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Fluid Mechanics and Applications MECN 3110

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Fluid Mechanics and Applications MECN 3110

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Fluid Mechanics and Applications MECN 3110

Inter American University of Puerto Rico

Professor: Dr. Omar E. Meza Castillo

Turbomachinery

- To select pumps, fittings, fans and turbo-machinery

Thermal Systems Design Universidad del Turabo

- In this lecture we will examine the performance characteristics of turbomachinery. The word turboimplies a spinning action is involved. In turbomachinery, a blade or row of blades rotates and imparts energy to a fluid or extracts energy from a fluid. Work is generated or extracted by means of enthalpy changes in the working fluid.
- In general, two kinds of turbomachines are encountered in practice. These are open and closed turbomachines. Open machines such as propellers, windmills, and unshrouded fans act on an infinite extent of fluid, whereas, closed machines operate on a finite quantity of fluid as it passes through a housing, casing, or duct. We will examine only turbomachines of the closed type.

- Turbomachines may be further classified into two additional categories: those that absorb energy to increase the fluid pressure, i.e. pumps, fans, and compressors, and those that produce energy such as turbines by expanding to lower pressures.
- Of particular interest are applications which contain pumps, fans, compressors, and turbines. These components are essential in almost all mechanical equipment systems such as power and refrigeration cycles. We will examine each of these components in detail, and address a number of operating issues in systems when more than one component exists.

- We begin by considering pumps and fans first, as their performance and operational characteristics are similar, with the exception that pumps are used with liquids and fans are used for gases usually air.
- Pumps are fluid machines which increase the pressure of a liquid, to enable the fluid to be moved from one location to another. Pumps are typically used to overcome losses due to friction in pipes over long distances, losses due to fittings, losses due to components, and elevation differences.
Classification:

- There are two basic types of pumps: positive-displacement and dynamic or momentum change pumps. There are several billion of each type in use in the world today

- Positive-displacement pumps (PDPs) force the fluid along by volume changes. A cavity opens, and the fluid is admitted through an inlet. The cavity then closes, and the fluid is squeezed through an outlet. The mammalian heart is a good example. A brief classification of PDP designs is as follows:

- All PDPs deliver a pulsating or periodic flow as the cavity volume opens, traps, and squeezes the fluid. Their great advantage is the delivery of any fluid regardless of its viscosity.

- Dynamics pumps simply add momentum to the fluid by means of fast-moving blades or vanes or certain special designs. There is no closed volume: The fluid increases momentum while moving through open passages and then converts its high velocity to a pressure increase by exiting into a diffuser section. Dynamic pumps can be classified as follows:

- Assuming steady flow, the pump basically increases the Bernoulli head of the flow between point 1, the eye, and point 2, the exit. Neglecting viscous work and heat transfer, this change is denoted by H:
- where hsis the pump head supplied and hfthe losses. The net head H is a primary output parameter for any turbomachine. Since the equation is for incompressible flow, it must be modified for gas compressors with large density changes.

- Usually V2 and V1 are about the same, z2 - z1 is no more than a meter or so, and the net pump head is essentially equal to the change in pressure head.
- The power delivered to the fluid simply equals the specific weight times the discharge times the net head change.
- This is traditionally called the water horsepower.

- The power required to drive the pump is the brake horsepower.
- Where ω is the shaft angular velocity and T the shaft torque. If there were no losses, Pwand brake horsepower would be equal, but of course Pwis actually less, and the efficiency of the pump is defined as

- The efficiency is basically composed of three parts: volumetric, hydraulic, and mechanical.
- The volumetric efficiency is
- where QLis the loss of fluid due to leakage in the impeller-casing clearances.
- Thehydraulic efficiency is

- where hfhas three parts: (1) shock loss at the eye due to imperfect match between inlet flow and the blade entrances, (2) friction losses in the blade passages, and (3) circulation loss due to imperfect match at the exit side of the blades.
- Finally, the mechanical efficiency is
- where Pf is the power loss due to mechanical friction in the bearings, packing glands, and other contact points in the machine.
- By definition, the total efficiency is simply the product of its three parts

- The key performance parameters of centrifugal pumps are capacity, head, BHP (Brake horse power), BEP (Best efficiency point) and specific speed. The pump curves provide the operating window within which these parameters can be varied for satisfactory pump operation. The following parameters or terms are discussed in detail in this section
- Capacity
Capacity means the flow rate with which liquid is moved or pushed by the pump to the desired point in the process. It is commonly measured in either gallons per minute (gpm) or cubic meters per hour (m3/hr).

- Capacity

The capacity usually changes with the changes in operation of the process. For example, a boiler feed pump is an application that needs a constant pressure with varying capacities to meet a changing steam demand.

The capacity depends on a number of factors like:

- Process liquid characteristics i.e. density, viscosity
- Size of the pump and its inlet and outlet sections
- Impeller size
- Impeller rotational speed RPM
- Size and shape of cavities between the vanes
- Pump suction and discharge temperature and pressure conditions

As liquids are essentially incompressible, the capacity is directly related with the velocity of flow in the suction pipe. This relationship is as follows:

- Head
- Significance of using Head instead of Pressure
The pressure at any point in a liquid can be thought of as being caused by a vertical column of the liquid due to its weight. The height of this column is called the static head and is expressed in terms of feet of liquid.

The same head term is used to measure the kinetic energy created by the pump. In other words, head is a measurement of the height of a liquid column that the pump could create from the kinetic energy imparted to the liquid. Imagine a pipe shooting a jet of water straight up into the air, the height the water goes up would be the head.

- Significance of using Head instead of Pressure

The head is not equivalent to pressure. Head is a term that has units of a length or feet and pressure has units of force per unit area or pound per square inch. The main reason for using head instead of pressure to measure a centrifugal pump's energy is that the pressure from a pump will change if the specific gravity (weight) of the liquid changes, but the head will not change. Since any given centrifugal pump can move a lot of different fluids, with different specific gravities, it is simpler to discuss the pump‘s head and forget about the pressure.

- Static Suction Head, hs
Head resulting from elevation of the liquid relative to the pump center line. If the liquid level is above pump centerline, hs is positive. If the liquid level is below pump centerline, hs is negative. Negative hs condition is commonly denoted as a “suction lift” condition.

- Static Discharge Head, hd
It is the vertical distance in feet between the pump centerline and the point of free discharge or the surface of the liquid in the discharge tank.

- Friction Head, hf
The head required to overcome the resistance to flow in the pipe and fittings. It is dependent upon the size, condition and type of pipe, number and

type of pipe fittings, flow rate, and nature of the liquid.

- Vapor Pressure Head, hvp
It is the pressure at which a liquid and its vapor co-exist in equilibrium at a given temperature. When the vapor pressure is converted to head, it is referred to as vapor pressure head, hvp. The value of hvp of a liquid increases with the rising temperature and in effect, opposes the pressure on the liquid surface, the positive force that tends to cause liquid flow into the pump suction i.e. it reduces the suction pressure head

- Pressure Head, hp
Its must be considered when a pumping system either begins or terminates in a tank which is under some pressure other than atmospheric. The pressure in such a tank must first be converted to feet of liquid. Denoted as hp, pressure head refers to absolute pressure on the surface of the liquid reservoir supplying the pump suction, converted to feet of head. If the system is open, hp equals atmospheric pressure head.

- Velocity Head, hv
Refers to the energy of a liquid as a result of its motion at some velocity ‘v’.

It is the equivalent head in feet through which the water would have to fall to acquire the same velocity, or in other words, the head necessary to accelerate the water. The velocity head is usually insignificant and can be ignored in most high head systems. However, it can be a large factor and must be considered in low head systems.

- Total Suction Head, Hs
The suction reservoir pressure head (hps) plus the static suction head (hs) plus the velocity head at the pump suction flange (hvs) minus the friction head in the suction line (hfs).

- Total Discharge Head, Hd
The discharge reservoir pressure head (hpd) plus static discharge head (hd) plus the velocity head at the pump discharge flange (hvd) plus the total friction head in the discharge line (hfd).

- Total Difference Head, HT
It is the total discharge head minus the total suction head

On the suction side of a pump, low pressures are commonly encountered, with the concomitant possibility of cavitation occurring within the pump. Cavitationoccurs when the liquid pressure at a given location is reduced to the vapor pressure of the liquid. When this occurs, vapor bubbles form the liquid starts to “boil”; this phenomenon can cause a loss in efficiency as well as structural damage to the pump.

Remember

- Pumps can pump only liquids, not vapors
- Rise in temperature and fall in pressure induces vaporization
- NPSH as a measure to prevent liquid vaporization

Net Positive Suction Head (NPSH) is the total head at the

suction flange of the pump less the vapor pressure converted to fluid column height of the liquid

- There are actually two values of NPSH of interest. The first is the required NPSH, denoted NPSHR, that must be maintained, or exceeded, so that cavitation will not occur. Since pressures lower than those in the suction pipe will develop in the impeller eye, it is usually necessary to determine experimentally, for a given pump, the required NPSHR.

- The second value for NPSH of concern is the available NPSH, denoted NPSHA which represents the head that actually occurs for the particular flow system. This value can be determined experimentally, or calculated if the system parameters are known. For example, a typical flow system is shown in figure.

The energy equation applied between the free liquid surface, where the pressure is atmospheric, and a point on the suction side of the pump near the impeller inlet yields

where ΣhL represents head losses between the free surface and the pump impeller inlet. Thus, the head available at the pump impeller inlet is

So that

For proper pump operation it is necessary that

Application Problems

If the flow is laminar, the frictional losses will be proportional to Q rather than Q2.

There is also a unique relationship between the actual pump head gained by the fluid and the flowrate, which is governed by the pump design (as indicated by the pump performance curve). To select a pump for a particular application, it is necessary to utilize both the system curve, as determined by the system equation, and the pump performance curve. If both curves are plotted on the same graph, as illustrated in the following figure, their intersection (point A) represents the operating point for the system.

That is, this point gives the head and flowrate that satisfies both the system equation and the pump equation.

On the same graph the pump efficiency is shown. Ideally, we want the operating point to be near the best efficiency point (BEP) for the pump. For a given pump, it is clear that as the system equation changes, the operating point will shift. For example, if the pipe friction increases due to pipe wall fouling, the system curve changes, resulting in the operating point A shifting to point B in previous figure with a reduction in flowrate and efficiency. The following example shows how the system and pump characteristics can be used to decide if a particular pump is suitable for a given application.

Application Problems

Brake Horse Power (BHP)

The work performed by a pump is a function of the total head and the weight of the liquid pumped in a given time period.

Pump input or brake horsepower (BHP) is the actual horsepower delivered to the pump shaft.

Pump output or hydraulic or water horsepower (WHP) is the liquid horsepower delivered by the pump. These two terms are defined by the following formulas.

Best Efficiency Point (BEP) is the capacity at maximum impeller diameter at which the efficiency is

highest. All points to the right or left of BEP have a lower efficiency.

Significance of BEP

- BEP as a measure of optimum energy conversion
- BEP as a measure of mechanically stable operation
- BEP as a measure of mechanically stable operation

Typical pump capacity coverage chart

- Typical pump capacity coverage chart is a complex figure and requires some examination.
- The composite chart is useful for locating a particular pump is the flow rate-head requirement is known. Generally, the information available from composite chart is not sufficient for pump-selection or system-analysis purposes, and complete performance characteristics are needed for each pump within the family.
- The specific pump number 2x3-10 contains three pieces of information: (1) the first number is the volute discharge diameter, 2 in.; (2) the second number is the suction (inlet) diameter, 3 in.; and (3) the last number is the maximum impeller (rotor) diameter, 10 in.

Typical pump performance curve

Superposition of system curve and pump performance curve

Homework5 Webpage

Due, Wednesday, April ??, 2011

Omar E. Meza Castillo Ph.D.