Heat Transfer and Fluid Flow

Explain the General Energy Equation

(KE + PE + FE + U + Q)in =(KE + PE + FE + U + W)out + (KE + PE + FE + U)stored

Describe heat exchanger flow paths.

1. Crossflow heat exchanger - perpendicular action relative to the tube-side flow. 2. Parallel flow heat exchanger - shell side flow and tube side flow in the same direction. 3. Counterflow heat exchanger - shell side flow and tube side flow in opposite directions. Counterflow heat exchangers provide more heat transfer capabilities.

Saturation Temperature

the temperature at which the water first begins to evaporate into steam, while under a given pressure. Saturation is achieved when additional heat is supplied to the water and the water evaporates into steam instead of getting hotter.

Describe parallel pump operation and series pump operation.

Parallel Operation - More than one pump discharging into the same system increases capacity, while maintaining approximately the same discharge pressure or head. Series Operation - Series operation is when one pump discharges into the suction of the other pump. This increases the head for a given capacity.

Describe causes of water hammer.

Subcooled water with condensing steam in a vertical pipe (water cannon) Steam and water counterflow in a horizontal pipe (steam/water counterflow) Pressurized water entering a vertical steam-filled pipe (steam pocket collapse) Hot water entering a low pressure line (low pressure discharge) Steam-propelled water slug (water slug) Rapid valve actuation (valve slam) Filling of a voided line (column rejoining)

Steam Tables Consist of Three Sets of Tables

Table 1 - Saturated Steam Table By Temperature Table 2 - Saturated Steam Table By Pressure Table 3 - Superheated Steam Table

Critical Heat Flux (CHF)

The bubble motion greatly increases turbulence and mixing of the fluid, further increasing heat flux. As the temperature difference between the heated surface and the fluid is further increased, the limit of region II is approached and heat flux reaches a maximum value. This point of maximum heat flux is called departure from nucleate boiling (DNB) and the heat flux is termed critical heat flux (CHF).

Quality

Vapor Quality is the amount of vapor present in the mixture. When the mixture is steam, it is usually refereed to as steam quality. Quality is often given as a percentage, with a quality of 100% corresponding to saturated, or dry, steam.

First Law of Thermodynamics

also called the Conservation of Energy, Energy is neither created nor destroyed. One kind of energy can be transformed into another kind of energy, but the sum of the energies entering the process must equal the sum of energies stored or leaving the process. Energy In = Energy Out + Stored Energy

Heat Transfer Coefficient

depends on both the properties of the fluid and the nature of the flow (laminar or turbulent). Example Air, still = 1.7 btu/hr whereas Air, 15 mph = 6.0 btu/hr.

Natural Convection

does not involve external devices which move the fluid, but instead results from density gradients which develop in the fluid due to temperature gradients. Example: flat iron used to press clothing. When the iron is placed on its end with the heated surface near vertical, a current of rising hot air can be felt for some distance above the iron.

Mollier Diagram

graph of enthalpy versus entropy and is a graphic representation of the information presented in the steam tables. It is used when quality if above 50% and for superheated steam.

Internal Energy

(U) is the sum of energy in a substance. A substance possesses several microscopic forms of energy due to rotation, vibration, translation, and interactions among molecules of the substance.

Thermal Conductivity

(k), measure of how well a material transfers heat. Thermal conductivity of a material varies as a function of temperature.

Elements of Thermodynamic Cycle

1. Working Fluid 2. Device to move the working fluid (pump) 3. Heat source or high temperature reservoir 4. An engine for conversion of heat energy to work (turbine) 5. A heat sink or low temp reservoir (condenser)

Identify the six heat transfer flow types found in a fuel channel.

A. Mist Flow B. Annular Flow C. Slug Flow D. Bubble Flow E. Subcooled Boiling F. Single-Phased Forced Convection

Bulk Boiling

Bulk boiling occurs when the entire liquid is at or above saturation temperature for the existing pressure. When steam bubbles form at nucleation sites and move away from the heated surface they do not collapse, and the bulk of the fluid exists as a two-phase mixture of liquid and vapor.

Describe pump cavitation and gas binding.

Cavitation involves the formation and subsequent collapse of vapor bubbles formed in the suction side of the pump. Cavitation can be recognized by: fluctuating discharge pressure, oscillating motor amps, noise and vibration. Gas binding is a problem commonly caused by inadequate venting or entrained gases in the liquid, caused by fittings or lines trapping gases in the piping. The process of filling the pump with liquid and evacuating all gases is called priming. Adequate priming can normally be assured once a solid stream of fluid is obtained from the casing vent valve.

Define:

Closed System - A closed system has no transfer of fluid across its boundaries but often has a transfer of energy with its surroundings. An example of a closed system is the pressurized water reactors such as the reactor coolant system and the condensate feedwater system. Open System - An open system has a transfer of both mass and energy with its surroundings. An example of an open system is the condenser circulating water system that is either open to a lake or cooling tower.

Describe system draining and filling.

Closed systems require draining to perform maintenance. It may be necessary to drain a portion or the entire system. Prior to a draining evolution, power to equipment such as pump or valve motors must be isolated and tagged to prevent operation. Drain valves and high point vents are opened to drain the system. Upon completion of maintenance, it is desirable to fill the system from the lowest point. High point vents in piping or components such as heat exchangers and pumps are opened to allow air to vent. They are then closed when the system is water solid.

Describe how heat is transferred in a reactor fuel rod.

Conduction heat transfer takes place from the center of the fuel to the outer surfaces of the clad. Convection heat transfer takes place at the clad outer surface. The energy produced by the fuel results in a temperature profile from the center of the fuel rod to the reactor coolant. In addition to the radial temperature profile, the temperature in a reactor fuel road varies axially along the rod. Primary reasons are: 1. the neutron flux varies along the rod. 2. the reactor coolant temperature and the nature of heat transfer vary along the rod.

Isenthalpic Process

Constant Enthalpy

Isentropic Process

Constant Entropy

Isobaric Process

Constant Pressure

Isothermal Process

Constant Temperature

Explain mass flow and volumetric flow of a fluid in a pipe as described by the Continuity Equation.

Continuity Eqn: v1A1p1 = v2A2p2 Continuity of flow or steady state flow occurs when the same mass flow (ṁ) exists everywhere in a pipe. The continuity equation is a statement of the continuity of flow and is commonly in terms of mass flow rate. where v = average fluid velocity (ft/hr), A = cross-sectional area of flow (ft2), ρ = density (lbm/ft3), and ν = specific volume (ft3/lbm).

Departure from nucleate boiling (DNB)

DNB is the end of nucleate boiling and the beginning of decreased heat transfer.

Departure from nucleate boiling ratio (DNBR)

DNB is the end of nucleate boiling and the beginning of decreased heat transfer. A PWR must be operated so that the critical heat flux (CHF) is not exceeded at any point. One PWR thermal limit is departure from nucleate boiling ratio (DNBR). DNBR = Critical Heat Flux/Actual Heat Flux @ spec. loc. DNBR is typically maintained above 1.3 during all modes of operation to maintain adequate margin.

Describe direct contact and indirect contact heat exchangers.

Direct contact heat exchangers - (not very common), transfer heat from one fluid to another by their physical contact in which heat and mass is transferred as the fluids mix. Examples: cooling towers, cooling ponds, deaerators. Indirect contact heat exchangers - (most common in plant) no physical contact between the two fluids that are exchanging heat. The fluids are physically separated by a metallic tube wall boundary. Can be further broken down into two categories: shell and tube; plate and frame.

Describe methods to prevent water hammer.

Ensure piping systems are properly filled and vented prior to starting a pump in the system. Ensure pumps in the system are properly filled and vented before operating. Open and close system valves slowly. Start centrifugal pumps with the discharge valve closed. Warm system steam lines prior to initiating flow. If possible, defeat automatic opening of pump discharge valves if the system has been in an extended shutdown. Open valves manually, and slowly, at the local operator. If possible, reduce system flow prior to tripping large-capacity pumps.

Enthalpy (H)

Enthalpy is the amount of heat content used or released in a system at constant pressure. h = (PV + U) / m (BTU/lbm)

Define the following terms:

Fluid - substance that deforms continuously when acted on by a shearing stress of any magnitude. By this definition air, water, and tar are all considered fluids, with very different properties. Density - fluid's mass per unit volume. Specific Volume - volume per unit mass. reciprocal of the density. Specific Weight - weight per unit volume. dens. x grav. Specific Gravity - density of fluid/density of water Viscosity - measure of fluid's resistance to being sheared or deformed. Pressure - average force of the molecules on the wall per unit area.

Describe heat exchanger tubes, materials, and considerations for selection of materials.

Generally, tube wall thickness is minimized to enhance conduction through the wall. The selection of material is based on the cooling water chemistry, entrained particulates in the water, fluid velocity, and expected stagnant conditions. Heat exchangers in nuclear plants that use natural or raw water sources are normally configured with this water on the tube side. Usually the shell side is a closed system and the water chemistry is monitored and controlled. Heat exchangers used as backup trains, such as in essential service water systems, may have stagnant conditions and must have tubes that are resistant to attack in stagnant water conditions. Heat exchangers that use water containing high silt or other suspended solids must have tubes that have erosion-corrosion resistance.

Describe pump:

Head Flow Curves - Centrifugal pump head versus flow curves vary with types and designs. Every centrifugal pump has a fixed design geometry so that all the flow areas are optimized to produce a given head and flow with minimal losses. System Resistance Curves - A pump will always operate at the intersection of the pump performance curve and the system resistance curve. When developing the system resistance curve, all of the system's operating conditions from minimum to maximum flow should be considered. Integrated Curves - For convenience, many pump manufacturers will give all of the performance curves for a given speed and impeller diameter on one figure. This is known as an integrated curve.

Describe single phase and two phase heat exchangers.

Heat exchangers provide the means for transferring heat from one system or component to another. Heat exchangers can be divided into two major categories: Single Phase - the cooling or heating fluid remains in its initial gaseous or liquid phase. Examples: Primary Side Component cooling and Residual Heat Removal, Nuclear Service Water, Various Turbine Generator lube oil, hydraulic oil, and generator windings, various motor coolers. Two-Phase - either the cooling or heating fluid changes phase. Examples: Main turbine condenser, steam generator, feed water heaters, turbine gland seal condenser.

Wet Vapor

If a saturated liquid is heated, the liquid gradually evaporates, forming a mixture of liquid and vapor. As long as some liquid is present, any heat added will be used to vaporize the remaining liquid, and the temperature will not rise. The vapor-gas mixture will move across the vapor dome from left to right. The vapor is defined as saturated, or dry, at the point when the last of the liquid has boiled off and become vapor.

Describe the role of pump head from the perspective of the Bernoulli Equation.

In order to design piping systems and size the pumps and motors which drive the flow, it is necessary to calculate the total pressure head which the pumps must overcome. This pressure head includes friction losses, losses due to pipe fittings and valves, and pressure due to velocity and elevation changes. The Bernoulli equation is used to calculate this pressure head.

Describe the use of the general energy equation, in terms of heat exchangers.

In the General Energy Equation, the heat removed from the hot fluid, Qh, must equal to the heat gained by the cold fluid, Qc. Qh = Qc The heat rate (Q) removed by one fluid in a heat exchanger flowing either on the shell side or tube side is dependent on the following: The fluids flow rate (m) The specific heat capacity of the fluid (Cp) The temperature differential between the fluids entering and exiting temperature (ΔT).

Describe and compare the characteristics of laminar flow and turbulent flow.

Laminar flow - fluid particles move in parallel or concentric layers with each layer moving smoothly over adjacent layers, with minimal mixing between layers. particles move in definite fixed path or streamlines. If dye is injected into a fluid stream, the dye will remain as a well-defined line with only slight blurring as it flows downstream. Turbulent flow - A distinguishing characteristic of turbulence is its irregularity, with a lack of clear (or discernible) streamlines, and no observable pattern. If the dye experiment is repeated, you notice that the dye immediately becomes blurred and spread across the entire pipe in a random fashion. Pressure drop for turbulent flow in pipes is also greater, as are heat transfer rates. Whether a flow is laminar or turbulent can be predicted by calculating a dimensionless parameter called the Reynolds number, which will be discussed later in the course.

Local or Sub-Cooled Nucleate Boiling

Local boiling, or sub cooled nucleate boiling, occurs when a hot surface is in contact with a liquid which is below the saturation temperature for the existing pressure. Steam bubbles form at surface irregularities called nucleation sites. The bubbles move away from the heated surface due to natural or forced convection. These bubbles collapse since the bulk of the liquid is subcooled.

Moisture Content (M)

M = mass of liquid / (mass of liquid + mass of vapor) Quality (x) is defined as: x = 1-M

Describe system heating and overpressure protection.

Mass changes and heat transfers affect the pressure of a closed system. Caution must be taken during heat up or cooldown of systems to prevent overpressurization. An example is admission of steam to the shell side of a feedwater heater before the tube side flow path is opened. Heat up of the trapped liquid inside the tubes causes pressure to increase. Certain plant components and piping systems are often protected from overpressure by relief valves.

Describe multi-pass heat exchangers.

Multiple pass heat exchangers contain a divider plate(s) or pass partition(s) in the channel that separates the fluid entering and leaving the heat exchanger. On a straight tube, two-pass heat exchanger, the return head has no baffle on the opposite end. The number of passes for the tube side fluid can be increased by the addition of divider plates on either channel head. Channels are normally bolted on with a gasket located between the channel and the tube sheet to provide a watertight seal.

Second Law of Thermodynamics

No heat engine, actual or ideal, when operating in a cycle can convert all the heat supplied to it into mechanical work. (i.e., you cannot have a 100% efficient cycle).

Adiabatic Process

No loss or gain of heat

Describe heat exchanger degradation.

Potential Causes: Excessive fouling, reduced transfer area due to plugging of leaks, gas binding due to improper venting, corrosion or vibration induced clearance between the baffles and shells/tubes, Bent divider plants, transient operating conditions, variations of flow from design.

Four Forms of Energy

Potential, Kinetic, Flow, Internal

Describe pump affinity laws.

Pump affinity laws are used to estimate performance at various speeds. Simply Stated: 1. Flow varies directly with speed. 2. Head varies with square of speed. 3. Power varies with the cube of speed.

Describe pump run out and pump deadhead.

Pump run out refers to the maximum flow rate at the lowest anticipated system head. It is caused by a pump operating in an oversized system where system head loss is too low. Pump deadheading, or shutoff head, is when a pump runs with little or no flow. This typically occurs when the pump discharge valve is closed or the system resistance is higher than the pump discharge pressure. In many applications, pumps are intentionally started at a deadhead to prevent water hammer and to enable pump starting under low load conditions.

Describe the overall heat transfer equation.

Q=UAΔTlm where U is the overall heat transfer coefficient in BTU / hr-ft2-°F; A is the effective heat exchanger heat transfer surface area in ft2; and ΔTlm is the logarithmic mean temperature difference (LMTD) in °F. This equation establishes the heat exchanger design parameters to transfer the required amount of heat from one side of the heat exchanger to the other side, based on selected tube material and fluid conditions. This equation determines the required heat transfer surface (A) to transfer the heat (Q) with the heat transfer losses accounted for in (U ) and the required inlet and outlet fluid temperatures.

Four Regions of the Pool Boiling Curve

Region 1. Natural Convection - represent the time between the initial application of heat and the onset of bubble formation at nucleation sites. Region 2. Nucleate Boiling - During the initial part of this phase, bubbles formed at nucleation sites move away from the heated surface and collapse since the bulk of the liquid is below saturation. The bubble motion greatly increases turbulence and mixing of the fluid, further increasing heat flux. As the temperature difference between the heated surface and the fluid is further increased, the limit of region II is approached and heat flux reaches a maximum value. This point of maximum heat flux is called departure from nucleate boiling (DNB) and the heat flux is termed critical heat flux (CHF). Region 3. Transition Boiling - This steam blanket covers an ever-increasing portion of the heated surface as temperature difference is increased. The area beyond DNB on the pool boiling curve is called the boiling crisis, since heat is being transferred primarily by conduction and radiation through the steam layer. Region 4. Film Boiling - begins at the point where heat flux reaches a local minimum and once again begins to increase. This region is called film boiling. Even though the heat transfer mechanisms are less favorable in this region, the heat transfer rate increases due to the extreme temperature difference. The point where heat flux again reaches the DNB value is called dry out.

General Energy Equation for Turbines

The purpose of a turbine is to extract work from a process. w = h1 - h2

Thermodynamics

Thermodynamics branch of science that deals with energy, the transformation of energy, and the associated changes in the state of matter. Working Substance - any fluid that receives, transports, and transfers energy in a system. Thermodynamic Properties - temperature, pressure, specific volume (density), internal energy, enthalpy, entropy. Phases of Substance - Solid, Liquid, Gas. A substance may exist in a combination of these phases such as solid-liquid or liquid-gas (vapor). At least two independent properties must be known in order to specify its phase of existence. Intensive Properties - independent of mass and therefore don't depend on the size of the sample being examined. Other examples are viscosity, electrical resistance, thermal conductivity, specific volume, pressure, and temperature. Extensive Properties - depend directly on the mass of the sample being examined. Examples are volume, mass, and energy. Sensible Heat - Temp vs. Heat Addition (sloping line), in which the substance experiences a change in temperature - in this case, a change of state but not a change in phase. Latent Heat - Temp vs. Heat Addition (flat line), in which the substance experiences a change in phase - therefore a change in state also, but not a change in temperature. Specific Volume - defined as the volume occupied by a unit mass of the substance. The specific volume v is the total volume (V) divided by the mass of that volume. v = V/m (ft^3/lbm) Density - the reciprocal of specific volume and is defined as the mass of a unit volume of the substance. p = 1/v (lbm/ft^3)

Describe the following:

Total Dynamic Head - Total dynamic head is defined as the the net discharge head minus the net suction head and is the total amount of energy added to the fluid by the pump. Net Suction Head - Net suction head (Hs) is the total energy of the fluid entering the pump inlet. It includes the static suction head (hs), plus the pressure head (if any) in the suction tank (hp), plus the suction velocity head (hv), minus the friction head (hf) in the suction piping. Net Discharge Head - Net discharge head (Hd) is the total energy of the fluid leaving the pump. It includes the static discharge head (hd), plus the discharge velocity head(hv), plus the friction head in the discharge piping (hf), plus the pressure head (if any) in the discharge tank (hp). Required Net Positive Suction Head - the minimum fluid energy required at the inlet to the pump and is specified by the pump manufacturer. Available Net Positive Suction Head - the fluid energy at the inlet to the pump above the fluid's vapor pressure.

Entropy

When considering how much work can be produced with an amount of heat, we must know the temperature at which heat is transferred in addition to the amount of heat transfer. Entropy is a property used to describe both the amount of heat transferred and the temperature at which it is transferred. Change in entropy is normally defined instead of entropy itself.

Thermodynamic Cycle

When the working fluid of a system goes through different changes of state, or processes, and then returns to its initial state. Thus, a thermodynamic cycle is a recurring series so thermodynamic processes used for the transformation of energy to produce a useful effect.

Define water hammer.

Wter hammer is the liquid shock imposed on a piping system that results from rapidly starting or stopping system flow, opening and closing system valves, condensation of steam, or any other action that imposes a shock within the piping system.

Describe shell and tube heat exchangers, including the differences between straight tube and U-tube heat exchangers.

consists of tubes that contain one fluid and a shell that contains another fluid. The tubes are the separation boundary between the two fluids. The shell forms the outer heat exchanger and provides the heat exchanger containment for the fluid outside the tubes. generally fall into two arrangement classes: Straight Tube Type - The fluid inside the tube travels from one end to the other without any change in direction. The tube bundles in straight tube heat exchangers can also be divided into multiple passes in order to increase heat transfer. U-Tube Type - The tubes are bent into a "U" shape with the inlet and outlet on the same end, and a divider plate separating the inlet from the outlet. Examples: feed water heaters, steam generator.

Superheated Vapor

defined as vapor heated beyond the saturated vapor state.

Radiation and Emissivity Values

emissivity factor depends on the nature of the material surface. For example, the surface of a black automobile gets hotter from radiation from the sun than a lighter color automobile.

Conduction

energy flows through a medium (solid, liquid, or gas) by virtue of a temperature gradient within the medium. The rate of heat transferred (watts or BTU/s) can be calculated using Fourier's law of conduction.

Rankine Cycle

heat released from nuclear fission provides the heat required to vaporize water for use in the turbines.

Kinetic Energy

is the mass's energy of motion. KE = mv^2 / 2 where: m = mass, v = velocity of fluid

Potential Energy

is the stored energy of position, and exists due to vertical distance (z) over which gravitational forces can be exerted on a system's mass. PE = mgz where: m = mass, g = gravitational constant, and z = vertical height of mass.

Flow Energy

is the work done by the working fluid on its surroundings as it moves from one point to another in a system. FE = PV where: P = pressure, V = volume

Subcooled Liquid

liquid existing to the left of the saturated liquid line.

Convection

occurs when thermal energy is transported away from the system boundary by a moving medium. Example, cold water flowing through the hot tubes of a heat exchanger. The energy is first conducted from the tube walls into the colder liquid, and then transported by the bulk motion of the liquid.

General Energy Equation for Boilers

q = (h2 - h1); amount of heat added to the system can be calculated from the change in enthalpy across the boiler by subtracting the entering enthalpy from the exiting enthalpy.

General Energy Equation for Condensers

q = h1 - h2

Forced Convection

some external device such as a pump, fan or blower, is used to produce the bulk fluid motion. The bulk fluid motion transports the thermal energy. This forced flow usually results in high convection coefficients and high heat transfers. Example: radiator in car.

Radiation

transport of energy by electromagnetic radiation. Does not require a medium. Example, the sun heats the earth.

Explain the relationships between the four temperature scales: Fahrenhiet Celsius Rankine Kelvin

triple point of water; where the vapor, solid, and liquid phases exist together in thermodynamic equilibrium. 273.16 Kelvin or 491.69 degree Rankine. T(R)=1.8T(K) The Celsius scale is defined so that the temperature of the ice point (what we usually think of as the freezing point of water) is 0.00° C or 273.15 K and the steam point is 100.00° C or 373.15 K. The Fahrenheit scale assigns a value of 32° F to the ice point and 212° F to the steam point Freezing: 0.00 C or 273.15 K or 32 F Steam: 100.0 C or 373.15 K or 212 F

General Energy Equation for Pumps

w = h2 - h1