Back Calculation of Air-side Coefficient from Design Conditions

As was the case with water-to-water heat exchangers discussed in Chapter 16, the air-side convection heat transfer coefficient for the AWHX may be found for the noncondensing normal mode of operation from vendor data to eliminate the need for hot-side heat transfer correlations specific to the geometry and configuration of the HX. Table 17.4

TABLE 17.4

Design Basis or Test Conditions for Normal Noncondensing Mode of Operation

	Total service water flow rate
	Service water flow rate per coil
	Entering water temperature
	Exiting water temperature
	Average water temperature
	Tube-side thermal conductivity
	Tube-side absolute viscosity
	Tube-side specific heat
	Tube-side density
	Tube-side temperature rise
	Tube-side heat transfer rate
	Entering air dry-bulb temperature
	Exiting air dry-bulb temperature
	Average air dry-bulb temperature
	Hot-side thermal conductivity
	Hot-side absolute viscosity
	Hot-side specific heat
	LMTD correction factor
	Tube-side flow rate per coil
	Face velocity out of air side
	Relative humidity
	Total atmospheric pressure

presents a list of the required design basis parameters for operating in the normal, noncondensing mode to be able to back calculate the air-side coefficient of heat transfer.

The design fouling resistance on the air side and the tube side are specified based on the tube and fin materials and the corresponding resistances to heat transfer.

The overall heat transfer coefficient at design conditions, U_design, is calculated for the normal noncondensing mode of operation in Table 17.5.

The tube-side convection coefficient may be computed from the Petukhov correlation as in Chapter 16 (Table 17.6).

TABLE 17.5

Verification of U_design for Normal Noncondensing Mode of Operation

	Greater terminal temperature difference		(17.33)
	Lesser terminal temperature difference		(17.34)
	Log mean temperature difference		(17.35)
	Effective mean temperature difference		(17.36)
	Design overall heat transfer coefficient		(17.37)

TABLE 17.6

Tube-Side Convection Coefficient

	Mass flow rate/tube		(17.38)
	Volumetric flowrate/tube		(17.39)
	Tube area		(17.40)
	Tube velocity		(17.41)
	Prandtl number		(17.42)
	Reynolds number		(17.43)
	Fanning friction factor		(17.44)
	Nusselt number		(17.45)
	Tube-side film coefficient		(17.46)

The hot-side convection coefficient may be computed as follows: where and

and k, is the tube material thermal conductivity.

Calculation of Air-side Mass Flow Rate and Heat Transfer

The air-side volumetric flow is converted to mass flow using the ideal gas laws, and the air-side heat transfer rate is calculated as shown in Table 17.7.

TABLE 17.7

Air-Side Mass Flow Rate and Heat Transfer

	Volumetric flow rate		(17.50)
	Saturation pressure at Th,		(17.51)
	Partial pressure of the water vapor in the air		(17.52)
	Partial pressure of the air3		(17.53)
	Humidity ratio2		(17.54)
	Mass flow rate of air4-5		(17.55)
	Mass of the water vapor		(17.56)
	Total mass flow rate on the air side		(17.57)
	Specific heat of moist air1		(17.5S)
	Density of air		(17.59)
	Hot-side flow measurement per coil		(17.60)
	Air-side heat transfer rate		(17.61)

Note: 1. c_p._m and c_p._m, are the specific heats of dry air and water vapor, respectively.

• 2. m„ and m_a are the molecular weights of water and air, respectively.
• 3. P„ is the pressure of the air.
• 4. V is the volumetric flow rate.
• 5. R is the gas constant, and T + 460 is the temperature of the air in “Rankinc.

Calculation of Air-side Coefficient at Test Conditions

The value for h_h on the air side based on the test conditions may be computed based on a correlation by Taborek.¹ If one assumes that the actual value for h_h is a function of some ideal value for the air-side thermal conductivity for pure cross-flow, then

where J_T is a correction factor that is a function of the various leakage and bypass paths and, therefore, remains constant for a given HX.

Therefore,

and

Reference 3 suggests the following correlation for AWHX:

Substituting,

Computing “Apparent” Fouling Resistance

Therefore, the total “apparent” fouling resistance as determined by the test may be computed as follows:

Calculating Heat Transfer Rate at Reference Design Basis Accident Conditions

The overall heat transfer coefficient at the design basis limiting conditions, U*, may be expressed as follows:

where A* is calculated as in the case of the design and test conditions (see Section 16.8). Therefore,

It should be noted that the above analysis is applicable only if condensation is not occurring during the AWHX test. The calculation of U* is not valid for accident conditions when water is being condensed from saturated air as a result of a pipe rupture. Such analyses are the purview of the nuclear steam supply system (NSSS) provider based on proprietary tests.

Uncertainty

The method for calculating the uncertainties contained herein is the same as in Section 16.9. However, the uncertainty of the “apparent” fouling as it applies to AWHX deserves additional emphasis.

Fouling resistance measured during a test is defined as follows:

As may be seen from the equations above, the uncertainty of the fouling resistance is a function of the uncertainties of U,_esp h,„ and h_c. The sensitivity coefficients, в, and uncertainty of the fouling are determined numerically by perturbing each parameter plus and minus by the amount of the uncertainty to determine the impact on the fouling

The sensitivity coefficients are

and

The overall coefficient of heat transfer indicated by the test conditions, U_test, may be calculated as follows:

The uncertainty of U_tes, may be determined by first calculating the sensitivity coefficients for the variables Q_ave and EMTD. The area, A, is assumed to be constant.

The weighted average heat transfer rate and the uncertainty of the average heat transfer rate may be calculated as follows:

One may calculate the uncertainty of the EMTD as a function of the uncertainties of the temperatures measured. In addition, Example K.l in Reference 4 includes additional uncertainty to account for the uncertainty associated with possible variation in the HX fouling by assuming a Biot number of 0.5 for a water-to-water HX (see Appendix G of Reference 4).

Defining

An additional uncertainty in the EMTD of 2% is assumed for incomplete mixing in the HX.

The sensitivity coefficients for EMTD to temperature as found in Appendix В of Reference 4 may be computed as follows:

The sensitivity coefficients for the variation in fouling and incomplete mixing are 1.0.

The hot-stream and cold-stream heat transfer rates may now be calculated as follows:

For the heat transfer rate, Q, the independent variables are the mass flow rate, the specific heat, and the inlet and outlet temperatures. The overall uncertainty of the heat transfer rate is the root mean square of the sum of the uncertainty contributions. For example, the uncertainty of Q_c would be as follows:

Table B.2 of Reference 4 shows the resulting equations for the sensitivity coefficient for each independent variable:

References

• 1. Thomas, L. C., Heat Transfer -Professional Version, Prentice Hall. Englewood Cliffs, NJ. 1993, p. 739.
• 2. Gardner, K. A., Fin Efficiency of Extended Surfaces, Transactions of the ASME, vol. 67, 1945. p. 621.
• 3. ASME PTC 30-1991, Air Cooled Heat Exchangers, American Society of Mechanical Engineers, 1991.
• 4. ASME PTC 12.5-2000, Single Phase Heat Exchangers, American Society of Mechanical Engineers, September, 2000.