Steam Boiler: Fluid Flow in Pipe

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Flow through Rectangular Ducts

Figure 1: Flow through Rectangular Ducts
(Source: Book-Babcock-Wilcox)

Flow through rectangular ducts is important to be learned. Rectangular duct system will generate pressure loss which is caused by change in direction just like cylindrical pipe. Nevertheless, an additional aspect, the design of the duct in terms of the bend direction, should be considered into consideration. This can be known as the factor ratio, and that is understood to be the duct proportion of actual width (b) to the actual depth (d) dimension namely b/d ratio as shown in Figure 1.

The loss of bend pertaining to the similar ratio of radius reduces when the factor ratio raises, due to the lesser in proportion impact of this flows within the steady stream. The mixed impact of radius and also factor ratios on bends 1.57 rad (90 deg) in the duct is presented with regards to velocity heads as shown in Figure 1.

The loss variables found in Figure 1 are common values of experiment final results upon the ducts. Pertaining to the provided variety of factor ratios, the losses are reasonably separate of the Reynolds number. Other this variety, the variance along with Reynolds number is irregular. It's thus suggested in which the values of Nb intended for b/d = ½ be applied with regard to all factor ratios a smaller amount compared to b/d = ½, and also values pertaining to b/d = 2 be applied for ratios higher in comparison with b/d = 2. The bend loss pertaining to other angle of 1.57 rad (90 deg) is usually regarded for being proportionate to the angle of bend in the process of fluid flow through rectangular ducts.

Flow through Bends

Flow through bends will always occurs because there is not piping system in the boiler plant or power plant which only consists of straight pipes but also some bends. Bends in a piping system or perhaps duct process generate losses in pressure induced by momentum exchanges and also friction in fluid which in turn effect on alterations in flow way.

Due to the fact the length of axial bend is usually integrated with the friction reduction of straight length in the piping system or perhaps ducts process, it's practical to take away a computed equal to friction reduction in straight length which experimentally establish the factor of pressure loss in the bends. These kinds of adjusted records form empirically in the base of the loss aspect (Nb) in the bends.

The amount of pressure losses pertaining to fluid flow through bends inside circular pipe in surplus of direct pipe friction change marginally together with Reynolds numbers under 150, 000. Regarding Reynolds numbers over 150, 000, they're realistically consistent and rely only on the ratio of bend radius to the pipe internal diameter (r/D). Regarding industrial pipe, the impact of Reynolds number is minimal. The mixed influence of bend angle and the ratio of radius, with regard to velocity heads will be established in Figure 1.

Figure 1: Flow through Bends
(Source: Book-Babcock-Wilcox)

Bernoulli’s Equation

Bernoulli’s equation is the most fundamental and generally utilized law within fluid flow. Bernoulli’s equation is fundamentally law in energy conservation. It is the total of kinetic/velocity energy and pressure in fluid flow is convertible each other and does not change its value. Mentioned diversely, for a ideal and constant flow of fluid that cannot compressible, the overall energy composed of datum energies, kinetic and pressure, is consistent at every position within the fluid.

p₁ + (V₁²/ 2g) + Z₁ = p₂ + (V₂²/ 2g) + Z₂

where:

Z = elevation of fluid (m)

V = Velocity of fluid (m/s)

p = pressure head of fluid (m) → pressure head is pressure (kg/m²) which is multiplied with specific volume (m³/kg)

Fluid Machinery

Fluid machinery is machinery that serves to transform mechanical energy into potential energy and vice versa. The fluid which is used can be water, steam, and gas.

Based on definition above, fluid machinery can be classified into two types as follow:

Working machinery type which serves to transform mechanical energy into fluid energy, for example: pumps, blower, compressor, and others.
Power machinery type that serves to convert fluid energy into mechanical energy such as water turbine, steam turbine, windmill, and others.

Friction Factor in Pipe Flow

Friction factor in pipe flow (fo) is defined as:

where τ0 is shear stress in the wall pipe and U∞ is fluid velocity outside boundary layer. Friction factor in pipe flow is associated with decrease in pressure as stated in the following equation for a pipe with length L and diameter D.

Friction factor in pipe flow is a function of Reynolds number (R_eD). This function can be derived analytically for laminar flow, but depend on experimental data correlation for turbulent flow.

Friction factor for fully developed laminar flow in a smooth pipe is:

while the friction factor for fully developed turbulent flow in a smooth pipe is expressed as:

Besides using the equations above, the friction factor for turbulent flow can be found in Figure 1. In the Figure 1, surface roughness effects are classified according to the ratio e/D, where e is the equivalent roughness height. f values in the Figure 1 is four times the value of fo, (f = 4.fo). Friction factor for rough surfaces that have Reynolds number above the value listed in the Moody chart is no longer as a function of Re.

In fact, the surface of pipe is not perfectly smooth, and friction factor of turbulent flow is strongly influenced by the condition of pipe surface. Nevertheless, this does not occur in laminar flow. An explicit equation is quite useful for turbulent flow (10⁴ > Re > 4.10⁸) both in the smooth pipe and rough pipe had been given by Chen NH (1979), namely:

Figure 1: Friction factor in Pipe Flow - the Moody Diagram

Heat Exchanger Applications

There are many applications of heat exchanger in our daily life. The following below is some examples heat exchanger applications and its function:

Chiller

Chiller is one of heat exchanger applications that is used to cool fluid until low temperature. Temperature of fluid that is resulted from cooling process in the chiller is lower than temperature of cooling fluid cooling which is performed by cooling water. For this chiller, used cooling medium normally is ammonia or Freon.

Condenser

Condenser is one of heat exchanger applications that is used to cool steam or mixture of steam, so it turns into liquid phase. Cooling medium used is usually water or air. Steam or steam mixture will release latent heat to the coolant, for example in steam boiler power plants that use condensing turbine. Used steam from turbine will be entered into condenser, and then condensed into condensate.

Cooler

Cooler is one of heat exchanger applications that is used to cool liquids or gases by using water as cooling medium. Here no phase change, with today's technological developments then cooler use cooling medium as air with the aid of fan.

Evaporator

Evaporator is one of heat exchanger applications that is used for evaporation of liquid into steam. Evaporation process convert liquid phase into steam phase. Evaporator utilizes latent heat to convert liquid phase into steam phase.

Re-boiler

Re-boiler is one of heat exchanger applications that serve to re-boil and partially vaporize the liquid being processed. The heating medium is often used steam or hot substance that is being processed itself. One of example application of re-boiler is oil refinery system that use oil (665 F) as a medium evaporator, the oil will come out of boiler and flows inside tube.

Heat Exchanger

Heat exchanger is one of heat exchanger application which is intended to utilize heat of fluid flow to another. Heat exchanger has two functions as follow:

- Heating the fluid

- Cool the hot fluid

Temperatures in and out of both fluid types are set according to its needs.

Fluid Flow in Pipe

At the pump we will meet Bernoulli equation. This equation is the conservation energy of fluid so as to approximate a pump installation should consider kinetic energy and potential energy.

(P/ρ) + (V²/2) + gz = constant

For ideal fluid, friction is ignored.

(P₁/ρg) + (V₁²/2g) + z₁ = (P₂/ρg) + (V₂²/2g) + z₂ = constant

Energy equation and head equation can be written as follows:

Energy equation

m{(P₁/ρ) + (V₁²/2) + gz₁} + W_shaft = m{(P₂/ρ) + (V₂²/2) + gz₂} + m.g Σ(head loss total)

Head equation

{(P₁/ρg) + (V₁²/2g) + z₁} + H_shaft = {(P₂/ρg) + (V₂²/2g) + z₂} + ΣHl_total

At the amount of total head loss is divided into two parts between major head loss and minor head loss. Major head loss is head loss due to surface roughness, pressure drop and length of pipe flow.

h_{major loss} = f . (L/D) . (V²/2)

where:

f = friction factor

L = Length of pipe

D = Diameter of pipe

V = flow velocity

g = Acceleration of gravity = 9.81 m/s²

While minor head loss is head loss due to fitting of elbow, gate valve, check valve, change in cross section flow and straight. This head loss due to components that are intentionally installed and have different function.

H_{minor loss} = k . (V²/2)

k = f . (L_e/D)

The value of f is obtained by using Reynolds number contained in the Moody chart, while Le/D is obtained from the table component.

Forced Convection

Forced convection is a process or form of heat transfer where fluid movement is produced by an additional supply such as suction machine, forced draft fan, induced draft fan, pump, and others. Force convection can occurs in our daily life like air conditioning, heat exchanger, steam boiler and other devices.

Heat transfer process in steam boiler occurs in air heater and economizer. This heat transfer type is forced convection because convection occurs due to flue gases are blown by force draft fan / primary air fan to air heater and economizer.

Forced convection heat transfer can be determined by the following equation (use Newton’s Law of Cooling):

Q = h A (Ts - T∞) or Q = h A ΔT

Where:

Q = forced convection heat transfer rate (W)

h = heat transfer coefficient (W/m² K)

A = exposed area of metal

Ts = temperature of surface heating transfer element (K)

T∞ = free stream temperature (K)

Forced convection is different with natural convection. But sometimes in some cases forced convection is mixed with natural convection. The problem is how to distinguish whether this heat transfer is categorized as forced convection or natural convection. Most engineers use Archimedes number (Ar) parameter to determine dominant convection heat transfer type. The following formula is Archimedes number equation:

Ar = Gr / Re²

Where:

Ar = Archimedes number

Gr = Grashof number

Re = Reynolds number

If the value of Ar more than 1, then natural convection is dominant, if the value of Ar less than 1, then forced convection is dominant.

Balance Energy of Fluid

Fluid will flow with the energy, the form of these energies are kinetic energy, potential energy and thermal energy. Figure 1 will show balance energy of fluid that occurs.

If the potential energy and kinetic energy are ignored, then the fluid flow is only affected by thermal energy which is possessed by fluid. If fluid flow has different temperatures with the surrounding environment, it the heat transfer will happen so temperature of fluid will change. This heat transfer can occur by convection, conduction, or radiation.

In general, the amount of energy transfer is formulated as follows:

Q = m c_p (T₂ - T₁)

The rate of energy which is transferred by convection is formulated as:

Q = h A (T₂ - T₁)

Where:

h = coefficient of heat which is transfer by convection (W/m²K)

The rate of energy which is transferred by conduction is formulated as:

Q = k A (T₂ - T₁) / x

Where:

k = thermal conductivity (W/mK)

The rate of energy which is transferred by radiation is formulated as:

Q = ε A σ (T_s⁴ - T_sur⁴)

Where:

ε = emissivity (0 <ε <1)

σ = Stefan-Boltzmann constant (5.67 E-8 W/m²K⁴)

T_s = Surface temperature (K)

T_sur = surrounding temperature (K)

Fully Developed Flow

A fluid flow can be categorized as fully developed flow if the fluid velocity profile in the pipe does not change anymore. Fully developed flow will occur if the condition of fluid in the pipe is quite.

The condition of fully developed flow in pipe is indicated by the ratio between the incoming length (Le) with pipe diameter (D). If the calculation result is:

Le / D ≈ 0.06 Re, so the fully developed flow in pipe is laminar

Le / D ≈ 4.4 Re^1/6, so the fully developed flow in pipe will be turbulent

Assumption that viscosity of fluid is constant is used to analyze fully developed flow in pipe.

Laminar and turbulent flow

Laminar flow is form of flow that describes velocity of a point in the pipeline is constant at all times. While turbulent flow describes velocity of a point in the pipeline different and random in each time.

The condition flow type that occurs inside pipe can be determined by calculating Reynolds number in the flow. Reynolds number (Re) is defined as following formula:

Re = (ρ V d) / μ

Where:

Re = Reynolds number

Ρ = density of fluid (kg/m³)

μ = surface coarseness of pipe (m)

d = inside diameter of pipe (m)

V = velocity of fluid inside pipe (m/s)

Re equal to 2300 is the maximum value for laminar flow. Re equal to 4000 is the minimum value for turbulent flow. While the value of which indicates the type of transition flow.

The type of flow that occurs inside pipe will give big influence on the amount of energy which is discharged. This condition is indicated by the magnitude of pressure drop that occurs along pipeline. Each type of flow will have any kind of different pressure drop calculations.