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Fluid Dynamics for Brewing Fluids

Fluid Dynamics for Brewing Fluids. Lecture 1. Fluid Dynamics Lecture 1- P 1. Learning Objective – Goals for Today. Definition of fluids Fluid physical properties Fluid flow characteristics Laminar flow concept Turbulent flow concept Dimensionless number groups (Reynolds number).

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Fluid Dynamics for Brewing Fluids

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  1. Fluid Dynamics for BrewingFluids Lecture 1 Fluid Dynamics Lecture 1- P 1

  2. Learning Objective – Goals for Today • Definition of fluids • Fluid physical properties • Fluid flow characteristics • Laminar flow concept • Turbulent flow concept • Dimensionless number groups (Reynolds number) Problem set #1 will cover these topic areas Fluid Dynamics Lecture 1- P 2

  3. Learning Objective – Goals for Today • What is a fluid? • What fluids are we concerned about as brewers? • How do we use fluids in the brewery? Fluid Dynamics Lecture 1- P 3

  4. Definition of Fluids A fluid is a substance that will “deform” or flow when a force or “shear stress” is applied. Fluid Dynamics Lecture 1- P 4

  5. Definition of Fluids • In our everyday speech, we generally use the word “fluid” when talking about a liquid substance (e.g. “spinal fluid” or “brake fluid”), but a substance doesn’t need to be a liquid in order to be classified as a fluid. • Types of substances that can be classified as fluids include • Liquids • Gases • Plasmas Let’s look into each of these in more detail…… Fluid Dynamics Lecture 1- P 5

  6. Definition of Fluids - Liquids • A substance that is classified as a liquid is comprised of molecules that are very close together, but the molecules are not permanently bonded to one another. • Molecules in a liquid are held together by temporary intramolecular bonds that are continually breaking and re-forming. • Because the bonds are not permanent, the molecules of a liquid are able to move around among one another. Fluid Dynamics Lecture 1- P 6

  7. Definition of Fluids - Liquids • Properties that are characteristic of liquids include: • Able to flow • Assumes the shape of the container in which stored • Distributes pressure evenly within container • Virtually incompressible • Volume only slightly dependent upon temperature Fluid Dynamics Lecture 1- P 7

  8. Definition of Fluids - Gases • A substance that is classified as a gas is comprised of molecules that are widely separated from one another • Molecules in a gas are moving rapidly, and the intramolecular bonds that might exist between molecules is far too weak are to hold the molecules together Fluid Dynamics Lecture 1- P 8

  9. Definition of Fluids - Gases • Properties that are characteristic of gases include: • Able to flow • Assumes the shape of the container in which stored • Distributes pressure evenly within container • Compressible • Volume depends on temperature Fluid Dynamics Lecture 1- P 9

  10. Definition of Fluids The most important fluids in brewing are liquids and gasses • The most important liquids are generally water based: • Hot/cold liquor for mashing • Wort • Beer • Cleaning solutions • The most important gases are • Carbon dioxide • Saturated steam (as a heating source) • Compressed air (used to actuate valves, pumps, etc.) Fluid Dynamics Lecture 1- P 10

  11. Fluid Physical Properties • Fluids are physical things and they have some physical properties that are common to many substances: • Melting point • Freezing point • Boiling point • They also have physical properties that might not be as familiar: • Density • Specific Gravity • Viscosity • Heat Capacity • Surface Tension • Thermal Expansion coefficient • Thermal conductivity • etc….. Fluid Dynamics Lecture 1- P 11

  12. Fluid Physical Properties • The fluid physical properties that are most important to understand within the study of Fluid Dynamics are: • Density • Specific Gravity • Viscosity • These physical properties are important in Fluid Dynamics because they are intimately involved in the calculations necessary to understand, define and model the physical systems in which the fluids are moving. Let’s look into each of these important physical properties in more detail. Fluid Dynamics Lecture 1- P 12

  13. Fluid Physical Properties - Density • The Density of a material is defined as the mass of a material that fills a particular amount of space. • More succinctly stated, Density is Mass per unit Volume. • Even more succinctly stated, Density is: Where: • ρ = Density (kg/m3, lb/ft3, g/cm3….) (pis the Greek letter rho) • M = Mass (kilograms, pounds, grams….) • V = Volume (m3, liters, ft3, gallons….) • Density = Mass per unit Volume Fluid Dynamics Lecture 1- P 13

  14. Fluid Physical Properties - Density • The Density of a material can be thought of as the amount of matter contained within a unit volume of space. • At a molecular level, the density of a substance depends upon how close together the molecules are, and on the atomic mass of the individual molecules M1 = 10 kg V1 = 1 liter ρ1 = M1/V1 ρ1 = 10 kg/liter M2 = 5 kg V2 = 1 liter ρ2 = M2/V2 ρ2 = 5 kg/liter Fluid Dynamics Lecture 1- P 14

  15. Fluid Physical Properties - Density • The density of a fluid is usually temperature dependent: • The density of gasses is highly temperature dependent. • The density of liquids is less temperature dependent. ρ = f(T) Density = Mass per unit Volume Fluid Dynamics Lecture 1- P 15

  16. Fluid Physical Properties - Density • Here are some examples of the dependence of density on temperature for air and water: Air Water Note that as temperature increases, density decreases…usually…. Fluid Dynamics Lecture 1- P 16

  17. Fluid Physical Properties - Density • The reason that density decreases with increasing temperature is because at higher temperatures, as more energy is added to the system, the molecules within the system vibrate faster and with greater vibrational amplitude. • When the molecules vibrate with greater amplitude they are, on average, farther apart. • When the molecules within the system are farther apart, the system has effectively “expanded” and increased its volume. • Since ρ = f(M,V), the density is changed when the volume changes Fluid Dynamics Lecture 1- P 17

  18. Fluid Physical Properties - Density • There are, of course, exceptions to this rule, and one is quite important to our life on planet Earth. • Notice again the table showing the relationship between density and temperature for water • The value for density at 0°C is lower than the value of density at 4°C. This happens because of the way that water molecules begin to arrange themselves as the temperature of the system approaches the freezing point. • This is very good for us because this means that ice floats ! Water If ice didn’t float, life for us on Earth would be very different…….. Fluid Dynamics Lecture 1- P 18

  19. Fluid Physical Properties - Density • Lets work an example: • Problem: If you have a completely filled 5 gallon bucket of water, and the mass of the water contained in the bucket is precisely measured to be 41.7 lbs, what is the density of the water. • Solution: It is a good thing to remember that, at room temperature: Density of Water = 1 g/ml = 1 kg/ liter = 1000 kg/m3 = 62.4 lb/ft3 = 8.34 lb/gal Fluid Dynamics Lecture 1- P 19

  20. Fluid Physical Properties – Specific Gravity • The Specific Gravity of a material is defined as the ratio of the density of a substance relative to the density of water. • Succinctly stated, Specific Gravity is: Where: • SG = specific gravity of a substance (dimensionless) • ρsubstance = density of a substance (kg/m3, lb/ft3, g/cm3….) • ρwater = density of water (kg/m3, lb/ft3, g/cm3….) Be sure that densities are stated in the same units ! Fluid Dynamics Lecture 1- P 20

  21. Fluid Physical Properties – Specific Gravity • Specific Gravity is an important thing for brewers because it serves as a way to infer the density of a solution and allows a brewer to determine the amount of fermentable material that is dissolved within wort. • When a liquid solution contains dissolved substances, the mass of a given volume the solution increases as more and more of the solute is dissolved. Mass per unit volume (density) increases with increasing concentration. • Because it is more difficult to directly measure density than specific gravity, brewers use hydrometers to measure specific gravity in order to infer the concentration of fermentables in the wort. Fluid Dynamics Lecture 1- P 21

  22. Fluid Physical Properties – Specific Gravity • Hydrometers are tools used to measure the specific gravity of a liquid • Hydrometers are placed in liquid and sink until immersed enough for the buoyant force from the liquid equals the downward force of gravity. Fluid Dynamics Lecture 1- P 22

  23. Fluid Physical Properties – Specific Gravity The curved upper surface of the liquid is called the “meniscus” (taken from the Greek word for crescent) Read the value that is level with the bottom of the meniscus Fluid Dynamics Lecture 1- P 23

  24. Fluid Physical Properties – Specific Gravity • Lets work an example: • Problem: If you have a completely filled 1 gallon container of gasoline, and the mass of the gasoline is 6.3 lbs, what is the specific gravity of the gasoline? • Solution: It is a good thing to remember that, at room temperature: Density of Water = 1 g/ml = 1 kg/ liter = 1000 kg/m3 = 62.4 lb/ft3 = 8.34 lb/gal Fluid Dynamics Lecture 1- P 24

  25. Fluid Physical Properties – Specific Gravity • Lets work another example: • Problem: If the specific gravity of beer is 1.012, what is the mass of beer contained in a completely filled beer barrel (31 gallons)? • Solution: It is a good thing to remember that, at room temperature: Density of Water = 1 g/ml = 1 kg/ liter = 1000 kg/m3 = 62.4 lb/ft3 = 8.34 lb/gal Fluid Dynamics Lecture 1- P 25

  26. Fluid Physical Properties - Viscosity • The viscosity of a fluid is a measure of the resistance of the fluid to deformation by an applied force or shear stress • For fluids, this can generally be thought of as the “thickness” of the liquid. Think “thick liquids flow slow”……. Fluid Dynamics Lecture 1- P 26

  27. Fluid Physical Properties - Viscosity • Viscosity is a strong function of temperature, so viscosity data always includes some reference to the temperature for which the provided data is correct. • Viscosity of a fluid can also be a function of pressure, and, in the case of a solution, is also a function of the composition of the solution. It is common in the U.S. to see viscosity data stated in units of centipoise (cP) Fluid Dynamics Lecture 1- P 27

  28. Fluid Physical Properties - Viscosity • Viscosities of different fluids can vary across a range of many orders of magnitude: It is common in the U.S. to see viscosity data stated in units of centipoise (cP) Fluid Dynamics Lecture 1- P 28

  29. Fluid Physical Properties - Viscosity Water T = cooler Molecules closer together μ = higher Water T = warmer Molecules farther apart μ = lower Fluid Dynamics Lecture 1- P 29

  30. Fluid Physical Properties - Viscosity Pressure Pressure Pressure Pressure Water P = higher Molecules (slightly) closer together μ = higher (slightly) Water P = Lower Molecules (slightly) farther apart μ = lower (slightly) Fluid Dynamics Lecture 1- P 30

  31. Fluid Physical Properties - Viscosity - + + F F - - F + + + + High Intermolecular Forces (e.g Water) F = higher Molecules more attracted μ = higher Lower Intermolecular Forces (e.g Methane) F = Lower Molecules less attracted μ = lower (slightly) Fluid Dynamics Lecture 1- P 31

  32. Fluid Physical Properties - Viscosity O O H H H H F F Smaller Molecules (e.g Water) SA = Smaller Less total force between molecules μ = lower Larger Molecules (e.g Glucose) SA = Higher More total force between molecules μ = higher Fluid Dynamics Lecture 1- P 32

  33. Fluid Physical Properties - Viscosity Flow Flow “Sphere-Like” Molecules (e.g Water) SA = Smaller, Entanglement = lower Less total interaction during flow μ = lower Chain/Spider-Like Molecules (e.g sucrose) SA = Higher, Entanglement = higher More total interaction during flow μ = higher Fluid Dynamics Lecture 1- P 33

  34. Fluid Physical Properties - Viscosity Lower Concentration Solute molecules farther apart Weaker forces between solute molecules μ = lower Higher Concentration Solute molecules closer together Stronger forces between solute molecules μ = higher Fluid Dynamics Lecture 1- P 34

  35. Fluid Flow characteristics • In the brewery we are primarily concerned with “water-like” fluids flowing through systems of pumps, pipes, hoses, valves, and nozzles. • Let’s closely examine how a fluid flows in a pipe. • We will start by looking at pipe with relatively slow-moving liquid flowing through it. Fluid Dynamics Lecture 1- P 35

  36. Fluid Flow characteristics – Laminar Flow • For a relatively slow-moving fluid, the fluid velocity of a discrete volume element within the pipe changes from a value that is effectively zero (V=0) at the pipe wall, to a value that is a maximum velocity (Vmax) at the centerline of the pipe. In this situation, average velocity (Vavg) of flow within the pipe is given by: • Looking at a cross-section of the “face” of the fluid flow front we see that is has the shape of a parabola. Fluid flowing in this way is said to be experiencing “Laminar” flow. Vavg = ½ Vmax V=0 at wall Parabolic Curve Vmax Vavg Fluid Dynamics Lecture 1- P 36

  37. Fluid Flow characteristics – Laminar Flow • Fluids that are experiencing Laminar flow are moving in a smooth, non-turbulent way within the pipe. Laminar flow is characterized by smooth streamlines and highly-ordered motion. • The fluid can be thought of as moving kind of like what we see when we pull a radio antenna to its full length; one cylinder pulls along within a larger cylinder, which pulls along within a still larger cylinder, etc…… Laminar Flow in Pipe Fluid Dynamics Lecture 1- P 37

  38. Fluid Flow characteristics – Turbulent Flow • Turbulent flow occurs when the velocity of the fluid in the pipe is large enough such that the momentum force of the moving fluid elements reaches a point that exceeds the viscous drag forces within the system. • In this situation, the velocity profile looks much less like a parabola. The velocity profile is much closer to being constant across the face of the fluid flow. V=0 at wall V Vmax Fluid Dynamics Lecture 1- P 38

  39. Fluid Flow characteristics – Turbulent Flow • Fluids that are experiencing Turbulent flow are moving in a way that is far more chaotic, and “violent” within the pipe. Turbulent flow is characterized by velocity fluctuations and highly disordered motion. • The fluid can be thought of as rolling around on itself, back-mixing and churning….. Turbulent Flow in Pipe Fluid Dynamics Lecture 1- P 39

  40. Fluid Flow characteristics – Transition Flow • There is also a flow situation in which the fluid flowing in the pipe experiences a back-and-forth change between Laminar and Turbulent flows. This is called “Transition flow”. • Transition flow is characterized by rapid, surging pressure changes within the system, and generally chaotic, unpredictable flow patterns. Transition Flow in Pipe

  41. Fluid Flow characteristics • It is important to understand if a system is experiencing Laminar, Turbulent or Transition flow because pumps and fluid transport systems and control valves must be designed to work properly under the real-world conditions that exist. • Fortunately, there is a way to predict whether a system is experiencing Laminar, Turbulent or Transition flow……. Fluid Dynamics Lecture 1- P 41

  42. Dimensionless Number Groups • The transition from Laminar to Turbulent flow in pipes depends on myriad physical parameters within the fluid-flow system including: • Geometry or the system • Roughness of the pipes • Flow velocity • Fluid density • Fluid viscosity • Fluid temperature (affects density & viscosity) • After extensive experiments in the 1880s, a man named Osborne Reynolds discovered that the flow regime depends mainly on the ratio of Inertial Forces to Viscous Forces within the fluid. He then developed a relationship to express this ratio for particular physical situations using a single, dimensionless number. Fluid Dynamics Lecture 1- P 42

  43. Dimensionless Number Groups – NRe • This number is derived by mathematically combining the important components within the fluid-flow system in such a way that the units all cancel out. • When this is done, a pure number is derived that lets you infer information regarding the flow conditions within the system. For liquids flowing in a pipe, this number, called the Reynolds Number, is given by: Where: ρ = Density of the liquid V = Average liquid velocity in the pipe D = Diameter of the pipe μ = Dynamic viscosity of the liquid Fluid Dynamics Lecture 1- P 43

  44. Dimensionless Number Groups– NRe • It is generally observed that the flow characteristics for liquids in a circular pipe are described by the Reynolds number as follows: Fluid Dynamics Lecture 1- P 44

  45. Dimensionless Number Groups– NRe • Now that we have consistent units for the physical quantities, plug them into the equation for Reynolds number: = 2.85 x 104 = 28,500 NRe > 2300, so the flow is Turbulent Fluid Dynamics Lecture 1- P 45

  46. Dimensionless Number Groups– NRe • But what if we had a smaller pipe and slower flow? How would changing these physical characteristics affect Reynolds number? • Problem: Water is flowing through a 0.5 cm (0.005 m) diameter pipe at an average velocity of 0.1 m/s. The dynamic viscosity of the water is 1.05 x10-5 kg/m-s. The density of water is 998 kg/m3. What kind of flow is occurring? = 475 NRe < 2000, so the flow is Laminar Fluid Dynamics Lecture 1- P 46

  47. Dimensionless Number Groups– NRe • Let’s do one more practice problem with English units. • Problem: Water is being pumped through a 2 in i.d. pipe at a rate of 20 gallons/min. The dynamic viscosity of the water is 1.8 cP. The density of water is 8.34 lb/gal (62.4 lb/ft3). What kind of flow is occurring? • Solution: First, let’s determine the average flow velocity in the pipe. Fluid Dynamics Lecture 1- P 47

  48. Dimensionless Number Groups– NRe • determine the average flow velocity in the pipe (continued)… Pipe i.d. is 2 inches, but we need pipe diameter units of ft so: The cross-sectional area of the pipe is determined by: Fluid Dynamics Lecture 1- P 48

  49. Dimensionless Number Groups– NRe • determine the average flow velocity in the pipe (continued)… We now have: Dividing volumetric flow by the cross-sectional area gives average fluid velocity: Fluid Dynamics Lecture 1- P 49

  50. Dimensionless Number Groups– NRe • Now that we have the fluid velocity and diameter in the needed units, and we were given the density in the problem statement here’s what we have so far: • Using the conversion factor 1 cP = 6.721x10-4 lb/ft*s, we convert viscosity to the needed units: Fluid Dynamics Lecture 1- P 50

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