1. Fluid Dynamics for Brewing
Lecture 3
Fluid Dynamics Lecture 3- P 1

2. Problem set #3 will cover these topic areas
Learning Objective – Goals for Today
Pump Types
Centrifugal Pump
Air-operated Diaphragm Pump
Pump Properties & Pump Curves
Whirlpools
Theory
Practice
Problem set #3 will cover these topic areas
Fluid Dynamics Lecture 1- P 2

3. Pumps
Fluids are moved through pipes or ducts using pumps, fans, blowers and compressors.
These devices impart mechanical energy to the fluid which can be used to move the fluid (increase its velocity), increase the pressure in the fluid, or lift the fluid vertically against the force of gravity
Fluid Dynamics Lecture 3- P 3

4. Pumps
The term pump, fan, bower and compressor are often used rather loosely and do not really have a universally accepted, precise definition
We generally speak of pumps moving liquids, while fans, compressors, or blowers either move or compress gases.
Pumps move liquids.
Fluid Dynamics Lecture 2- P 4

5. Pumps
In a brewery, you are most likely to encounter pumps that are widely used throughout industry and available from many different commercial vendors.
Common types of pumps that you might see in the brewery include:
Centrifugal pumps
Air-operated Diaphragm pumps
Of these, the centrifugal pump is generally the “workhorse” within the brewery
Fluid Dynamics Lecture 3- P 5

6. Pumps - Centrifugal
Although there are many, many different types of pumps available in the marketplace, the kind of pump that is most often used to move most kinds of liquids in a brewery is a centrifugal pump.
A centrifugal pump is a fairly simple machine that is designed to impart energy to a fluid. The energy can cause the fluid to rise against gravity or flow through a closed system (pipes).
Fluid Dynamics Lecture 3- P 6

7. Pumps - Centrifugal
The centrifugal pump achieves liquid movement and flow by “slinging” the fluid out of the impeller using centrifugal force.
The two main parts of a centrifugal pump head are the impeller and the diffuser (or volute).
The impeller is the only moving part within the pump head
The impeller spins within the pump head housing and the diffuser captures and directs the flow of liquid from the impeller.
Fluid Dynamics Lecture 3- P 7

8. Pumps - Centrifugal
Liquid is drawn into the pump head near the center of the impeller and pushed outwards by the movement of the blades on the impeller
The liquid is “slung out” by the movement of the spinning impeller
Fluid Dynamics Lecture 3- P 8

9. Pumps - Centrifugal
Here’s a picture to help you visualize what’s going on inside the pump head housing:
Fluid Dynamics Lecture 3- P 9

10. Pumps - Centrifugal
For a centrifugal pump, the flow rate that can be achieved is an inverse function of pressure. A centrifugal pump will deliver less flow when pumping against a higher back-pressure.
The specific way in which this relationship holds true depends upon the details of the pump design.
In general, as back-pressure increases, flow decreases.
Fluid Dynamics Lecture 3- P 10

11. Pumps - Centrifugal ℎ 𝐿𝑝𝑖𝑝𝑒 =𝑓 𝐿 𝐷 𝑉 2 2𝑔 ℎ 𝐿𝑐𝑜𝑚𝑝 = 𝑖=1 𝑛 𝐾 𝑛 𝑉2 2𝑔
The velocity of fluid flow within a particular piping system is an important consideration as it directly impacts the overall restive pressure associated with moving liquid through the system.
Higher liquid flow rates will result in higher resistive pressure within the system due to pipe friction; recall that the pressure drop due to pipe friction and component friction is directly proportional to the square of the velocity of the liquid flowing through a pipe:
ℎ 𝐿𝑝𝑖𝑝𝑒 =𝑓 𝐿 𝐷 𝑉 2 2𝑔
ℎ 𝐿𝑐𝑜𝑚𝑝 = 𝑖=1 𝑛 𝐾 𝑛 𝑉2 2𝑔
Fluid Dynamics Lecture 3- P 11

12. Pumps - Centrifugal
Here is a graph that illustrates the general relationship between flow velocity, system pressure and centrifugal pump capability:
Fluid Dynamics Lecture 3- P 12

13. Pumps - Centrifugal Operating Point
This graph also illustrates how actual pump performance for a particular system is determined.
The blue curve is known as the system curve, and it shows how backpressure within the system varies with flow rate
The orange curve is the pump performance curve and it shows how the capability of a centrifugal pump to deliver a given flow rate is affected by system pressure.
The intersection of the two curves is known as the “operating point “ for the system.
Operating
Point
Fluid Dynamics Lecture 3- P 13

14. Pumps - Centrifugal
The characteristics of the system curve change depending upon the physical configuration of the system
The system curve characteristics depend upon the height to which liquid must be pumped, the diameter and length of the piping within the system, and the number and types of fittings, valves, etc. within the system
Recall that hLtot= hLelev+ hLpipe+ S hLcomp
Fluid Dynamics Lecture 3- P 14

15. Pumps - Centrifugal
This means that we are able to manipulate the flow rate of liquid delivered by the pump by increasing or decreasing the total amount of back pressure within the system
We can do this by increasing or decreasing the friction within the system by closing or opening a valve
Increasing and decreasing the friction within the system will shift the system curve and change the operating point within the system
Fluid Dynamics Lecture 3- P 15

16. Pumps - Centrifugal
Here’s a graph that illustrates the concept using the opening & closing of a valve:
System Curve
With Fully
Opened Valve
With 1/2
Pump
Capability
Curve
Head,
ftH2O
Flow,
gpm
100 90 80 70 60 50 40 30 20 10
Pressure
change due
to closing or
opening valve
Flow rate
Fluid Dynamics Lecture 3- P 16

17. Pumps - Centrifugal
There are several ways to modify the flow output of a centrifugal pump
Change impeller diameter
Change impeller speed
Increasing the impeller diameter will increase the flow output of a centrifugal pump. The extent to which the flow will change is shown on manufacturer’s pump curves.
Increasing the rotational velocity of the impeller will increase the flow output for a centrifugal pump. The amount of flow increase is directly proportional to the rotational velocity increase.
Changing the rotational velocity also has other operational performance implications. The relationship between impeller rotational velocity and flow, pressure head, and power requirements are know as the pump Affinity Laws.
Fluid Dynamics Lecture 3- P 17

18. Pumps - Centrifugal The pump Affinity Laws are: Succinctly stated: 𝑄∝𝑁
Flow is directly proportional to impeller speed
Pressure (head) is proportional to the square of impeller speed
Power requirement is proportional to the cube of impeller speed
Succinctly stated:
𝑄∝𝑁
𝐻∝ 𝑁 2
𝑃∝ 𝑁 3
Where:
Q = Flow rate
H =Delivered pressure (head)
P = Power required
Fluid Dynamics Lecture 3- P 18

19. Pumps - Centrifugal
We can write the pump affinity laws in another, equivalent, way:
Then use these forms of the pump affinity law equations to predict what happens when the rotational velocity of the impeller is changed.
𝑄 2 𝑄 1 = 𝑁 2 𝑁 1
𝑄 2 = 𝑄 1 𝑁 2 𝑁 1
𝐻 2 𝐻 1 = 𝑁 𝑁 1 2
𝐻 2 = 𝐻 𝑁 𝑁 1 2
𝑃 2 𝑃 1 = 𝑁 𝑁 1 3
𝑃 2 = 𝑃 𝑁 𝑁 1 3
Fluid Dynamics Lecture 3- P 19

20. Pumps - Centrifugal
Example Problem: Flow from a pump is measured to be 100 gpm. Delivered pressure head is 100 ftH2O. Power requirements are 5 h.p. The pump impeller rotational velocity is increased from 1750 rpm to 3500 rpm. What effect does increasing the impeller rotational velocity have on flow rate, delivered pressure and power consumption?
Fluid Dynamics Lecture 3- P 20

21. Pumps - Centrifugal
Solution: Use the pump affinity law equations and substitute the information in the problem statement:
Q1 = 100 gpm
H1 = 100 ftH2O
P1 = 5 h.p.
N1 = 1750 rpm
N2 = 3500 rpm
𝑄 2 = 𝑄 1 𝑁 2 𝑁 1 =100𝑔𝑝𝑚 𝑟𝑝𝑚 1750 𝑟𝑝𝑚 =200 𝑔𝑝𝑚
𝐻 2 = 𝐻 𝑁 𝑁 =100 𝑓𝑡 𝐻 2 𝑂 𝑟𝑝𝑚 𝑟𝑝𝑚 2 =400 𝑓𝑡 𝐻 2 𝑂
𝑃 2 = 𝑃 𝑁 𝑁 =5 ℎ.𝑝 𝑟𝑝𝑚 𝑟𝑝𝑚 3 =40 ℎ.𝑝.
Doubling impeller velocity increases flow by factor of 2, pressure by a factor of 4, and power consumption by a factor of 8

22. Pumps - Centrifugal
Another Example Problem: For an existing system, flow from a pump is measured to be 100 gpm. Maximum delivered pressure head is 100 ftH2O, and current power requirements are 8 h.p. at an impeller velocity of 875 rpm. Due to brewery expansion, a new, larger, heat exchanger is installed which increases the total system pressure head to 150 ftH2O. To what velocity must the pump impeller be increased in order to overcome the new higher system backpressure?
Fluid Dynamics Lecture 3- P 22

23. Pumps - Centrifugal
Solution: Write down the information in the problem statement:
Q1 = 100 gpm
H1 = 100 ftH2O
H2 = 150 ftH2O
P1 = 8 h.p.
N1 = 875 rpm
N2 = ? rpm
Then algebraically rearrange the relevant Affinity Law equation:
𝑁 2 = 𝑁 𝐻 2 𝐻 1
𝐻 2 = 𝐻 𝑁 𝑁 1 2
𝐻 2 𝐻 1 = 𝑁 𝑁 1 2
𝑁 𝐻 2 𝐻 1 = 𝑁 2 2
Fluid Dynamics Lecture 3- P 23

24. Pumps - Centrifugal
Then substitute in the appropriate values from the problem statement:
H1 = 100 ftH2O
H2 = 150 ftH2O
N1 = 875 rpm
And solve:
𝑁 2 = 𝑁 𝐻 2 𝐻 1
𝑁 2 = 𝑟𝑝𝑚 𝑓𝑡 𝐻 2 𝑂 100 𝑓𝑡𝐻 2 𝑂 = 765,625 𝑟𝑝𝑚 =1072 𝑟𝑝𝑚
Impeller velocity must be increased from 875 rpm to 1072 rpm, an increase of approximately 23%

25. Pumps - Centrifugal
In order for a pump to move liquid, it must do work on the liquid, and work requires energy. Doing more work requires more energy.
The rate at which energy is used and work is done (work per unit time) is the definition of power.
The amount of power required to move a liquid is dependent upon the liquid flow rate, the back pressure within the system and the efficiency of the motor.
For a centrifugal pump, the (hopefully familiar) equation that describes the relationship is:
𝑃= 𝑄∆ 𝑃 𝑡𝑜𝑡𝑎𝑙 1714𝜂
Where:
P = Power (h.p.)
Q = Flow rate (gallons/minute or gpm)
DPtotal = total system pressure (pounds/in2 or psi)
h = overall pump efficiency
Fluid Dynamics Lecture 3- P 25

26. Pumps - Centrifugal
Centrifugal pump manufacturers typically supply performance curves for each of their pumps.
These are normally referred to as “pump curves”, and are generally developed using water as the reference fluid.
Most centrifugal pump curves allow for direct reading or easy determination of:
System pressure (head) vs. flow rate for any fluid
Pump efficiency for any fluid
Pump energy (horsepower) requirements for a system pumping water
Fluid Dynamics Lecture 3- P 26

27. Pumps - Centrifugal
Here is an example of a pump curve provided by a manufacturer:
Efficiency
NPSH
Impeller
Diameter
Developed
Head
Horsepower
Flow Rate
Fluid Dynamics Lecture 3- P 27

28. Pumps - Centrifugal Net Positive Suction Head (NPSH)
Net positive suction head (NPSH) is the pushing force at the intake of a pump. It is the force of the liquid pushing into the pump due to gravity, plus other head pressures
It can be thought of as the net positive pressure of the liquid entering the pump intake, and is determined by liquid head height or liquid head pressure + gravity pressure, minus friction loss.
NPSH is the head (pressure and gravity head) of liquid in the suction line of the pump that will overcome the friction resistive forces.
Fluid Dynamics Lecture 3- P 28

29. Pumps - Centrifugal Net Positive Suction Head Required (NPSHR)
NPSHR is the minimum amount of liquid pressure required at the intake port of a pump
Net Positive Suction Head Available (NPSHA)
is the amount of positive pressure head available at the pump intake after pipe friction losses and head pressure contribution has been accounted for
It is very important that NPSHA > NPSHR
Why…..?
Fluid Dynamics Lecture 3- P 29

30. Pumps - Centrifugal
When a centrifugal pump is pulling liquid in through the suction side of the impeller it is creating a large low- pressure situation immediately upstream of the impeller
If liquid is unable to flow into the pump intake fast enough, this low-pressure situation can become a VERY low- pressure situation.
If the pump suction is strong enough, a pump can create a vacuum that is so strong that the pressure within the pipe immediately upstream of the impeller is low enough for the liquid to begin to boil
This situation is given the name “cavitation”
Cavitation decreases pump performance and can cause damage to the pump.
Fluid Dynamics Lecture 3- P 30

31. Pumps - Centrifugal
To avoid this situation, ensure that centrifugal pumps are properly specified and installed in a location that maximizes available suction head (i.e. near the low-point within the piping system).
Tank #1
Tank #2 ü
Pump
Tank #1
Tank #2
Pump X
Fluid Dynamics Lecture 3- P 31

32. Pumps – Air Operated Diaphragm
Another kind of pump that is often found in breweries is an Air Operated Diaphragm (AOD) pump.
An Air Operated Diaphragm pump uses a combination of the reciprocating action of one or more diaphragms and internal inlet and outlet check valves to move fluid.
AOD pumps use compressed air to provide the energy needed to move fluids.
Air supply is shifted from one internal chamber to another to cause the diaphragm(s) to flex back and forth. Check valves open and close as internal pressure pushes the liquid through the pump.
Fluid Dynamics Lecture 3- P 32

33. Pumps – Air Operated Diaphragm
Here are some examples of AOD pumps …….
Fluid Dynamics Lecture 3- P 33

34. Pumps – Air Operated Diaphragm
……… and a view of the internals…………..
Air
Chamber
Distribution
System
Discharge
Manifold
Liquid
Diaphragm
Intake
Outer
Inner
Check-Valve
Ball
Seat
Fluid Dynamics Lecture 3- P 34

35. Pumps – Air Operated Diaphragm
……… and a view of the internals
Fluid Dynamics Lecture 3- P 35

36. 1 2 3 4 5 NM NM NM NM NM NM NM NM GIF Animation of AOD Pump NM NM
NM = No Movement
Liquid Flow Direction
Air Flow Direction NM NM

37. Pumps – Air Operated Diaphragm
AOD pumps differ from centrifugal pumps in several important ways:
Energy source:
Centrifugal: Electric motor
AOD: Compressed air
Effect of system head pressure
Centrifugal: flow varies with system head pressure
AOD: flow remains constant with changing system pressure
Inlet Condition Requirements
Centrifugal: Liquid must be in pump head; not self-priming
AOD: Liquid not needed at inlet; self priming
Fluid Dynamics Lecture 3- P 37

38. Pumps – Air Operated Diaphragm
Like centrifugal pumps, AOD pumps also have performance curves, but the things that AOD pump performance curves describe are different
The physical parameters that affect AOD pump performance are
Compressed air inlet pressure
Compressed air consumption rate
These parameters affect AOD pump performance and determine the output parameters for the pump.
AOD pump output parameters are:
Discharge pressure
Liquid flow rate
Fluid Dynamics Lecture 3- P 38

39. Whirlpools What, exactly is a whirlpool?
The first thing that I think of is the appliance manufacturer………..
Fluid Dynamics Lecture 3- P 39

40. Whirlpools
….but that’s not really exactly what we are talking about today.
Fluid Dynamics Lecture 3- P 40

41. Whirlpools Here are several definitions of a Whirlpool:
a swirling body of water that is produced by the meeting of currents flowing in opposite directions
water in swift, circular motion, as that produced by the meeting of opposing currents, often causing a downward spiraling action
a vortex, spinning around a central point
It seems that most people can agree that a whirlpool is “swirling water”
Fluid Dynamics Lecture 3- P 41

42. Whirlpools
A whirlpool occurs when two currents are moving in opposing directions, or at an angle to each other in such a way as to allow friction between the two currents to cause the water to spin, creating the whirlpool. 3 1 2
Fluid Dynamics Lecture 3- P 42 4 5

43. Whirlpools
A whirlpool can also be generated by inducing a liquid to swirl around, either from mechanical agitation (stirring):
or by tangentially directing the flow of a fast-moving stream within the bulk of the liquid:
Side
Top
Side
Top
Fluid Dynamics Lecture 3- P 43

44. Whirlpools
In many breweries, “whirlpooling” is a specific step in the brewing process.
Whirlpooling is done in order to help separate suspended solids (hop particles, hot-break material, trub etc.) from the liquid wort
Whirlpooling, if performed, is done right after the boil:
Fluid Dynamics Lecture 3- P 44

45. Finished Beer (ageing)
Barley
Water
Hops
Adjuncts
Yeast
Energy
Milling
Grind
Settings
Ground
Barley
Strain
Yeast
Starter
More
Yeast
Amount
Temp.
Mashing
Water to
Grist Ratio
Wort
Temp.
Sparging
Rate
Wort
Water to
Grist Ratio
Temp.
Boil
Boiled Wort
Time
Isomerized a-acids
Maillard Reaction Products
Type
Finings
Addition /
Whirl pooling
Amount
Hot Break
Time
Method
Wort
Cooling
Cooled Wort
Temp.
Time
Method
Wort
Aeration
Oxygenated
Wort
Amount
Method
Transfer to
Fermenter
Wort in
Fermenter
Transfer
Rate
Yeast Pitching
Temp.
Fermentation
CO2
Time
Beer
Dry Hopping
Time
Temp.
Conditioning
Secondary
Ferment
CO2
Beer
Lagering
Keg
Packaging &
Carbonating
Packaged Beer
Finished Beer
Bottle
Carbonated Beer
Time
Storage
Temp.
Finished Beer (ageing)
Light
Exposure
Consumption
Temp.
Joy !
Amount

46. Whirlpools
Breweries sometimes even have tanks that are specifically designated for whirlpooling. Here’s a PFD to illustrate this:
Fluid Dynamics Lecture 3- P 46

47. Whirlpools
The moving liquid in a whirlpool causes suspended particulate matter to move to the center of the tank and form a cone:
Fluid Dynamics Lecture 3- P 47

48. Whirlpools But why does this happen?
Why does rotating liquid within a tank cause suspended particulate matter to move inward?
Shouldn’t centrifugal force cause the particulate matter to be slung outward toward the tank wall?
What’s going on…….?
Fluid Dynamics Lecture 3- P 48

49. Whirlpools
First of all, lets talk through a simple, representative physical system (one that has been extensively analyzed) and discuss the forces at work within it. Let’s talk about tea in a teacup. Specifically, loose leaves being stirred in a teacup.
When the tea leaves are being stirred, they are rotating around the bottom of a cup, following the motion of the water that is induced by stirring. When the spoon is removed, the leaves begin to move towards the center and collect on the bottom of the cup (just like our trub collects in the center of the whirlpool).
Fluid Dynamics Lecture 3- P 49

50. Whirlpools
This can be explained by the fact that the pressure (and water level) near the side walls of the cup is higher than the pressure in the center when the water is rotating.
Note that the shape of the surface of the water, while the tea is rotating, is concave from the viewpoint of the drinker.
This pressure variation is the result of the centripetal acceleration that balances the centrifugal acceleration of the rotating liquid water.
It is this pressure gradient that induces a vortex effect within the system
But why does this pressure gradient exist?
Fluid Dynamics Lecture 3- P 50

51. Whirlpools
The pressure gradient exists because water near the bottom of the cup cannot move as freely as the rest of the water within the cup.
The water moves much more slowly near the bottom of the cup because of frictional resistance to the movement.
The water touching the wall of the cup also experiences a similar frictional effect.
As a consequence of fluid friction, the angular momentum of the water near the bottom is not enough to oppose the effect of the radial pressure field created by the rotating water away from the bottom boundary layer.
The pressure variation is such that it pushes the water near the bottom of the cup towards the center.
Fluid Dynamics Lecture 3- P 51

52. Whirlpools
Because mass is conserved in this flow, the water that is caused to move towards the center of the cup then turns upward towards the surface.
When the water is near the surface, it then turns towards the side wall and finally moves down towards the bottom, replenishing the water that was originally there.
The tea leaves recirculate with the water and eventually become entangled with one another near the bottom-center of the cup.
Once they are clumped together, the upward movement of the water near the center is no longer sufficient to create a buoyant force that can overcome the force of gravity acting upon the leaves. When this happens, the leaves remain on the bottom at the center of the cup.
Fluid Dynamics Lecture 3- P 52

53. Whirlpools To summarize:
Moving water and tea leaves (or wort and trub) do experience centrifugal force, but the whirlpool effect "overpowers" the centrifugal force and circulates everything toward the center of the vessel in question. The fluid friction at the bottom of the vessel is actually responsible for this.
A vortex is induced because the water near the top is pushed out harder due to higher centrifugal force and less friction at the top of the liquid.
The water near the bottom is pushed out with less force because there is more friction and a lower centrifugal force near the bottom to push it out.
The weaker centrifugal force at the bottom of the vessel induces a pressure gradient that creates an inward recirculation flow.
Fluid Dynamics Lecture 3- P 53

54. Whirlpools
For a commercial brewer, there are several factors that are important to consider when operating a whirlpool vessel:
vessel geometry,
feed velocity, and
rotation time
Fluid Dynamics Lecture 3- P 54

55. Whirlpools
Vessel geometry is an important consideration for a whirlpool vessel because it directly impacts the fluid dynamics within the system and thus directly affects the systems ability to establish a good vortex. Commercial breweries usually use cylindrical or slightly cone-bottomed vessels with a depth:diameter ratio of between 1:1 to 1:5.
Feed velocity also affects the final results of the whirlpool. If the initial rotational velocity is too low, a poorly compacted trub cone (or no cone at all) will be formed. If the initial rotational velocity is too high, the trub cone may not hold together. Initial rotational velocities generally are determined by trial and error.
Rotation time is important because all of the fluid-dynamic-induced forces must have time to work their magic. Generally, commercial breweries allow a rotation time of between 10 and 40 minutes. Smaller tanks generally require less rotation time.
Fluid Dynamics Lecture 3- P 55

56. Whirlpools
The optimum rotational velocity and rotation time for a whirlpool system depends on:
the geometry of the vessel,
the amount of friction between the wort and the vessel and
the clumping properties of the trub that is being formed into a cone within the whirlpool.
Optimal rotational velocity also depends (to a small extent) on the O.G. of the wort; whirlpool effectiveness decreases as the O.G. of the wort increases due to the fact that the relative density-differential between the wort and the trub decreases with increasing wort O.G.
Fluid Dynamics Lecture 3- P 56

57. Whirlpools
When we began this discussion, we said that whirlpooling is done by brewers in order to help separate suspended solids (hop particles, hot-break material, trub etc.) from the liquid wort.
But aren’t there other ways to separate suspended solids from liquids?
What about simply filtering the wort? Wouldn’t that work?
What about just allowing the particles to settle out naturally using gravity? Wouldn’t that work?
The answers are “Yes” to all of the above questions, but there are reasons why brewers whirlpool anyway……
Fluid Dynamics Lecture 3- P 57

58. Whirlpools
Filtration is certainly a viable way to remove suspended solids. Filtering beer or wort is a good option for some styles of beer, but there are numerous reasons why this may not be the best choice:
Filtering removes flavor and color-producing compounds from the beer.
Filtering is also likely to increase the rate of oxidation of the beer by exposing it to more air than an equivalent unfiltered beer.
Filters cost money to purchase, cost money and time to operate and maintain, and can be a potential source for contamination within the brewery.
Using gravity to allow the particles to naturally settle is also a viable way to remove suspended solids, but this can be a very slow process when very small particles are involved.
Fluid Dynamics Lecture 3- P 58

59. Whirlpools
Summary:
Whirlpools are used in the brewery to separate solid, particulate matter from liquid wort.
Whirlpools work the way they do because friction forces within the vessel create pressure differentials within the liquid that affect flow patterns and velocities within the whirlpool vessel
Factors that affect whirlpool vessel operation include:
vessel geometry,
liquid feed velocity, and
rotation time
Fluid Dynamics Lecture 3- P 59