Design of Condensers/Condensing Zones P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Lowest Shell side Thermal Resistance !!!

HP CFWH

HP CFWH No. 8

Thermodynamic Layout of HP Closed Feed Water Heater Desuperheater Condensing Shell Drain Cooler HP Turbine TRAP Tbi, pbi, Tbsi Tfi+1 Tfi

Feedwater heater with Drain cooler and Desuperheater DC Feed Water in DS Bleed Steam Feed Water out C=Condenser DC=Drain cooler Feedwater heater with Drain cooler and Desuperheater DS=Desuperheater -TTD=Terminal temperature difference Bled steam T L DC C Condensate TTD DS

Number of Tubes The flow rate inside the tube is a function of the density of the fluid, the velocity of the fluid, cross-sectional flow area of the tube, and the number of tubes. By using above Eq. and replacing Ac by pdi2/4, number of tubes can be calculated as where di is the tube inside diameter.

Tubes in Shell and Tube Hx The number and size of tubes in an exchanger depends on the Fluid flow rates Available pressure drop. The number and size of tubes is selected such that the Tube side velocity for water and similar liquids ranges from 0.9 to 2.4 m/s. Shell-side velocity from 0.6 to 1.5 m/s. The lower velocity limit corresponds to limiting the fouling, and the upper velocity limit corresponds to limiting the rate of erosion. When sand and silt are present, the velocity is kept high enough to prevent settling.

Tube-Side Nusselt Number For turbulent flow, the following equation developed by Petukhov-Kirillov is used: Properties are evaluated at mean bulk temperature and constants are adjusted to fit experimental data. Validity range: 104 < Ret < 5 x 106 and 0.5 < Prt < 2000 with 10% error.

For laminar flow, the Sieder and Tate correlation is be used. is applicable for 0.48 < Prt < 16700 and (Ret Prt di/L)1/3 > 2. The heat transfer coefficient for the tube-side is expressed as follows:

Shell-diameter

HP Closed Feed Water Heater

General values of condensate loading for horizontal tubes: 0.01 to 0.05 kg/m.s This can be used to calculate a Reynolds number

Flow is considered laminar if this Reynolds number is less than 1800. The driving force for condensation is the temperature difference between the cold wall surface and the bulk temperature of the saturated vapor The viscosity and most other properties used in the condensing correlations are evaluated at the film temperature, a weighted mean of the cold surface (wall) temperature and the (hot) vapor saturation temperature

Onset of Turbulence & Turbulent Film Condensation The transition film Reynolds number for the tube bundle is adapted from a vertical plate turbulent transition criterion of 1600 (but also values of 1200, 1800 and 2000 have been proposed). Thus, the film will become turbulent on the tube bundle at ReΓ equal to 1600 and thus when ReΓ > 1600 the following expression should be used. The flow is nearly always laminar on single tube because of the short cooling length around the perimeter

Wall Temperatures It is often necessary to calculate the wall temperature by an iterative approach. The summarized procedure is: Assume a film temperature, Tf Evaluate the fluid properties (viscosity, density, etc.) at this temperature Use the properties to calculate a condensing heat transfer coefficient (using the correlations to be presented) Calculate the wall temperature. The relationship will typically be something like

5. Use the wall temperature to calculate a film temperature 6 5. Use the wall temperature to calculate a film temperature 6. Compare the calculated film temperature to that from the initial step. If not equal, reevaluate the properties and repeat.

Laminar Flow Outside Horizontal Tubes When vapor condenses on the surface of horizontal tubes, the flow is almost always laminar. The flow path is too short for turbulence to develop. Again, there are two forms of the same relationship: The constant in the second form varies from 0.725 to 0.729. The rippling condition (add 20%) is suggested for condensate Reynolds Numbers greater than 40.

Condenser tubes are typically arranged in banks, so that the condensate which falls off one tube will typically fall onto a tube below. The bottom tubes in a stack thus have thicker liquid films and consequently poorer heat transfer. The correlation is adjusted by a factor for the number of tubes, becoming for the Nth tube in the stack

The heat transfer coefficient on the Nth tube row The heat transfer coefficient on the Nth tube row in the bundle h(N) is Kern (1958) concluded from his practice experience in designing condensers that the Jakob tube row expression was too conservative and that this resulted in condensers that were consistently over-surfaced. To improve his thermal designs, he replaced the exponent of (-1/4) in the Nusselt expression with a value of (-1/6) so that corresponding equations become

Condensation on Horizontal Bundles: Prediction of Heat Transfer Coefficient in Nth Tube Row

Falling Film Condensation on Horizontal Tubes Falling-film heat exchangers are attractive because they provide good heat transfer performance and low working-fluid inventories. The design of falling-film heat exchangers has been largely based on empirical data. A thorough understanding of the falling-film flow and heat transfer interactions is important. An ability to predict the falling film mode would allow better data correlation and improve the modeling and analysis of heat transfer and fluid flow.

Modes of Condensation on Tube Bundle The droplet mode The jet mode The sheet mode

Flow Rate Vs Mode of Falling Film

Condensation on Horizontal Tube Bundles : Flow Map Hu and Jacobi (1996) proposed flow mode transition equations with ReΓ versus Ga+ (film Reynolds number vs. the Galileo number) for the following principal flow modes: sheet flow, column flow and droplet flow. The mixed mode transition zones of column-sheet and droplet-column were also considered as regimes, bringing the total to five. Hence, they presented four flow transition expressions (valid for passing through the transitions in either direction and hence the symbol ⇔):

Range of Validity of Model

Flow Transition Map

Identification Condensation Mode

Final Correlation

Onset of Turbulence & Turbulent Film Condensation The transition film Reynolds number for the tube bundle is adapted from a vertical plate turbulent transition criterion of 1600 (but also values of 1200, 1800 and 2000 have been proposed). Thus, the film will become turbulent on the tube bundle at ReΓ equal to 1600 and thus when ReΓ > 1600 the following expression should be used.

Condensation on Horizontal Tube Bundles : Turbulent Flow Turbulent flow of the condensate film may be reached in a condenser, which significantly increases heat transfer. Comparatively little has been published on turbulent film condensation on tube bundles compared to the information available for laminar films. Butterworth (1983) recommends adapting the Labuntsov expression for turbulent film condensation on a horizontal tubes for predicting local turbulent film condensation on the Nth tube row in horizontal tube bundles h

Overall Heat Transfer Coefficient for the Heat Exchanger The overall heat transfer coefficient for clean surface (Uc) is given by Considering the total fouling resistance, the heat transfer coefficient for fouled surface (Uf) can be calculated from the following expression:

Outlet Temperature Calculation and Length of the Heat Exchanger The outlet temperature for the fluid flowing through the tube is The surface area of the heat exchanger for the fouled condition is :

and for the clean condition where the LMTD is always for the counter flow. The over surface design (OS) can be calculated from :

The length of the heat exchanger is calculated by

Wall Temperatures It is often necessary to calculate the wall temperature by an iterative approach. The summarized procedure is: Assume a film temperature, Tf Evaluate the fluid properties (viscosity, density, etc.) at this temperature Use the properties to calculate a condensing heat transfer coefficient (using the correlations to be presented) Calculate the wall temperature. The relationship will typically be something like

5. Use the wall temperature to calculate a film temperature 6 5. Use the wall temperature to calculate a film temperature 6. Compare the calculated film temperature to that from the initial step. If not equal, reevaluate the properties and repeat.

The heat transfer coefficient on the Nth tube row The heat transfer coefficient on the Nth tube row in the bundle h(N) is Kern (1958) concluded from his practice experience in designing condensers that the Jakob tube row expression was too conservative and that this resulted in condensers that were consistently over-surfaced. To improve his thermal designs, he replaced the exponent of (-1/4) in the Nusselt expression with a value of (-1/6) so that corresponding equations become

Condensation on Horizontal Bundles: Prediction of Heat Transfer Coefficient in Nth Tube Row