM 284

3.6


Commissioning

• Observe the safety instructions (cf. Chapter 2, Page 5 ff.) • Install the measurement data acquisition program on the PC (cf. Chapter 3.5.1, Page 15f). • Connect the experimental unit to the PC using the USB cable provided (USB connection socket see no. 14 in Fig. 3.3, Page 13). 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

• Fill the water tank with potable water up to the height of the baffle plate. You may also add algae retardants to the water. NOTICE

• Evaporation may lead to calcium deposits in the water tank, therefore GUNT recommends draining the water should the device not be in operation for a long time (> 1 week).

• Bleed the transparent pump housings using the bleed valves. NOTICE

Risk of damage to the device. • Before connecting to the electrical power supply: Make sure that the laboratory power supply meets the specifications on the device's rating plate.

• Connect experimental unit to the mains power supply.


17

HM 284


• Turn main switch (no. 16 in Fig. 3.3, Page 13) to "1". • Turn on PC and launch program measurement data acquisition.

for

• Press "Tare" button to calibrate to zero. • Turn on the pump(s) via the program.

• Check that each component is functioning correctly. • Switch off pump. • Main switch to "0". • Disconnect experimental unit from mains electricity supply.

3.7

Operating modes

3.7.1

Pump in standalone operation

To set the experimental unit to standalone operation, valve V1 must connect the pump P1 directly to valve V3. To achieve this, the lever on valve V1 must be rotated until the symbol assumes the position as shown in Fig. 3.6.

Fig. 3.6

HM 284 in standalone operation

In this valve position, pump P2 has no function. Valve V2 must be closed so as to avoid possible backflow through pump P2. Pump P1 draws in water from the tank and pumps it through valve V1 and V3 back into the tank. By throttling the volume flow with valve V3, it is possible to vary the resistance against which the pump works. The behaviour of pump P1 can then be analysed.

18


HM 284

3.7.2


Pumps in series operation

To set the experimental unit to series operation, valve V1 must connect the pressure side of pump P1 to the suction side of pump P2. To achieve this, the lever on valve V1 must be rotated until the symbol assumes the position as shown in Fig. 3.7.


Fig. 3.7

HM284 in series operation

Pump P2 is only supplied with water from pump P1. Valve V2 must be closed so as to avoid flows into or out of the tank.

Pump P1 sucks in water from the tank. The pressure is increased and the water fed to pump P2, where a further pressure increase takes place. Before the water is pumped back to the tank, the volume flow can be throttled with valve V3. The pumps then work against an increased resistance.


19

HM 284

3.7.3


Pumps in parallel operation

To set the experimental unit to parallel operation, valve V1 must connect the pressure side of pump P1 directly to valve V3. To achieve this, the lever on valve V1 must be rotated until the symbol assumes the position as shown in Fig. 3.8.

Fig. 3.8

HM284 in parallel operation

Pump P2 provides additional volume flow to pump P1. Pump P2 requires a separate water supply for this purpose. This is done by opening valve V2 on the suction side. Pump P1 and pump P2 suck in the water out of the tank and compress it together via valve V3 back into the tank. By throttling the volume flow with valve V3, it is possible to vary the resistance against which the pumps work.

20


HM 284

3.8


Decommissioning, storage and disposal

• Observe the safety instructions (cf. Chapter 2, Page 5 ff.) • If not yet done: – Disconnect experimental unit from mains electricity supply. – Disconnect connection between PC and experimental unit (USB cable). • Thoroughly clean the entire experimental unit.


– Do not use any aggressive cleaning agents to clean the device. GUNT recommends a mild acetic cleaner. – Only soft cloths should be used for cleaning, in order to avoid chafing on the transparent water tank. Store the experimental unit and components under cover, clean, dry and free of frost.


21

HM 284

22



HM 284

4


Basic principles for GUNT Labline fluid energy machines

The basic principles set out in the following make no claim to completeness. For further theoretical explanations, refer to the specialist literature.

More detailed knowledge is examined in the subsequent section on device-specific basic principles. 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

4.1

Classification of fluid energy machines

Fluid energy machines are flowed through by a fluid; this can be a gas or a liquid. When flowing, energy is exchanged between the fluid energy machine and the fluid. The extensive field of fluid energy machines can be divided into many subject areas. This section on the basic principles looks at two key criteria for differentiation in more detail.

4 Basic principles for GUNT Labline fluid energy machines

23

HM 284

4.1.1


Power machines / work machines

The distinguishing characteristic of this classification is the direction of the flowing energy. Power machine: The fluid's energy is removed by the machine and converted into the shaft's mechanical energy. Typical examples include water turbines used in the provision of electricity. Work machine: The machine transfers energy to the fluid. The pressure and/or the flow velocity of the fluid increases. One typical application is a water pump.

4.1.2

Turbomachines / positive displacement machines

The distinguishing characteristic is the functional principle. Turbomachine: Energy is continuously added to or removed from the flow by deflection at stator and rotor blades. This kinetic energy of the fluid is converted into pressure energy (work machine) or mechanical energy (power machine). The fluid is conveyed continuously. No abrupt change in the energy transfer can be detected. Positive displacement machine: A changeable volume drives the fluid or is driven by the fluid. The pressure difference across the machine must be big enough to overcome flow resistances (work machine) or mechanical resistances (power machine). The fluid flow and the movement of the machine are coupled.

24


HM 284

4.2


Fundamental physical principles

The following section looks at the physical principles with reference to fluid energy machines.

4.2.1

Laws of conservation

The laws of conservation describe variables that do not change in the fluid energy machine, in other words that are preserved. 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

4.2.1.1

Continuity equation

The continuity equation states that the mass flow that flows through a system remains constant. ·

· m = V  

A = c = · = m · V =  =

=

c  A   = const

(4.1)

Cross-section area in m2 Flow velocity in m/s Mass flow in kg/s Volume flow in m3 /s Density in kg/m3

In incompressible fluids, the density  is not dependent on the pressure. Gases at low pressure differences can also be considered as incompressible. In this case, the formula can be reduced to: ·

V = c  A = const

(4.2)

Usually two points in the flow are compared to each other. The path traced by a fluid particle is referred to as the flow filament. These flow fila-


25


HM 284

ments are found in the flow conduit as a bundle, which represents the flowed-through shape. Nozzle

Flow filaments

Inlet

Outlet c 2

Fig. 4.1

In an incompressible medium it follows: c 1  A1

A1

c 1

The significance of the continuity equation is particularly evident when comparing diffuser and nozzle.

A2

Schematic change in velocity in the nozzle of a Pelton turbine

=

c 2  A2 and from this:

c 1

A 2

c 2

A1

----- = ------

(4.3)

A = Cross-section area in m2 c = Flow velocity in m/s

The velocities are inversely proportional to the flow cross sections. Nozzle

Flow filaments

c 1

c 2 A2 t e

A1

l t u O

Inlet Fig. 4.2

26

Nozzle: The flow velocity is accelerated by the cross section becoming smaller.

Fig. 4.1 shows an adjustable nozzle, as used in Pelton turbines. Fig. 4.2 is a nozzle in which the outlet cross section is reduced by means of blades and deflection.

Nozzle: change in velocity by means of flow deflecting blades



HM 284

Diffuser

Outlet A2 t e l n I

A1

c 1 Fig. 4.3 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

c 2

Diffuser: The flow velocity c is decelerated by the flow cross section becoming larger.

The diffuser in Fig. 4.3 is similar in design to the nozzle (Fig. 4.2). In this case though, the arrangement of the blades results in an increase in the size of the cross section A.

Flow filaments

With a known surface area ratio, it is therefore Diffuser: change in velocity by possible to calculate the resulting change in means of flow deflecting velocity. blades Fig. 4.4 shows the blades of an axial turbine. While the first blade row is formed as a nozzle, the second blade row initially only appears as a deflection.

Nozzle Fig. 4.4

Deflection

The nozzle of an axial turbomachine


27

HM 284

4.2.1.2


Conservation of momentum

Momentum is a kinetic quantity. The variables of mass m and velocity c are applicable: I

=

m  c

(4.4)

c = Flow velocity in m/s I = Momentum in Ns m = Mass in kg

A change in momentum takes place as a result of a change in the velocity c . The change in velocity -- . As a result of is caused by an acceleration a = c

t

this relationship, a force is connected to the term of the change in momentum: I

=

m  a  t = F  t

(4.5)

or for a mass flow: I a = F = · = m t =

=

· m  c  t = F  t

(4.6)

Acceleration in m/s² Force in N Mass flow in kg/s Time in s

The momentum is a directional quantity. The quantities I , c and F all point in the same direction.

28



HM 284

Looking at these formulae it can be seen that the momentum changes when a force acts.

c 2y

c 2

Fig. 4.5 shows how a water jet is deflected at a blade. While the value of the velocity c remains constant, the horizontal velocity component changes its algebraic sign.

c 2x F c 1y

c 1y

c 1 ·

m 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

Fig. 4.5

=

c 2y

c 1x

c 2x

= –

A force has to act on the blade so that the deflection can take place; with Formula (4.6) we get:

c 1x

A water jet is deflected at a blade

F

=

· m   c 2x – c 1x 

F

=

· m   2   – c 1x  

c = Flow velocity in m/s F = Force in N · m = Mass flow in kg/s

The momentum is transferred from one body to another when a force acts. Within a system that has no interaction with its surroundings, the momentum is constant. Nozzle

c 2y

c 2 c 2x

c 1

F x F y

Fig. 4.6

F

Changes in velocity also occur in the previous example of diffuser and nozzle. Forces are also acting here. Fig. 4.6 illustrates this schematically on the blade of a nozzle. The force F acting on the blade corresponds to the force which deflects the fluid.

Nozzle: retention force to keep the blade in position.


29


HM 284

4.2.1.3

Conservation of energy

Work and energy are similar quantities. Accordingly, energy is also stated in units of joules. Energy is the capacity to do work. Energy can be present in various forms (this list only represents a small selection): – Mechanical energy • Kinetic energy • Potential energy • Spring energy – Thermal energy – Electrical energy – Chemical energy – Hydraulic energy • Hydrostatic energy • Potential energy • Hydrodynamic energy The forms of energy can be converted from one form to another. In engineering, machines are used for this purpose. Fig. 4.7 shows one example.

Electrical energy Fig. 4.7

30

Electric motor

Pump Mechanical energy

Hydraulic energy

Energy conversion by a unit consisting of electric motor and pump


HM 284

4.2.1.4


Bernoulli's principle

Bernoulli's principle provides essential understanding in the consideration of fluid energy machines. It correlates energies present in a flow. No energy is added to or removed from the fluid in this approach. The important thing to remember when considering the various energies is the fact that the forms of energy can be transformed. 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

The following forms of energy are considered: • Hydraulic energy E hy d

=

p  V

(4.7)

E hyd = Hydraulic energy in J p = Static pressure in N/m2 V = Volume in m 3

• Potential energy E po t

=

m  g  h

(4.8)

E pot =Potential energy in J g = Gravitational acceleration in m/s 2 h = Height in m m = Mass in kg

• Kinetic energy E ki n

=

1 2 --  m  c 2

(4.9)

E kin = Kinetic energy in J c = Flow velocity in m/s


31

HM 284


Thermal energy can be ignored if the temperature is constant.

If we consider a fluid particle on its flow path, in practice we can assume that the total energy of the particle remains constant.

For this assumption, the formulae can be summarised to form Bernoulli's energy equation. Transposed we get: c 1

2

p 1

-------- + ----- +

2

c g h p 

= = = = =



2

g  h 1

c 2

p 2

2



= -------- + ----- +

g  h 2 (4.10)

Flow velocity in m/s Gravitational acceleration in m/s2 Height in m Static pressure in N/m2 Density in kg/m3

Strictly speaking this assumption is only valid for frictionless fluids, since friction leads to losses.

Usually two points in the flow are compared to each other. One possible energy conversion is shown again using the example of nozzle and diffuser.

32



HM 284

Nozzle

Diffuser

c 3

p 2 p 1 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

c 2

c 1

Fig. 4.8

p 4 p 3

Conversion of pressure energy into velocity kinetic energy and back again

The example of diffuser and nozzle (Fig. 4.8) shows the conversion of velocity and pressure. Pressure and velocity terms are coupled energetically; if one term falls, the other term rises.


33


HM 284

4.2.2

Work

Work in the physical sense is performed when a force acts along a path; in this case force F and distance s point in the same direction. W

=

F  s

(4.11)

F = Force in N W = Physical work in J s = Active distance of the force in m

An example related to fluid mechanics can be seen in the axial turbomachine shown previously.

Rotating impeller

Direction of movement Direction of force

Stationary guide wheel Fig. 4.9

Work done within a turbomachine

In a turbine, the stationary guide wheel provides the incident flow to the rotor blade. A force acts on the rotor blade in the direction of movement. According to Formula (4.11) work is done in this process while the Impeller is rotating. This work is transferred from the fluid to the turbine.

34


HM 284


Another example of work done can be shown using a piston pump. Flowing fluid

Direction of movement Direction of force p 1 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

Fig. 4.10

p 2

Transfer of work within a piston pump

During the stroke s of the piston pump in Fig. 4.10, fluid is conveyed out of the cylinder. This causes the pressure p required to overcome the flow resistances in the downstream system to build up in the fluid. The force F that has to be applied by the piston results from the pressure p of the fluid and the surface area A of the piston. Formula (4.11) becomes:

s p F

A Fig. 4.11

Variables at a piston pump

W A = F = p = W = s =

=

F  s = p  A  s

(4.12)

Cross-section area in m2 Force in N Pressure in Pa Physical work in J Active distance of the force in m


35

HM 284


This work is transferred from the pump to the fluid. Since the processes within a double stroke are uneven, it is better to calculate mean values in this case.

4.2.2.1

Specific work

The work W transferred within a fluid energy machine can be based on the mass of the fluid. This corresponds to the specific work: Y =

W m

-----

(4.13)

m = Mass in kg W = Physical work in J Y = specific work in J/kg

Because of the possibility of converting energy, this specific work can also be used to define the velocity head or pump head: h =

Y g

---

(4.14)

h = Height in m g = Gravitational acceleration in m/s2

The velocity head or pump head is an important quantity in the design and selection of turbines and/or pumps.

36



HM 284

4.2.3

Power

Power is the work done per unit of time t . As already explained in Chapter 4.2.1.3, energy is the ability to perform work. Accordingly, energy can be used in the same way as work. Generally speaking, power is defined as: P =


E = P = t = W =

W t

----- =

E t

---

(4.15)

Energy in J Power in watts Time in s Physical work in J

The key power calculations related to this series of equipment are:

Electrical power: P el P el U I

=

U  I

(4.16)

= Electrical power in W = Voltage in V = Current in A

Mechanical power P mech = M  

(4.17)

P mech = Mechanical power in W = Torque in Nm M  = Angular velocity in 1/s


37

HM 284


Hydraulic power in incompressible fluids

Powers can be calculated from all of the energies listed in Chapte Chapterr 4.2 4.2.1. .1.4, 4, P Page age 31 31.. Potential energy has a lesser role in the fluid energy machines considered here, because it is converted into pressure energy and/or kinetic energy before it enters the machine.

Hydraulic power of the fluid P hy d

=

·

p  V

(4.18)

Hydraulic lic powe powerr in W P hyd = Hydrau = Static Static pressu pressure re in N/m2 p · = Volum Volume e flow flow in in m3 /s V Kinetic power of the fluid P ki n

1 · 2  m  c 2

= --

(4.19)

Kinetic c power power in W P kin = Kineti = Flow Flow veloci velocity ty in m/s m/s c · = Ma Mass ss flow flow in in kg/s kg/s m

Note on energy and power: Energy is the quantity which is preserved. However, it is often used in calculations since it is easier to calculate from measured values.

Energy is converted in the fluid energy machine. Similarly, a proportion of energy is stored in each machine, for example in the rotational energy of the shafts and impellers.

38


HM 284


The stored energies are relatively small compared to the transferred power. If there is a change in the operating point, either spent power is stored over a short time or stored work is released over a short time. The change in speed to the new operating point happens quickly. This time response can be explained by Formu Formula la (4.15 (4.15), ), Pag Page e 37 37..


The forms of energy in fluid energy machines are quickly converted into each other. In contrast, lots of heat transfers with heating up and cooling down processes take place slowly.


39

HM 284

4.2.4


Efficiency

The efficiency is defined as the ratio of benefit to effort. P ou t  = -----------  100 % (4.20) P in P in = Incomi Incoming ng po power wer:: th the e effort effort in in W Outgoing ing powe power: r: the the ben benefi efitt in W P out = Outgo  = Effi Effici cien ency cy in %

Real energy conversions are subject to loss. Fig. 4.12 illustrates 4.12 illustrates this using the example of an electrically driven pump. The thickness of the arrows represents the transferred power.

Electrical input power

Hydraulic effective power

Mechanical power

P out P in

Electric motor

Pump

Losses: Electrical Mechanical Fig. Fig. 4.12 4.12

40

Losses: Hydraulic Mechanical

Energy Ene rgy conver conversio sion n by a unit unit consis consistin ting g of electr electric ic moto motorr and and pump pump



HM 284

4.2.5

Energy conversion in the motion of fluid

An energy balance can be established between 2 points of a flow conduit.

A1 p 1

1

h 1 A < A1=A2

· m


· m

A2 p 2

h 2

2 p 1

2 c 1



2

----- + ----- +

Fig. 4.13

g  h 1

p 2

2 c 2



2

= ----- + ----- +

g  h 2

2 points of a schematic flow conduit

For the flow conduit from Fig. 4.13 we can say, regardless of the direction of flow, that gravitational potential energy is converted into pressure energy from cross section 1 to cross section 2. Since the cross sections of the two points being considered are the same, we should not expect any change in velocity. If there is a flow, the flow velocity will be greatest in the middle between the points being considered. The energies of pressure, velocity and vertical height add up to the total energy. According to the (lossless) Formula (4.10) this total energy remains the same. Nevertheless, it is still possible to act on this energy by technical means. This is shown in Fig. 4.14 by means of an example. According to Bernoulli, changes in the velocity kinetic energy and/or pressure energy are also possible.


41


HM 284

p 1

1

A1 c 1

y g r e n E

d i u l f e h t f o y g r e n e e h t s e s a e r c n I

d i u l f e h t

h 1

Work machine

Power machine

e.g. pump

e.g. turbine Fluid energy machine

Mechanical work

m o r f y g r e n e s e v o m e R

Mechanical work

2 p 2 A2 c 2 h 2 2

p 1

c 1



2

----- + ----- +

Fig. 4.14

p 2

2

c 2

g  h 1  ----- + ----- + g  h 2 2 

Energy conversion at a pump/turbine

As shown in the figure, the action can occur on the fluid energy by means of: – Work machines (Pumps/ventilators/fans/compressors): These convert a mechanical rotational movement into the fluid's pressure energy or velocity kinetic energy. The structural design takes account of the required pressure ratios and mass flows as well as the size and direction of the connections. – Power machines (turbines): These convert pressure energy or velocity kinetic energy into mechanical energy. As with the work machines, pressure ratios and mass flows are critical variables that determine the structural design.

42


HM 284


The power of the fluid is dependent on the pressure and the volume flow. In a lossless machine, this would correspond to the shaft power on the machine (cf. Formula (4.17) and Formula (4.18)). By equating we get the expression: M  


M p · V 

= = = =

=

·

p  V

(4.21)

Torque in Nm Pressure in Pa Volume flow in m3 /s Angular velocity in 1/s

Looking at powers is equivalent to looking at the converted energy differences. In the case of mechanical power, it can be assumed that the lower levels of torque and velocity lie at zero. This is not necessarily the case when it comes to · hydraulic power. While the volume flow V can often be regarded as constant due to incompressible behaviour, under pressure it often has to be calculated with the pressure difference p 2 -p 1. This is because the lower pressure level does not have to correspond to the ambient pressure. The formula becomes: M  

=

·

 p 2 – p 1   V

(4.22)

The shaft power of the machine in this case is equivalent to the hydraulic power of the fluid. Initially it does not matter whether the shaft power is achieved by a large torque or high angular velocity. Likewise, the power of the fluid may signify a large volume flow or a high pressure difference.


43

HM 284


However, the technical implementation can only deliver high efficiency for one particular design case. The types of fluid energy machines differ depending on the objectives and the environmental conditions.

44


HM 284


5

Further basic principles for HM 284

5.1

Converting pressure energy into velocity

Pressure and velocity are both forms of energy. Pressure energy can be converted into velocity kinetic energy. The pump adds energy to the fluid. This happens as pressure and/or velocity kinetic energy. 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

Assuming that all of the pressure is converted into velocity kinetic energy, we can derive the following from Formula (4.10), Page 32: c =

2  p 

-----------

(5.1)

c = Flow velocity in m/s p = Static pressure in Pa  = Density in kg/m3

5.1.1

Supply pressure and head of centrifugal pumps

Centrifugal pumps generate a head which is independent of the density of the fluid. For the same head, a higher pressure is needed at higher density. The pressure is proportional to the weight of the fluid: p =   g  h g h p 

5 Further basic principles for HM 284

= = = =

(5.2)

Gravitational acceleration in m/s2 Head in m Static pressure in Pa Density in kg/m3

45

HM 284


Note: Where the pumped medium is water, the unit is often specified in "mWC". This non-SI compliant unit derives from " m etre W ater C olumn ".

This pressure results from the conversion of velocity to pressure. The impeller transfers velocity kinetic energy to the fluid as it passes through. From Formula (5.1) and Formula (5.2) we can transpose: 2

h = c g h p 

= = = = =

p c ----------- = ----------2  g   g

(5.3)

Flow velocity in m/s Gravitational acceleration in m/s2 Head in m Static pressure in Pa Density in kg/m3

Thus the velocity of the fluid is decisive for the resulting pressure and/or the head. This is directly related to the rotational speed of the impeller. Because the pressure is measured, it is this measured variable that is the focus of the description that follows. Conversion is possible by Formula (5.2): h =

p   g

(5.4)

----------

Some diagrams show the pressure in bar and also as a head in m. The factor has been adopted to the secondary y-axis with 10 m for better axis ba r scaling. ---------

46



HM 284

5.2

Pump characteristic

The pumps used are centrifugal pumps. They transfer energy to the fluid by accelerating the fluid on a circular path in the impeller. The inertia forces cause the water to be thrown outwards. The characteristic curves of centrifugal pumps can be approximated fairly well by parabolas. This is done in the figure below: 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

r a b n i p

e r u s s e r P

·

Volume flow V in L/min

Fig. 5.1

Schematic characteristic curve of a centrifugal pump

When talking about energy transfer it is possible to make a qualitative distinction between high pressures and high flow rates. The processes can be explained as follows:


47

HM 284


High pressures: At low flow rates, the fluid particles are moved in a narrower circular path. If there is no flow, the pump swirls the fluid in a circle. The centrifugal force is highest here. This force is seen as pressure. High flow rates: The trajectory of a fluid particle deviates more and more from the circular path with increasing flow rates and approaches a straight line that points outwards from the centre. The centrifugal forces responsible for the pressure build-up become smaller.

Note: The representation shows the relationships on a simple level. Detailed knowledge of energy transfer is dealt with in HM 283 "Experiments with a Centrifugal Pump".

5.3

System characteristic

Pumps are mainly used to pump fluids through pipe networks or systems. This requires that a certain pressure be applied to overcome the flow resistances.

The following proportionality can be derived from Formula (5.1) and Formula (4.2), Page 25: ·

V  c  p

(5.5)

c = Flow velocity in m/s p = Static pressure in N/m2 · V = Volume flow in m3 /s

48



HM 284

Therefore four times the pressure must be applied to realise double the flow through a system. If the pressure is plotted against the volume flow, we get a curve in the shape of a parabola:


r a b n i p

e r u s s e r P

·

Volume flow V in L/min Fig. 5.2

5.4

Schematic system characteristic

Operating point:

The operating point of a pump/system combination is located at the intersection of the system and pump characteristics. In order that the fluid can flow, it is necessary to overcome the system resistance. The pump allows for this by increasing the pressure of the fluid. If the system has a variable system resistance (e.g. by switching between different flow


49


HM 284

sections), then the operating point shifts on the pump characteristic. If the pump's output is varied by the speed, then the operating point shifts on the system characteristic.

Moving the operating point by varying the system characteristic

r a b n i

Operating point

p

e r u s s e r P Moving the operating point by varying the pump characteristic

·


50

Schematic characteristics. System characteristic and pump characteristic of a centrifugal pump


HM 284

5.5


Pumps in series and parallel connection

Specific circuits mean that two or more pumps can be connected to each other. This is useful in order to achieve operating points above the limit of a single pump.

Note: There are analogies to electrical engineering:

– Pump vs. energy source (battery) – Pressure vs. voltage – Volume flow vs. current



51


HM 284

5.5.1

Parallel connection

In parallel-connected pumps, the outputs of both pumps are joined together. The delivered volume flow is increased. The pressure cannot be increased above the level of a single pump. In the ideal case of a (non-existent) completely flat system characteristic, the volume flows are added together without losses. The following diagram indicates schematically how a real system behaves. Operating point 2 parallel r a b n i p

e r u s s e r P

Operating point single

2 parallel pumps Single pump

·


Schematic characteristics. Single and parallel centrifugal pumps.

Connecting the pumps in parallel increases the volume flow. However, the steep system characteristic requires a significantly increased pressure to further increase the throughput. As a result, in the assumed case the increase is not as steep.

52


HM 284

5.5.2


Series connection

In series-connected pumps, the output of the first pump is connected to the input of the next pump. The delivered volume flow remains constant. The subsequent pump increases the pressure of the volume flow being passed through. In the case of very steep system characteristics, the pressures are approximately added together. Lossless addition is only possible with the "0" volume flow.


As described in the Parallel connection section, the use of a series connection leads to the following result in the system characteristic:


53


HM 284

2 pumps in series r a b n i p

e r u s s e r P

Single pump

Operating point 2 in series Operating point single

·


Schematic characteristics. Single and series-connected centrifugal pumps.

The system characteristic is relatively flat. There is not enough resistance against the pumps, so that there is no increase to the possible pressure. The achieved increase is very small.

54



HM 284

5.5.3

Selecting the type of connection

The single pump characteristic can be extended by switching to an additional pump, as has already been discussed:

2 pumps in series


r a b n i p

e r u s s e r P

2 pumps in parallel

Single pump

·


Characteristics of single pump and parallel-connected and series-connected pumps

The characteristic in which the pump is to be used is crucial for the meaningful use of an additional pump. The following diagram provides an overview:


55


HM 284

r a b n i p

With 2 pumps cannot be achieved 2 pumps in series

e r u s s e r P

Single pump

2 pumps in parallel

·


Characteristics of single pump and parallel-connected and series-connected pumps

The diagram shows the previous pump characteristic curves with a boundary line that divides parallel and series connection into two regions. This line passes through the intersection point of the pump characteristic curves from series and parallel operation. This results in regions that are better suited for the single pump, the series-connected pumps or the parallel-connected pumps.

The applied pressure causes the flow of the fluid and is thus the cause of the volume flow. In each operating mode, the operating point appears as the intersection of the pump and system characteristics.

56


HM 284


When choosing a pump for an existing system, the required pressure is thus the criterion for selecting the pump. The system characteristic curve is also crucial. The diagram is divided into a region of steep system characteristic curves, which are preferably operated with pumps connected in series, and rather flat curves that bring benefits for pumps operating in parallel. If one pump is not sufficient for the real application, an additional pump may help.


At low pressures, parallel connection has its advantages in that it can provide a substantially greater volume flow than pumps operating in series. If the required pressures through an existing system are greater than the pressure of a single pump, then only series connection can be used. In principle, both types of connection are suitable for the low pressure region above the intersection of the pumps in series or parallel connection. This raises the question of whether we want to hold more reserves as maximum pressure or in the maximum volume flow. In the overall consideration we should not forget that a single larger pump may certainly be justified, depending on the procurement situation.


57

HM 284

58




HM 284

6

Experiments

The selection of experiments makes no claims of completeness but is intended to be used as a stimulus for your own experiments. The results shown are intended as a guide only. Depending on the construction of the individual components, experimental skills and environmental conditions, deviations may occur in the experiments. Nevertheless, the laws can be clearly demonstrated.


The measured values of the moving fluid are subject to constant fluctuations. This means that the measured values are always varying around the value of the operating point. Filtering is used to smooth the measured values before they are presented to the user. Since GUNT wants to use this device to demonstrate the physical relationships in practical operation, the interpretation of the measured values follows these relationships. When operating points are saved, so are all measured values and the derived calculation variables. The values listed in the tables below only represent a selection for a better overview. The measurements file created by the measurement data acquisition program is further processed in this instruction manual with MS Excel®.

6 Experiments

59

HM 284


6.1

Experiment 1: Recording a system characteristic curve

6.1.1

Objectives of the experiment

The system characteristic has to be recorded with pump P1 on the experimental unit. The objective is to be able to interpret this characteristic curve. The result shall be an awareness of the interaction of the flow rate and the pressure difference in a flow-through system.

6.1.2

Conducting the experiment

To record the system characteristic curve we shall proceed according to the following points: 1. Bleed the experimental unit 2. Set the experimental unit for standalone operation of pump P1. See Fig. 6.1 in Chapter 3.7.1, Page 18. 3. Open valve V3 fully Fig. 6.1

Circuit for standalone operation of pump P1

4. Use the Tare button to calibrate to zero 5. Leave pump P1 to run to 3300 1/min 6. Measured values for the suction pressure p 1, the pump outlet pressure p 2 and the volume · flow V should now be recorded 7. Reduce the volume flow bit by bit by gradually slowing the pump speed and take the measurements according to point 6 8. Repeat steps 6 and 7 until the volume flow is completely throttled

60

6 Experiments


HM 284

6.1.3

Measured values with calculations of the analysis ·


Speed of pump P1 n in 1/min


Pressure p 1 in bar

Pressure p 2 in mbar

·

V

----------- in p1

kg

--------------------

m

2

N

3300

47,5

-0,28

0,16

-0,081

3000

43,3

-0,23

0,13

-0,082

2700

38,6

-0,18

0,11

-0,081

2400

34,4

-0,15

0,09

-0,082

2100

29,8

-0,11

0,07

-0,080

1800

25,4

-0,08

0,05

-0,081

1500

21,1

-0,06

0,04

-0,081

1200

16,7

-0,04

0,03

-0,080

900

12,4

-0,02

0,01

-0,077

600

7,7

-0,01

0,01

-0,074

300

3,4

0,00

0,01

-0,058

0

0

0,00

0,00

Tab. 6.1

Volume flows and pressures in the unthrottled system at various speeds

6.1.4

Analysis

If we plot the measured values of pressure over volume flow in the diagram, we can clearly see a quadratic dependence. The following diagram shows quadratic trend lines assigned to the measurements:

6 Experiments

61


HM 284

r a b n i e r u s s e r P

m n i d a e H

Suction side Pressure side

Volume flow in L/min Fig. 6.2

Characteristics of the system in operation with pump P1

The dependency concerns the section upstream of the pump that is flowed through ( suction side, piping from tank to p 1) and downstream of the pump (pressure side, from p 2 to tank). Pressure changes into velocity. This can be demonstrated particularly well on the suction side. The dependency can be attributed to Bernoulli's energy equation Formula (4.10), Page 32: 2

c 0

p 0

2



-------- + ----- +

c g h p 

62

= = = = =

g  h 0

c 1

2

p 1

= -------- + ----- +

2



g  h 1

(6.1)

Flow velocity in m/s Gravitational acceleration in m/s² Height of the liquid column in m Static pressure in Pa Density in kg/m³

6 Experiments

HM 284


While the pump is being operated the pressure level on the pump suction side falls, so that the higher pressure in the water tank leads to the flow of the fluid. Formula (6.1) is used in the following to compare the "water tank" location (= index "0") with the pressure measuring point p 1 location (= index "1") in terms of energy. Since the height difference of the pressure measuring points is eliminated during zero calibration, this part of the formula can be ignored.


Velocity components c 0 in the relatively large water tank are negligible. The pressure in the water tank is greater than the location of the pressure measurement by the amount of p 1 (  p 0 1 = p 1 ). –

p 1

c 1

2

-------- = --------



2

(6.2)

Thank to the constant density of water, we can derive from Formula (6.2) that the flow velocity is proportional to the square root of the pressure: c 1 

p 1

(6.3)

c = Flow velocity in m/s p = Static pressure in Pa  = Density in kg/m³

6 Experiments

63

HM 284


In the experiment, this proportionality is demonstrated by the volume flow. This is also proportional to the flow velocity: ·

V = A  c thus: ·

V 

(6.4)

p 1 and also:

(6.5)

·

V

------------

=

const

(6.6)

p 1 A = c = p = · V =

Flowed through cross-sectional area in m² Flow velocity in m/s Pressure in Pa Volume flow in m³/s

The results are listed in the table of measurement kg results. The unit in is given by 2 m  N Formula (6.6). --------------------

The values oscillate rapidly around the value of 0,08 2kg . --------------------

m  N

Flow resistances were ignored in this calculation. This simplification can be made on the suction side due to the relatively undisturbed flow. A more precise consideration of flow resistances is outside the scope of this manual, which is why there is no analysis of the pressure side. However, pressure is also converted into velocity, which corresponds to a quadratic function.

64

6 Experiments


HM 284

6.1.5

Evaluation

The system characteristic curve indicates what flow resistance a system has at a certain volume flow. Flowing through the system with a volume flow requires a certain pressure differential. This pressure differential is applied by the pump. The pressure differential is the same as the pump's supply pressure. This is the pressure differential that the pump applies between the suction side and pressure side. The calculation is as follows:


 p P1

=

p 2 – p 1

(6.7)

 p P1 = Pressure differential or supply pressure

p 1 p 2

6 Experiments

over pump P1 in Pa = Pressure upstream of P1 in Pa = Pressure downstream of P1 in Pa

65


HM 284

r a b n i e r u s s e r p y l p p u S

System characteristic

m n i d a e H


System characteristic with pump P1 from the suction and pressure side (p2-p1)

A portion of this energy is used up in flow resistances. This occurs particularly in bends and abrupt changes in cross section. The system's flow resistance can be altered by valve V3. The next experiment shall address this in more detail. From the proportionality of Formula (6.3) ( c 1  p 1 ) we can further deduce that four times the pressure is needed to double the volume flow (the velocity).

66

6 Experiments


HM 284

6.2

Experiment 2: Determining the reference speed

6.2.1

Objective of the experiment:

This experiment is used to improve the results of the following experiments. The reference speed of the two pumps is determined. This is the speed at which the pumps have the same delivery characteristics. 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

Deviations from the theoretically equal speed are possible due to manufacturing tolerances. The reference speed is roughly in the range of 2850 1/min.

6.2.2


To find the reference speed we shall proceed according to the following points: 1. Bleed the experimental unit. 2. Set up the experimental unit for series operation. See Fig. 6.4 in Chapter 3.7.2, Page 19. 3. Close valve V3 fully. Fig. 6.4

Circuit for operating the pumps in series

4. Use the Tare button to calibrate to zero 5. Switch on pump P2. 6. Switch to pump P1 and gradually increase the speed until the ratio of the two pressures p 3 / p2 is equal to 2. 7. Note down the reference speed: ___________________ 1/min.

6 Experiments

67

HM 284


6.3

Experiment 3: Determining the pump characteristic curve

6.3.1


The objective of the experiment is to create a pump characteristic curve for pump P1. By using valve V3 we can influence the system characteristic. In doing so, it is possible to operate the pump at different system resistances and to plot the relationship between pressure differential over the pump and volume flow. 6.3.2


To record the pump characteristic curve we shall proceed according to the following points: 1. Bleed the experimental unit 2. Set the experimental unit for standalone operation of pump P1. See Fig. 6.5 in Chapter 3.7.1. 3. Open valve V3 fully Fig. 6.5

Circuit for standalone operation of pump P1

4. Use the Tare button to calibrate to zero 5. Leave pump P1 to run to reference speed (see: Chapter 6.2). (The characteristic at this speed allows a direct comparison with the subsequent experiments). 6. Measured values for the suction pressure p 1, the pump outlet pressure p 2 and the volume · flow V should now be recorded. 7. Reduce the volume flow bit by bit by gradually closing valve V3 and take the measurements according to point 6. 8. Repeat steps 6 and 7 until the volume flow is completely throttled

68

6 Experiments


HM 284

6.3.3 Speed of pump P1 n in 1/min


Measured values · Volume flow V in L/min

Pressure p 1 in bar

Pressure p 2 in bar

Hydraulic power P hyd in W

Electrical power P el in W

Efficiency in %

2760

39,5

-0,2

0,11

20

221

9

2760

32,3

-0,13

0,42

30

214

14

2760

27,1

-0,09

0,58

30

211

14

2760

22,6

-0,07

0,72

29

206

14

2760

18,7

-0,04

0,81

27

196

14

2760

14,1

-0,03

0,88

21

187

11

2760

9,3

-0,01

0,93

15

181

8

2760

4,9

0,00

1,01

8

173

5

2760

0

0,00

1,09

0

169

0

Tab. 6.2

Volume flows and pressures of the device at different throttling

6.3.4

Analysis

6.3.4.1

Pump characteristic

The pressure difference compared to the volume flow produced with one pump is the interesting factor. The pressure difference, or the supply pressure, can be calculated according to Formula (6.7):  p P1

6 Experiments

=

p 2 – p 1

69


HM 284

This results in the following diagram for the pump characteristic curve:


m n i d a e H

Pump


Pressure differential over volume flow of pump 1 generated at 2760 1/min

The result is a profile of the measured points which can be closely approximated by a parabola. The maximum pressure is applied when the pump is not producing any volume flow. According to the measurements taken by GUNT this was 1,090 bar (at reference speed). When valve V3 is opened, the maximum possible flow rate is 39,5 L/min. With a lower system pressure loss, a higher volume flow could be implemented.

70

6 Experiments


HM 284

Pump r a b n i e r u s s e r p y l p p u S


System

m n i d a e H


Pump and system characteristic curves, pump at 2760 1/min

Fig. 6.7 shows the measuring points from the measured pump and system characteristic curves. We can see that the pump characteristic curve is limited at the bottom due to the lowest possible system curve (valve V3 open). Each operating point is an intersection point of the pump characteristic and system characteristic. To illustrate this point, the system characteristic curves from which the operating points result are inserted mathematically as a parabola.

6.3.4.2

Efficiency

The experimental unit also offers the possibility of studying pump P1 in standalone operation in more detail.

6 Experiments

71

HM 284


In terms of energy, the interesting factor is the efficiency which arises from the pump characteristic curve. The efficiency is the ratio of benefit to effort. The effort corresponds to the electrical power that the pump motor requires at the respective operating point. It is measured and displayed directly by the experimental unit . The benefit of a pump is defined as the hydraulic output. This can be calculated from pressure and volume flow, see Formula (4.18), Page 38. For the pump in standalone operation, this corresponds to: P hy d

=

·

 p P1  V

(6.8)

P hyd = Hydraulic power in W

To calculate the pump efficiency, we need the shaft power at the pump. In contrast to the input power of the electric motor, this is relatively difficult to determine, which is why the total system efficiency at the coupling of the electric motor and pump is often used. The system efficiency can be calculated as follows: P hy d  = ------------  100 (6.9) P el  = Efficiency in %

72

6 Experiments


HM 284

This calculation relationship:

results

in

the

following

Pump System





% n i 

y c n e i c i f f E


Pump and system characteristic curves

The efficiency increases with increasing volume flow until it reaches a maximum point and then falls off again. This is due to the value of the hydraulic power. At the axis intersection points this is zero, because here either pressure or volume flow is equal to zero. The incoming electrical power is converted into hydraulic power by the pump. Different mechanisms during operation also consume energy, which ultimately can no longer be converted into hydraulic power.

6 Experiments

73

HM 284


This mainly includes • Friction Mechanical friction on bearings and seals, as well as friction in the fluid • Gap losses Overflow between the impeller and housing • Electrical losses Ohmic losses, magnetisation losses • Turbulence In the conversion of velocity into pressure

The efficiencies for small systems are lower compared to large systems, since the electrical losses and the gap losses increase disproportionately.

Note: The ability to operate the pumps in series and parallel at different speeds means it makes sense to only study the efficiency in standalone operation.

Efficiency in series and parallel operation is therefore set to -1.

74

6 Experiments


HM 284

6.3.5

Evaluation

The curve shows centrifugal pump.

the

characteristic

of

a

Operating points are intersection points of pump characteristic and system characteristic. An efficiency can be calculated for each operating point. The efficiency increases until it reaches a maximum point and then falls off again. If system and pump are not well matched to each other, it may be that this maximum is not reached. This is the case if, for example, the system line is too steep or the pump curve is too flat.


6 Experiments

75

HM 284


6.4

Experiment 4: Pumps in series operation

6.4.1


In this experiment, the pumps are operated in series one after the other. The goal is to apply knowledge gained so far to this case and to expand upon it.

6.4.2


To record the measurements in this operating mode, we shall proceed according to the following points: 1. Bleed the experimental unit . 2. Set up the experimental unit for series operation. See Fig. 6.9 from Chapter 3.7.2, Page 19. 3. Open valve V3 fully. Fig. 6.9

Circuit for series operation

4. Use the Tare button to calibrate to zero. 5. Leave pump P1 to run to reference speed (see: Chapter 6.2). (Pumps P1 and P2 have the same delivery properties). 6. Switch to pump P2. 7. Measurements for the pump inlet pressure p 1, the pump outlet pressure p 2 and p 3 and the · volume flow V should now be recorded. 8. Reduce the volume flow a bit by gradually closing valve V3 and take the measurements according to point 7. 9. Repeat steps 7 and 8 until the volume flow is completely throttled.

76

6 Experiments


HM 284

6.4.3

Measured values · Volume flow V in L/min

Speed of pump 1 & 2 n in 1/min


Pressure p 1 in bar

Pressure p 2 in bar

Pressure p 3 in bar

2760

39,0

-0,19

0,14

0,10

2760

35,3

-0,16

0,29

0,44

2760

29,6

-0,11

0,49

0,88

2760

25,3

-0,08

0,64

1,20

2760

19,7

-0,05

0,78

1,50

2760

14,6

-0,03

0,87

1,70

2760

10,6

-0,02

0,92

1,82

2760

5,4

-0,01

1,00

1,96

2760

0,00

0,00

1,08

2,16

Tab. 6.3

Volume flows and pressures during series connection and at different throttling

6.4.4

Analysis

The differential pressure (supply pressure) is plotted against the volume flow of pump P1 (cf. formula (6.7)):  p P1

=

p 2 – p 1

And the increase through both pumps:  p P1 3 –

=

p 3 – p 1

(6.10)

 pP1-3 = Pressure differential across

p 3 = p 1 =

6 Experiments

pump P1 and pump P2 in Pa Pressure downstream of pump P2 in Pa Pressure downstream of pump P1 in Pa

77


HM 284

This results in the following diagram:

Series Standalone


m n i d a e H


Single pump and pumps in series operation

Pump 1 generates a differential pressure corresponding to curve 1. This is increased by the differential pressure of pump P2. At the maximum volume flows (as in the previous experiment) the minimum system characteristics are almost identical, but it should not be forgotten that the connecting section between pump P1 and pump P2 also generates pressure losses, which has to be applied by both pumps. To better understand this effect, the pump characteristic of pump P2 is added to the standalone pump characteristic of pump P1.

78

6 Experiments


HM 284

The calculation is as follows:  p P2

=

p 3 – p 2

(6.11)

 p P2 = Pressure differential across pump P2 in Pa p 3 = Pressure downstream of pump P2 in Pa p 2 = Pressure downstream of pump P1 in Pa

There is a difference between the identical pumps, which represents the additional pressure drop through the connecting section:



Pump 2 Connecting section m n i d a e H

Pump 1


Pumps characteristic curves in series operation

At maximum volume flow, pump P2 cannot quite fully compensate for this additional pressure drop. This results in the slightly negative supply pressure.

6 Experiments

79

HM 284

6.4.5


Evaluation

The resulting curve is an addition of the two pressures of pump P1 and pump P2. By connecting the pumps in series operation, the pressure can be raised to roughly double.

80

6 Experiments


HM 284

6.5

Experiment 5: Pumps in parallel operation

6.5.1


In this experiment, the pumps are operated in parallel. The previously acquired knowledge is applied to this case in a practical-oriented manner.

6.5.2 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A


To record the measurements in this operating mode, we shall proceed according to the following points: 1. Bleed the experimental unit. 2. Set up the experimental unit for parallel operation. See Fig. 6.12 in Chapter 3.7.3, Page 20. 3. Open valve V3 fully. Fig. 6.12

Circuit for parallel operation

4. Use the Tare button to calibrate to zero. 5. Leave pump P1 to run to reference speed (see: Chapter 6.2). (Pumps P1 and P2 have the same delivery properties). 6. Switch to pump P2. 7. Measurements for the pump inlet pressure p1, the pump outlet pressure p 2 and p 3 and the · volume flow V should now be recorded. 8. Reduce the volume flow a bit by gradually closing valve V3 and take the measurements according to point 7. 9. Repeat steps 7 and 8 until the volume flow is completely throttled.

6 Experiments

81


HM 284

6.5.3

Measured values ·

Speed of pump 1 & 2 n in 1/min


Pressure p 1 in bar

Pressure p 2 in bar

Pressure p 3 in bar

2760

68,5

-0,14

0,36

0,35

2760

64

-0,12

0,44

0,42

2760

60,2

-0,11

0,50

0,49

2760

52,9

-0,08

0,61

0,60

2760

45,6

-0,06

0,72

0,71

2760

37,7

-0,04

0,81

0,81

2760

30,0

-0,03

0,88

0,87

2760

23,8

-0,01

0,92

0,92

2760

17,6

-0,01

0,97

0,97

2760

11,0

0,00

1,01

1,00

2760

5,2

0,00

1,08

1,07

2760

0,0

0,00

1,10

1,10

Tab. 6.4

Volume flows and pressures during parallel connection and at different throttling

6.5.4

Analysis

A comparison of the pump output pressures shows almost the same values. By operating at the reference speed, we should expect the same pressure differential and the same volume flow across the two pumps. In experiment 1 we showed that the system characteristic is composed of the suction part upstream of the pump and the pressure part downstream of the pump. Since the two pumps produce the same pressure differential, this means that the suction pressures of the two pumps are equal.

82

6 Experiments


HM 284

For the analysis the differential pressure (supply pressure) that results across the pumps is calculated with the values of pump P1 (cf. formula (6.7))  p P1

=

p 2 – p 1

=

 p P 2

and plotted against the volume flow. This results in the following diagram: 3 1 0 2 / 9 0 y n a m r e G , l e t t ü b s r a B , u a b e t ä r e G . T . N . U . G , d e v r e s e r s t h g i r l l A

Parallel Standalone r a b n i e r u s s e r p y l p p u S

m n i d a e H


Pumps in parallel operation, head over volume flow

As we have already seen, the system characteristic curve with the lowest pressure loss can be found mathematically from the operating point with maximum volume flow. The corresponding parabolas are inserted into the chart as dotted lines.

6 Experiments

83

HM 284

6.5.5


Evaluation

A higher supply volume is achieved with the pumps connected in parallel. The new fluid flow results in a new system characteristic curve. This must be re-evaluated in comparison to the previous operating modes. In the representation of the system characteristics in Fig. 6.13 we can see that this new system characteristic is flatter than the system characteristic in standalone operation. By doubling the suction cross-section, the flow velocity is halved and the pressure loss during intake is reduced to a quarter of the characteristic (cf. Chapter 6.1.4, Page 61).

84

6 Experiments


HM 284

6.6

Final analysis of the experiments and proposal for further experiments

The HM284 experimental unit makes it possible to learn in a practical manner how pumps behave in standalone operation, and when connected in series and in parallel. The following diagram shows the curves already discussed in the individual experiments:


Series r a b n i e r u s s e r p y l p p u S

Parallel Standalone

m n i d a e H


6 Experiments

Pressure difference over volume flow of pumps in standalone, series and parallel operation

85

HM 284


The main findings of the experiments: • The system system characte characteristi ristic c curve curve indicates indicates the amount of pressure required to flow through the system at a certain volume flow. • The system system characte characterist ristic ic is composed composed of the pressure side and suction side of the system. • The pum pump p charact character erist istic ic curve curve indica indicates tes how how much pressure the pump can deliver at a certain volume flow. • System System curv curve e and p pump ump curv curve e inter intersec sectt at the the operating point. • Valve Valve 3 can can be be used used to to influe influence nce the system system characteristic curve. • In series series operation operation,, the the pressur pressures es of of the the pumps pumps are added together. • In paral parallel lel oper operat ation ion,, the volu volume me flows flows of of the pumps are added together. • Flow Flow contr control ol has has an imp impact act on tthe he syst system em characteristic curve. These conditions are due to physical factors.

86

6 Experiments

HM 284


7

Appendix

7.1

Technical data Dimensions

Length x Width x Height: Weight:

67 x 60 x 67 cm cm 62 kg

Connections

Electric power supply: Phases:


Rated input (power):

230 V, 50 Hz 1 650 W

Microfuse 6,3 A delayed-action at 230 V Alternatives optional, see rating plate. Pumps Pumps in 50 50 Hz version version

Speed range pump P1: Speed of pump P2:

0...3300 1/ 1/min approx. 2800 1/ 1/min*

Impeller:

Diameter: Diameter Diameter at blade inlet: inlet: Blade depth:

98 mm** 48 mm 5 mm

Varian Variantt at 60 60 Hz

*Speed of pump P2: **Diameter of pump P2:

approx. 3300 1/ 1/min 80 mm

Water tank

Filling volume:

7 Appendix

approx. 15 L

87

HM 284


Sensors

Suction side pressure range:

-1...1 ba bar

Pressure side pressure range:

-5...5 ba bar

Volume flow sensor:

10...140 L/min

Measurement data acquisition

Program environment: LabVIEW Runtime System requirements: PC with Pentium IV processor, 1 GHz Minimum 1024 MB RAM Minimum 1 GB free hard disk space 1 CD-ROM drive 1 USB port Graphic card resolution min. 1024 x 768 pixels, True Color Windows XP / Windows Vista / Windows 7 Accessories supplied

Power connector cable USB connection cable Software CD To be provided by customer

PC with Windows operating system, USB port Filling with water

88

7 Appendix


HM 284

7.2


7 Appendix

List of formula symbols and units Formula symbols

Mathematical/physical value

Unit

A

Area (flowed through)

m²

c

Flow velocity

m/s

g

Gravitational acceleration

m/s²

h

Height (of the liquid column)

m

n

Rotational speed

1/min

p

General pressure

Pa

p 1

Pressure upstream of pump P1

Pa

p 2

Pressure downstream of pump P1

Pa

p 3

Pressure downstream of pump P2

Pa

p P1

Pressure across pump 1 (differential pressure, supply pressure)

Pa

p P2

Pressure across pump 2 (differential pressure, supply pressure)

Pa

p P1-2

Pressure across pump 1 and 2

Pa

P

General power

W

P el

Electrical power

W

P hyd

Hydraulic power

W

· V

Volume flow

m³/s



Difference



Efficiency



Density

kg/m³

89

HM284_e - V1.5

Recommend Documents