So Far: Conservation of Mass, Flow Rates Fluid Flow, Re No., Laminar/Turbulent

So Far:Conservation of Mass, Flow Rates

Fluid Flow, Re No., Laminar/TurbulentPressure Drop in PipesBernoulli’s EquationFlow Measurement, ValvesTotal Head, Pump Power, NPSH

This Week:Pump Sizing, Types of PumpsConservation of Energy

Pump Sizing

1. Volume Flow Rate (m3/hr or gpm)

2. Total Head, h (m or ft)

2a. P (bar, kPa, psi)

3. Power Output (kW or hp)

4. NPSH Required

hgP

Pumps

Centrifugal

Impeller spinning inside fluid

Kinetic energy to pressure

Flow controlled by Pdelivery

Positive Displacement

Flow independent of Pdelivery

Many configurations

Centrifugal Pumps

Constantρgzρv2

1P 2

Impeller

SuctionVolute Casting

Delivery

Centrifugal Pumps

Flow accelerated (forced by impeller)

Then, flow decelerated (pressure increases)

Low pressure at center “draws” in fluid

Pump should be full of liquid at all times

Flow controlled by delivery side valve

May operate against closed valve

Seal between rotating shaft and casing

Centrifugal PumpsAdvantages

Simple construction, many materialsNo valves, can be cleaned in placeRelatively inexpensive, low maintenanceSteady delivery, versatileOperates at high speed (electric motor)Wide operating range (flow and head)

DisadvantagesMultiple stages needed for high pressuresPoor efficiency for high viscosity fluidsMust prime pump

Centrifugal PumpsH-Q Chart

Head

(or P)

Volume Flow Rate

Increasing Impeller Diameter

A B C

Centrifugal PumpsH-Q Chart

Head

(or P)

Volume Flow Rate

A B C

Increasing Efficiency

Required NPSH

Centrifugal PumpsH-Q Chart

Head

(or P)

Volume Flow Rate

A B C

Centrifugal PumpsH-Q Chart

Head

(or P)

Volume Flow Rate

Required Flow

CapacityActual Flow

Capacity

Required Power

Centrifugal PumpsPump sizing example.

Let’s say we need a pump for the following application:

Total head: 40 mFlow rate: 2.5 m3/hrNPSH available: 2 m

Using the pump curve provided last week. Select the appropriate impeller and determine the flow capacity with that impeller, pump power input, NPSH required and efficiency.

Centrifugal Pumps

What if available NPSH is less than required NPSH?

Increase Available NPSH1. Increase suction static head (pump location)

2. Increase suction side pressure

3. Decrease fluid vapor pressure

4. Reduce friction losses on suction side

Decrease Required NPSH1. Reduce pump speed

2. Select a different pump

Centrifugal Pumps

Curves created for specific speed, viscosity and density

Often, use more charts or correction factors to “fine tune” pump selection

Variable speed motor has same effect as impeller size

Multiple pump/impeller combinations may work

Centrifugal Pumps

Closed ImpellerMost common, low solidsWater, beer, wortFlash pasteurizationRefrigerants

Open ImpellerLower pressuresSolids okayMash to lauter turnLiquid yeast, wort, hops

Positive Displacement Pumps

Theory: Volume dispensed independent of delivery head

Practice: As delivery head increases, some slippage or leakage occurs

Speed used to control flow rate, use of valves could cause serious damage

Self-priming

Good for high viscosities, avoiding cavitation

Positive Displacement Pumps

Piston Pump

Volumetric Efficiency High Pressures

Metering hop compounds, detergents, sterilents

Suction Valve

Delivery Valve

Positive Displacement Pumps

Peristaltic Pump

Positive Displacement Pumps

Gear Pump

High Pressures

No Pulsation

High Viscosity Fluids

No Solids

Difficult to Clean

Positive Displacement Pumps

Lobe Rotor Pump

Both lobes driven

Can be sterilized

TransferYeastTrubBulk Sugar Syrup

Liquid-Solid Separation

Types of FiltrationGravity, Vacuum, Pressure, Centrifugal

Driving Force

MechanicalDialysis Electrostatic Magnetic

Filtration Sedimentation

FiltrationMedia

Glass fiberPaper fabricMonofilament clothMetal or plastic mesh or screenPack beds

Bridging effect of filter cloth

Filter cake buildup becomes

“filter media”

Filtration

Performance of Filters• Ability to retain solids (high surface area)• Low flow resistance• Mechanical strength• Low cost• Inert to cleaning/processing chemicals

Brewery applications of filtrationMash or Lauter tun – gravity filtrationFiltering wort and beer – pressure filtrationSeparating beer from yeast – pressure filter

Liquid-Solid Separation

Sedimentation – gravity or centrifugal

Terminal settling velocity – time required

TSV increases with:

Larger particles

Greater density difference

between fluid, particle

Lower fluid viscosity

Next Slide: Shift Gears to Properties, First Law

Weight

Drag Force

Steam Table ExamplesDetermine the phase, enthalpy and specific volume of the following:

P = 1 bar, T = 25C

P = 1 bar, T = 160C

T = 150C, v = 0.5 m3/kg

ExampleDetermine the amount of energy required to heat 500 gallons of water from 20C to 220C at constant pressure (1.0 bar).

Enthalpy of fusion: 333.55 kJ/kgEnthalpy of vaporization: 2260 kJ/kgSpecific heat of ice: 2.1 kJ/kg.KSpecific heat of liquid water: 4.2 kJ/kg.KSpecific heat of steam (cp): 2.2 kJ/kg.K)

1 m3 = 264.2 gal

Laws of Thermodynamics• First Law – Energy is conserved• Second Law – Energy has quality, processes go in certain directions only

Forms of Energy• Potential energy = mgh• Kinetic energy = (0.5)mv2

• Internal energy (U) – microscopic forms

Conservation of Energy

systemoutin dt

dEEE

Systemoutin EEE

Energy Interactions• Heat transfer – Temperature difference• Work – Shaft, electrical, boundary, etc.• Mass flow – U + PV = Enthalpy (H)

Closed System Energy Equation

systemoutout

outoutoutout

inin

inininin

Egzv

umWQ

gzv

umWQ

2

2

2

2

1212 )( TTmcuumE vsystem No Phase Change

Open System Energy Equation

for steady flow systems

or

dt

dEgz

vhmWQ

gzv

hmWQ

systemout

outoutoutoutout

inin

inininin

2

2

2

2

0dt

dEsystem

tQQ t

QQ

ExampleA 2 m3 tank is filled to a pressure of 150 psig using an air compressor. After the tank has been filled, it’s temperature is 157F. Over the course of 20 hours, the tank cools to 56F. (cv = 0.718, cp = 1.04 kJ/kg.K).

a) Determine the mass of air in the tank.b) Determine the pressure in the tank after it has cooled.c) Determine the amount and average rate of heat transfer during the cooling process in kJ and W, respectively.

A 500 gallon water tank is filled with 220 gallons of hot water at 80C and 280 gallons of cold water at 10C. Assume that the specific heat of water is 4.2 kJ/kg.K.

a) Determine the temperature in the tank after it has been filled.

b) How much heat must be added to the tank to bring its temperature to 65C?

c) If a 30 kW electric heater is used, how long will the heating process take?

500 kg of grain (25C) is mixed with hot (80C) and cold (10C) water for mashing. The water to grain ratio (by weight) is 3:1 and the specific heat capacities of the water and grain are 4.2 and 1.7 kJ/kg.K, respectively.

a) If the desired “mash in” temperature is 38C, how much hot and cold water should be added?

(Continued) A three step mashing process, with 20 minute-long rests at 50, 62 and 72C, is desired. The mash should be heated quickly, but not too quickly between rests; with an optimal rate of 1C per minute. Neglect heat losses to the surroundings.

b) Plot the mash temperature vs. time.

c) Determine the heating power required, in kW.

d) Determine the total heat required for the mashing process, in kJ.

Two types of heat sources are available for mashing, electric resistance heaters and steam. The steam enters a heating jacket around the mash as dry, saturated steam at 300 kPa and it exits the system as wet, saturated steam at the same pressure (enthalpy of vaporization = 2150 kJ/kg).

(e) What is the total power required for the electric heaters, in kW?

(f) If steam is used, what is the total mass of steam required, in kg?

At the location of our brewery, electricity costs $0.14/kW-hr and the steam can be generated for $0.03 per kg.

(g) What is the mashing cost when electric resistance heaters are used?

(h) What is the cost with steam?