# Recuperators

In a recuperator, heat is transferred from the warmer fluid (with mass flow rn1 and thermal capacity c1) convectively, with a heat transmission coefficient of hc1, to the partition and after thermal conduction by the partition material convectively with hc2 to the colder fluid (with mass flow m2 and thermal capacity c2).

For a high transmission rate of a heat exchanger, as high a heat transition coefficient U as possible is necessary. The heat transition coefficient is dominated by the convective transition resistances. The thermal resistance R = s / Я of the plate material (with plate

thickness s [m] and heat conductivity of the plate X [W/mK]) is normally negligible. The heat transfer coefficient of a recuperator with an even partition surface is given by

The proportion of the radiation to the heat transfer is negligible due to the virtually identical temperatures of the individual partition surfaces.

The heat transfer coefficient by convection hc is determined in practice by model tests. These test results can then be transferred to other geometrically and hydrodynamically similar heat transfer conditions.

Nu (Re, Pr )X

L

Nu: NuBelt number [-]

X: heat conductivity of the fluid [W/mK]

The characteristic length L depends on the respective geometry of the heat exchanger. The most important NuBelt correlations as a function of the Reynolds and Prandtl numbers (Re, Pr), of the overall length of the heat-transferring gap/tube/channel l, and of the characteristic length L, are summarised in Table 4.2. The calculation of the material properties of air as well as of the Reynolds and Prandtl numbers can be found in Chapter

3.2 (solar air collectors).

Table 4.2: Relevant NuBelt correlations for heat exchanger calculations.

 Geometry Flow condition Nufielt correlation Characteris­tic length Reference gap/ channel laminar (Re < 2300) Nu = 7,5413 +1,84dRePrL +{ 2 1 (RePrL1 [ V l 1^1 + 22 • Pr 1 { l1 J L = 2h Al Amouri, 1994 turbulent (Re > 8000) Nu = 0,116 • (Re23-125) • Pr23 1 + |y^ L = 4-^ C Gregorig, 1959 tube laminar (Re < 2320) Nu = |^49,0 + 4,17 • Re – PrL l = d Hering et al., 1997 turbulent (Re > 2320) Nu = 0,116-(Re23 -125)-Pr13 • 1 + |^ l = d Gregorig, 1959

h: distance between heat-transferring surfaces (gap/channel)

Afree: free area for flow

C: circumference

d: inside diameter of the pipe

The amount of heat Q given off by the warmer fluid is taken up completely by the colder fluid flow, ignoring heat losses to the external environment, and is calculated from the heat transfer rate of the heat exchanger. This results from the product of the two-dimensional elements dA, the heat transfer coefficient U, and the locally varying temperature difference T1-T2 between the two fluid flows.

Q = JUx ( (x, y) – T (x, y) )dA = mC ( – Tl out) = m2c2 ( – T2 .n) (4.33)

Normally only the inlet temperatures of the warm and cold fluids into the heat exchanger are known, for example in the sorption system the temperature of the warm dried supply air (T1>;„) and the temperature of the colder space exhaust air (T2>1„). To calculate the transferred heat as a function of the inlet temperatures, the heat recovery efficiency is introduced, which is also known as an operational characteristic and is defined as the ratio of actually transferred power to maximum transferred power.

Q = miC1 Tin – T2,in )Ф = miC1 (T, n – T1,ou, ) = m2C2 (T, out – T2,in )

ф_ m 1C1 (T1,,n – T1 ,ou, ) = m2C2 (Tout – T2,in ) (4-34)

miC1 {Tun – T2,in ) m1C1 iTUn – T2,in )

Only at identical thermal capacity streams of the two sides rh1C1 = m2c2 are the two temperature difference ratios (defined by the heat recovery efficiency) the same.

The heat recovery efficiencies of the most important recuperators (same-, counter – and crossflow heat exchangers) depend functionally on the ratio of heat transfer performance UA and thermal capacity stream C = hic, which are called NTU (number of transfer units).

The heat recovery efficiency for a counter-current heat exchanger with the thermal capacity stream C < C2 is given by Bosnjakovic (1951):

In the infinite series it is sufficient to calculate the terms n = 0 to n = 5.

A pure crossflow heat exchanger is defined by the fact that no lateral mixing of the individual fluid lines is possible, and occurs in practice with heat exchangers whose heat­transferring surface consists of flat or corrugated plates (plate-type heat exchangers). Typical gap widths for a plate-type heat exchanger are between 5-10 mm.

If in a tube heat exchanger the fluid in the pipes is flowed around perpendicularly by another fluid over the whole cross-section, a mixing of the fluid lines of the outside fluid can occur transverse to the direction of flow, and a so-called one-side agitated crossflow heat exchanger is the result. The larger the number of the tubing rows, the stronger is the approximation to the pure cross current.

One-side agitated cross current: shell and tube heat exchanger:

Current C remains unmixed, current C2 is agitated (with C < C2)

(4.42)

Example 4.2

Calculation of the heat recovery efficiency of a counter-current plate-type heat exchanger for a sorption system with 20 000 m3/h of both supply air and exhaust air flow rate.

 Geometry H = 1.5 [m] Height of recuperator B = 1.5 [m] Width of recuperator l = 1.5 [m] Length of channel n = 250 [-] Number of plates spi = 0.0002 [m] Thickness of individual plates Xpi = 229 [W/mK] Heat conductivity of plate material dg = 0.0058 [m] Gap width (distance between individual plates) Ac = 1.09 [m2] Free cross section of recuperator (one direction) Api = 2.25 [m2] Area of individual plates (length x width) Afree _ 0.009 [m2] Free flow cross section (one channel) dh = 0.012 [m] Hydraulic diameter L = 0.012 [m] Characteristic length Ahx = 562.50 [m2] Heat transferring surface area Warm air: Cold air: V/t = 5.56 5.56 [m3/s] Volume flow T = 45.50 20.00 [°C] Temperature ^air _ 0.0258 0.0251 [W/m K] Heat conductivity air Pair = 1.0933 1.1884 [kg/m3] Density air cp. air _ 1008.3 1007.0 [J/kg K] Heat capacity air U air = 1.76E-05 1.52E-05 [m2/s] kinematic viscosity air vg = 5.11 5.11 [m/s] Mean gap velocity

Prandtl number Reynold number NuBelt number

Updated: August 4, 2015 — 11:52 pm