Lesson 37 Transmission Of Air In Air Conditioning Ducts

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1 Lesson 37 Transmission Of Air In Air Conditioning Ducts Version 1 ME, IIT Kharagpur 1

2 The specific objectives of this chapter are to: 1. Describe an Air Handling Unit (AHU) and its functions (Section 37.1). Discuss the need for studying transmission aspects of air in air conditioning (Section 37.) 3. Discuss airflow through air conditioning ducts, Bernoulli and modified Bernoulli equations, Static, dynamic, datum and total head, Fan Total Pressure (FTP) and power input to fan (Section 37.3) 4. Discuss estimation of pressure loss through air conditioning ducts (Section 37.4) 5. Estimation of frictional pressure drop of circular and rectangular ducts using friction charts and equations (Section 37.4) 6. Estimation of dynamic pressure drop in various types of fittings (Section 37.5) 7. Static regain (Section 37.6) At the end of the lecture, the student should be able to: 1. Apply Bernoulli equation and modified Bernoulli equation to air conditioning ducts and estimate various pressure heads, pressure loss, FTP and fan power input. Estimate frictional pressure drops through circular and non-circular ducts using friction charts and equations 3. Estimate dynamic pressure drop through various fittings used in air conditioning ducts using tables, charts and equations 4. Define static regain and calculate static regain factor for various types of duct enlargements Introduction: In air conditioning systems that use air as the fluid in the thermal distribution system, it is essential to design the Air Handling Unit (AHU) properly. The primary function of an AHU is to transmit processed air from the air conditioning plant to the conditioned space and distribute it properly within the conditioned space. A typical AHU consists of: 1. A duct system that includes a supply air duct, return air duct, cooling and/or heating coils, humidifiers/dehumidifiers, air filters and dampers. An air distribution system comprising various types of outlets for supply air and inlets for return air Version 1 ME, IIT Kharagpur

4 rise. This rise is called as Fan Total Pressure (FTP). Then the required power input to the fan is given by:. Q air.ftp Wfan (37.4) ηfan The FTP should be such that it overcomes the pressure drop of air as it flows through the duct and the air finally enters the conditioned space with sufficient momentum so that a good air distribution can be obtained in the conditioned space. Evaluation of FTP is important in the selection of a suitable fan for a given application. It can be easily shown that when applied between any two sections 1 and of the duct, in which the fan is located, the FTP is given by: ρ(v V1 ) p1) + + ρg(z z1) + ρghl FTP (p (37.5) g Thus to evaluate FTP, one needs to know the static pressures at sections 1 and (p 1, p ), air velocities at 1 and (V 1, V ), datum at 1 and (Z 1, Z ) and the head loss H l. Normally, compared to the other terms, the pressure change due to datum ρ g(z z1) is negligible. If the static pressures at the inlet and exit are equal, say, to atmospheric pressure (p1 p p atm) and the duct has a uniform cross section (v 1 v ), then FTP is equal to the pressure loss due to friction. Thus to find FTP, one has to estimate the total pressure loss as air flows through the duct from one section to other Estimation of pressure loss in ducts: As air flows through a duct its total pressure drops in the direction of flow. The pressure drop is due to: 1. Fluid friction. Momentum change due to change of direction and/or velocity The pressure drop due to friction is known as frictional pressure drop or friction loss, Δp f. The pressure drop due to momentum change is known as momentum pressure drop or dynamic loss, Δp d. Thus the total pressure drop Δp t is given by: Δ p Δp + Δp (37.6) t f Evaluation of frictional pressure drop in ducts d The Darcy-Weisbach equation is one of the most commonly used equations for estimating frictional pressure drops in internal flows. This equation is given by: L ρv Δp f f D (37.7) Version 1 ME, IIT Kharagpur 4

5 where f is the dimensionless friction factor, L is the length of the duct and D is the diameter in case of a circular duct and hydraulic diameter in case of a non-circular ρvd duct. The friction factor is a function of Reynolds number, Re D and the μ relative surface roughness of the pipe or duct surface in contact with the fluid. For turbulent flow, the friction factor can be evaluated using the empirical correlation suggested by Colebrook and White is used, the correlation is given by: 1 f k s.51 log10 + (37.8) 3.7D (ReD) f where k s is the average surface roughness of inner duct expressed in same units as the diameter D. Evaluation of f from the above equation requires iteration since f occurs on both the sides of it. In general in air conditioning ducts, the fluid flow is turbulent. It is seen from the above equation that when the flow is turbulent, the friction factor is a function of Reynolds number, hydraulic diameter and inner surface roughness of the duct material. Table 37.1 shows absolute roughness values of some of the materials commonly used in air conditioning: Material Absolute roughness, ε (m) Galvanized Iron (GI) sheet Concrete to Riveted steel to Cast Iron (CI) Commercial steel Table 37.1: Average surface roughness of commonly used duct materials Of the different materials, the GI sheet material is very widely used for air conditioning ducts. Taking GI as the reference material and properties of air at 0 o C and 1 atm. pressure, the frictional pressure drop in a circular duct is given by: air Q L Δ p f in N / m (37.9) D where Qair is the volumetric flow rate of air in m 3 /s, L is the length and D is the inner diameter of the duct in meters, respectively. Using the above equation, friction charts have been created for estimation of frictional pressure drop of standard air through circular ducts made of GI sheets. Figure 37.1 shows the standard chart for estimating frictional pressure drop in circular ducts made of GI sheets at standard air conditions. Version 1 ME, IIT Kharagpur 5

6 Pressure loss, Pa/m Fig Chart for estimating frictional pressure drop in circular GI ducts It can be seen from the chart that one can estimate frictional pressure drop per unit length if any two parameters out of the three parameters, i.e., flow rate Qair, diameter D and velocity V are known. Correction factors have to be applied to the pressure drop values for ducts made of other materials and/or for air at other conditions. For small changes in air density (ρ) and temperature (T in K), one can use the following relation to obtain frictional pressure drop from the standard chart.. Δp Δp f,1 f, ρ ρ 1 and Δp Δp f,1 f, T T (37.10) The chart shown above is valid only for circular ducts. For other shapes, an equivalent diameter has to be used to estimate the frictional pressure drop. Version 1 ME, IIT Kharagpur 6

7 Rectangular ducts: Even though circular ducts require the least material for a given flow rate and allowable pressure drop, rectangular ducts are generally preferred in practice as they fit easily into the building construction thus occupying less space, and they are also easy to fabricate. The ratio of the two sides a and b of the rectangle (a/b) is called as aspect ratio of the duct. Since square ducts with aspect ratio 1.0 come close in performance to a circular duct, it is preferable to use an aspect ratio as close to unity as possible for best performance. One can use equation (37.9) and friction chart for circular ducts for estimating pressure drop through a rectangular duct by using an equivalent diameter. A rectangular duct is said to be equivalent to a circular duct, if the volumetric. flow rate Qair and frictional pressure drop per unit length (ΔPf/L) are same for both. Equating these two parameters for a rectangular duct and an equivalent circular duct, it can be shown that the equivalent diameter is given by: Deq 0.65 (ab) (a + b) (37.11) The above equation is found to be valid for aspect ratio less than or equal to 1:8. Thus from the known values of the two sides of the duct a and b, one can find the equivalent diameter D eq. From the equivalent diameter and the air flow rate, one can estimate the frictional pressure drop per unit length by using either Eq.(37.9) or the friction chart Fig However, when using equivalent diameter and flow rate to find the frictional pressure drop from the chart, the velocity values shown on the chart are not the actual velocities. The actual velocities have to be obtained from the flow rate and the actual cross-sectional area of the rectangular duct. If a rectangular duct has to be designed for a given flow rate and a given frictional pressure drop, then one can first find the equivalent diameter from the friction chart or from Eq.(37.9) and then find the required dimensions of the duct either by fixing the aspect ratio or one of the sides Dynamic losses in ducts: Dynamic pressure loss takes place whenever there is a change in either the velocity or direction of airflow due to the use of a variety of bends and fittings in air conditioning ducts. Some of the commonly used fittings are: enlargements, contractions, elbows, branches, dampers etc. Since in general these fittings and bends are rather short in length (< 1 m), the major pressure drop as air flows through these fittings is not because of viscous drag (friction) but due to momentum change. Pressure drop in bends and fittings could be considerable, and hence should be evaluated properly. However, exact analytical evaluation of dynamic pressure drop through actual bends and fittings is quite complex. Hence for almost all the cases, the dynamic losses are determined from experimental data. In turbulent flows, the dynamic loss is proportional to square of velocity. Hence these are expressed as: Version 1 ME, IIT Kharagpur 7

8 ρv Δp d K (37.1) where K is the dynamic loss coefficient, which is normally obtained from experiments. Sometimes, an equivalent length L eq is defined to estimate the dynamic pressure loss through bends and fittings. The dynamic pressure loss is obtained from the equivalent length and the frictional pressure drop equation or chart, i.e., ρ f.l V eq ρv Δp d K (37.13) Deq where f is the friction factor and L eq is the equivalent length Evaluation of dynamic pressure loss through various fittings: a) Turns, bends or elbows: The most common type of bends used in air conditioning ducts are 90 o turns shown in Fig. 37.(a). 1 R R 1 C b W/H 1/4 1/ 1 1 (a) Fig.37.: Airflow through a 90 o bend (elbow) R 1 /R (b) The cross-section of the elbow could be circular or rectangular. Weisbach proposed that the dynamic pressure loss in an elbow is due to the sudden expansion from the vena contracta region (1 ) to full cross-section as shown in Fig.37.(a). The dynamic pressure drop due to the elbow or 90 o turn is found to be a function of the aspect ratio (W/H), inner and outer radii of the turn (R 1 and R ) and the velocity pressure ρv /, i.e., ρv ( ) ρv Δp d, b Cb f (W / H),R,R 1 (37.14) Version 1 ME, IIT Kharagpur 8

9 The value of dynamic loss coefficient C b as a function of aspect ratio (W/H), inner and outer radii of the turn (R 1 and R ) is available in the form of tables and graphs (Fig.37.(b)). It can be seen from Fig. 37.(b) that the pressure loss increases as (R 1 /R ) decreases and/or the aspect ratio W/H decreases. As a result, installing turning vanes in the bends reduces the dynamic pressure drop as it is equivalent to increasing W/H, as shown in Fig. 37.(c). Turning vanes Fig.37.(c): Use of turning vanes in a 90 o bend (elbow) The equivalent lengths are available as function of geometry for other types of turns and bends. b) Branch take-offs: Branch take-offs (Fig. 37.3) are commonly used in air conditioning ducts for splitting the airflow into a branch and a downstream duct. The dynamic pressure drop from the upstream (u) to downstream (d), Δp u-d is given by: Vd p ρ Vd Δ u -d V (37.15) u where V d and V u are the air velocities in the downstream and upstream ducts, respectively. The dynamic pressure drop from the upstream (u) to branch (b), Δp u-b is given by: Δ p u-b ρ Vd C u -b (37.16) Version 1 ME, IIT Kharagpur 9

10 u b d β Fig.37.3: A branch take-off The value of dynamic loss coefficient C u-b is available in the form of tables and graphs as a function of the angle β and the ratio of branch-to-upstream velocity, V b /V u. C u-b is found to increase as β and V b /V u increase. c) Branch entries: Branch entries (Fig. 37.4) are commonly used in return air ducts. Similar to branch take-offs, the values of dynamic pressure loss coefficients from upstream-to-downstream (C u-d ) and from branch-to-downstream (C u-d ) are available in the form of tables and graphs as functions of upstream, branch and downstream velocities and the angle β. u β d b Fig.37.4: A branch entry d) Sudden enlargement: The pressure loss due to sudden enlargement, shown in Fig. 37.5(a), ΔP d,enl is given by Borda-Carnot equation as: A1 p ρ V1 Δ d, enl 1 A (37.17) where V 1 is the velocity before enlargement, and A 1 and A are the areas before and after enlargement, respectively. The above expression, which is obtained analytically using modified Bernouille s equation and momentum balance equation is found to Version 1 ME, IIT Kharagpur 10

11 over-predict the pressure loss when the air flow rates are high and under-predict when the flow rate is low. Correction factors are available in the form of tables for different enlargements. Vena contracta Fig.37.5(a): Sudden enlargement Fig.37.5(b): Sudden contraction e) Sudden contraction: A sudden contraction is shown in Fig. 37.5(b). Similar to sudden enlargement, the dynamic pressure loss due to sudden contraction ΔP d,con can be obtained analytically. This expression is also known as Borda-Carnot equation. It is given by: ρ ρ V A V 1 Δpd, con 1 1 (37.18) A1' Cc where V is the velocity in the downstream, and A 1 and A are the areas at vena contracta and after contraction, respectively. The coefficient C c is known as contraction coefficient and is seen to be equal to area ratio A 1 /A. The contraction coefficient C c is found to be a function of the area ratio A /A 1, and the values of C c as obtained by Weisbach are shown in Table A /A 1 C c Table 37.3: Values of contraction coefficient C c for different area ratios Comparing the expressions of pressure loss for sudden enlargement and sudden contraction, it can be seen that for the same flow rates and area ratios, the Version 1 ME, IIT Kharagpur 11

12 pressure drop due to sudden enlargement is higher than that due to sudden contraction. f) Miscellaneous fittings, openings etc.: The dynamic pressure loss coefficients for other types of fittings, such as suction and discharge openings are also available in the form of tables. These values depend on the design of the fitting/opening. For abrupt suction opening the dynamic loss coefficient (K) is found to be about 0.85, while it is about 0.03 for a formed entrance. For discharge openings where the downstream pressure is atmospheric, all the kinetic energy of the air stream is dissipated at the exit, hence, the dynamic loss coefficient is equal to 1.0 in this case. Filters, cooling and heating coils, dampers etc.: The pressure drop across air handling unit equipment, such as, air filters, dampers, cooling and heating coils depend on several factors. Hence, normally these values have to be obtained from the manufacturer s data Static regain: Whenever there is an enlargement in the cross-sectional area of the duct, the velocity of air decreases, and the velocity pressure is converted into static pressure. The increase in static pressure due to a decrease in velocity pressure is known as static regain. In an ideal case, when there are no pressure losses, the increase in static pressure (Δp s) is exactly equal to the decrease in velocity pressure (Δp v) and th e total pressure (p t ) remains constant as shown in Fig.37.6(a). Thus for the ideal case: Δp v p - p Δp p v,1 v, p p t,1 s t, s, - p s,1 (37.19) However, for sudden enlargements or for other non-ideal enlargements, the decrease in velocity pressure will be greater than the increase in static pressure, and the total pressure decreases in the direction flow due to pressure losses as shown in Fig. 37.6(b). The pressure loss is due to separation of the boundary layer and the formation of eddies as shown in Fig.37.6(b). Thus, for sudden or non-ideal enlargement: Δp p - p > Δp p v p v,1 t,1 p v, t, s + Δp loss s, - p s,1 (37.0) The pressure loss due to enlargement Δp loss is expressed in terms of a Static Regain Factor, R as: ( 1 R) Δ (1 R)(p p ) Δp v v,1 v, loss p (37.1) Version 1 ME, IIT Kharagpur 1

13 where the static regain factor R is given by: Δps ( ps, ps,1) R (37.1) Δp v ( pv,1 pv, ) Thus for ideal enlargement the Static Regain Factor R is equal to 1.0, whereas it is less than 1.0 for non-ideal enlargement. 1 p t p p s p v L Fig.37.6(a): Ideal enlargement 1 p t p p s p v L Fig.37.6(b): Sudden enlargement Version 1 ME, IIT Kharagpur 13

14 Questions and answers: 1. State which of the following statements are TRUE? a) An air handling unit conveys air between the conditioned space and the plant b) An air handling unit consists of supply and return air fans c) The fan used in an air conditioning system consumes large amount of power d) All of the above Ans.: d). State which of the following statements are TRUE? a) Under ideal conditions, the static pressure through an air conditioning duct remains constant b) Under ideal conditions, the total pressure through an air conditioning duct remains constant c) A fan is required in an air conditioning duct to overcome static pressure loss d) A fan is required in an air conditioning duct to overcome total pressure loss Ans.: b) and d) 3. State which of the following statements are TRUE? a) In a duct of uniform cross section, the static pressure remains constant b) In a duct of uniform cross section, the static pressure decreases along length c) In a duct of uniform cross section, the total pressure decreases along length d) In a duct of uniform cross section, the dynamic pressure remains constant Ans.: b), c) and d) 4. State which of the following statements are TRUE? a) The pressure drop in an air conditioning duct is due to frictional effects b) The pressure drop in an air conditioning duct is due to friction as well as momentum change c) Frictional pressure drop increases with duct length d) Momentum pressure drop takes place over relatively short lengths Ans.: b), c) and d) 5. Rectangular ducts are generally preferred over circular ducts in buildings as: a) For a given flow rate, the pressure drop is less compared to a circular duct b) For a given pressure drop, it requires less material compared to a circular duct c) Rectangular ducts are easier to fabricate d) Rectangular ducts match better with building profile Ans.: c) and d) Version 1 ME, IIT Kharagpur 14

15 6. State which of the following statements are TRUE? a) Dynamic pressure drop in an elbow of rectangular cross-section reduces as the aspect ratio increases b) Use of turning vanes increase the aspect ratio c) Compared to sudden enlargement, the dynamic pressure drop in sudden contraction is less d) Compared to sudden enlargement, the dynamic pressure drop in sudden contraction is more Ans.: a), b) and c) 7. State which of the following statements are TRUE? a) The static regain factor always lies between 0 and 1 b) The static regain factor is 0 for an ideal enlargement c) The static regain factor is 1 for an ideal enlargement d) In an actual enlargement, reduction in dynamic pressure is always greater increase in static pressure Ans.: a), c) and d) than 8. 1 m 3 /s of air is conveyed through a straight, horizontal duct of uniform cross- required fan power input when a) A circular duct is used, and b) A rectangular duct of section and a length of 40 m. If the velocity of air through the duct is 5 m/s, find the aspect ratio 1:4 is used. Take the efficiency of the fan to be 0.7. If a GI sheet of 0.5 mm thick with a density of 8000 kg/m3 is used to construct the duct, how many kilograms of sheet metal is required for circular and rectangular cross sections? Assume standard conditions and the static pressure at the inlet and exit of the duct to be same. Ans.: From continuity equation; the required cross-sectionagiven area of the duct is by: a) Circular duct: A cs (Flow rate, Q/Velocity, V) (1.0/5.0) 0. m The required diameter of the duct, D (4A cs /π) m Then using the equation for frictional pressure drop; air L (1.0) Q Δ p f 6.7 N / m D ( ) Since the duct is straight, the dynamic pressure drop fittings, hence: is zero in the absence of any Version 1 ME, IIT Kharagpur 15

16 Fan Total Pressure, FTP ΔPf 6.7 N/m Hence the required fan power input, W is: fan W fan. Qair η.ftp 1.0 x fan The required mass of the duct is given by: W (Ans.) m circular (πd)x(thickness)x(density) 6.34 kg (Ans.) b) Rectangular duct: of aspect ratio (a:b) (1:4) As before, cross sectional area, A cs 0. m a x b a x 4a a m and b 4a m The equivalent diameter, Deq is given by: 0.65 (ab) Deq (a + b) 0.65 (0.) ( ) m Using the friction equation, the frictional pressure drop is: air Q L (1.0) 40 Δ p f D (0.4636) Hence, the required fan power is: 41.4 N / m W fan. Q air.ftp 1.0 x W η 0.7 fan (Ans.) The required mass of the rectangular duct is given by: m rectangular (a+b)x(thickness)x(density) 8.94 kg (Ans.) Thus for the same flow rate and velocity, a rectangular duct consumes 54.5% higher fan power and weighs 41% compared to a circular duct. Version 1 ME, IIT Kharagpur 16

17 9. Air at a flow rate of 1. kg/s flows through a fitting with sudden enlargement. The area before and after the enlargements are 0.1 m and 1 m, respectively. Find the pressure drop due to sudden enlargement using Borda-Carnot Equation. What is the pressure drop if the same amount of air flows through a sudden contraction with area changing from 0.1 m and 1 m. Ans.: Assuming standard air conditions, the density of air is approximately equal to 1. kg/m 3. Hence the volumetric flow rate of air, Q is given by: S udden enlargement: Q (mass flow rate/density) (1./1.) 1. 0 m 3 /s From Borda-Carnot Equation; pressure drop due to sudden enlargement is given by: Δp d, enl ρv 1 1 A A 1 Velocity V 1 Q/A 1 1.0/ m/s and A 1 /A 0.1/ Substituting the above values in the equation, we get: V d, enl 1 A 1 1.x A ρ ( 1 0. ) Δp 48.6 N/ m (Ans.) Sudden contraction: Pressure drop due to sudden contraction is given by Borda-Carnot equation: ρ ρ V A V 1 Δpd, con 1 1 A1' Cc From Table 37.3, for an area ratio (A /A 1 ) of 0.1, the contraction coefficient C c is The velocity after contraction (V ) is 10 m/s. Hence substituting these values in the above equation: V 1 1.x10 ρ 1.0 d, con N/ m Δp C (Ans.) c It can be seen from the example that for the same area ratio and flow rate, the pressure drop due to sudden enlargement is larger than that due to sudden contraction by about 34.4%. Version 1 ME, IIT Kharagpur 17

18 10. Air at a flow rate of 1 m 3 /s flows through a fitting whose cross-sectional area increases gradually from 0.08 m to 0.1 m. If the static regain factor (R) of the fitting is 0.8, what is the rise in static pressure (static regain) and total pressure loss as air flows through the fitting? Ans.: The velocity of air at the inlet and exit of the fitting are: V in 1/A in 1/ m/s and V out 1/A out 1/ m/s Taking a value of 1. kg/m 3 for the density of air, the velocity pressure at the inlet and exit are given by: P (ρv )/ (1. x 1.5 )/ N/m v,in P v,out (ρv out )/ (1. x 8.33 )/ N/m Static pressure rise through the fitting (static regain) is given by: (P s,out P s,in ) R(P v,in P v,out ) 0.7 x ( ) N/m (Ans.) The loss in total pressure is given by: in ΔP t,loss (1 R) (P v,in P v,out ) 0.3 x ( ) N/m (Ans.) Version 1 ME, IIT Kharagpur 18

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