Entropy generation analysis in a tube heat exchanger integrated with triple blade vortex generator inserts

ABSTRACT

The present study mainly concerns the analysis of entropy generation for a heat exchanger tube integrated with triple blade vortex generator as an inserts. The Augmentation entropy generation number is adopted as the performance evaluation criterion for heat exchanger. In addition to entropy generation, heat transfer in terms of Nusselt number and frictional characteristics are also presented. The data for analysis is obtained from rigorous experiments that are performed in a tube integrated with triple blade vortex generator inserts. The variable geometrical parameters of triple blade vortex generator are pitch ratio (2,3, and 4) and the perforation index (0%, 25%). The operating parameter is Reynolds number having a range of 6,000–24,000. The results reveal the maximum Nusselt number and friction factor of 252.4 and 3.10, respectively for pitch ratio of 1% and 0% perforation index. Entropy generation rate in triple blade vortex generator inserts equipped tube is less in regard of smooth tube. Entropy generation as a result of heat transfer is very high in comparison of entropy generation resulting from the friction. All values of augmentation entropy generation number are less than 1, and minimum is achieved for pitch ratio of 1% and 0% perforation index.

KEYWORDS:

• Heat exchanger
• entropy generation
• bejan number
• augmentation entropy generation number
• triple blade vortex generator

Nomenclature

Symbol-Title-Unit

A_s-Surface area of tube-m²

Be-Bejan number-

C_p-Specific heat of air at constant pressure-J/kg K

D-Internal diameter of the tube-m

H-Convective heat transfer coefficient-W/m² K

K-Thermal conductivity of air-W/m K

L-Length of the tube-m

_ṁ-Mass flow rate of fluid-kg/s

ΔP-Pressure drop across test section-Pa

Q-Heat transfer rate-W

Q-heat flux-W/m²

T_i-Fluid inlet temperature-K

T_o-Fluid outlet temperature-K

ΔT_m-Log mean temperature difference-K

V-Velocity of air-m/s

Ρ-Density of air-kg/m³

µ-Dynamic viscosity-kg/m-s

Φ-Irreversibility distribution ratio-

Ψ-Non dimension entropy generation rate-

F-Friction factor-

f_s-Friction factor of smooth tube-

_Re-Reynolds number-

_L-Spacing between two consecutive insert geometry-m

_Pr-Prandtl number-

N_s-Augmentation entropy generation number-

_Nu-Nusselt number-

_Nus-Nusselt number of smooth tube-

Ṡ_gen-Entropy generation rate-W/K

_T-Thickness of insert blade-m

_TR-Thickness Ratio-

_PR-Pitch ratio-

_PI-Perforation Index-%

_BA-Blade angle-°

_TBVG-Triple blade vortex generator-

2. Nusselt Number

$Nu=\frac{hD}{K}$

$\frac{\delta Nu}{Nu}={\left[{\left(\frac{\delta h}{h}\right)}^2+{\left(\frac{\delta D}{D}\right)}^2+{\left(\frac{\delta K}{K}\right)}^2\right]}^{0.5}$

$\frac{\delta Nu}{Nu}={\left[{\left(0.0284\right)}^2+{\left(0.000936\right)}^2+{\left(0.00526\right)}^2\right]}^{0.5}$

$\frac{\delta Nu}{Nu}=0.0289$

Hence, uncertainty in Nusselt number is 2.89%.

3. Friction factor

$f=\frac{2{\left({\mathrm{\Delta }}_p\right)}_{d}D}{4\rho L{V}^2}$

$\frac{\delta f}{f}={\left[{\left(0.0741\right)}^2+{\left(0.000816\right)}^2+{\left(0.000936\right)}^2+{\left(0.0000667\right)}^2+{\left(0.00769\right)}^2\right]}^{0.5}$

$\frac{\delta f}{f}=0.0744$

Hence, uncertainty in friction factor is 7.44%.

4. Entropy generation due to temperature difference

$({\dot{S}}_{gen}{)}_{\mathrm{\Delta }T}=\frac{q^2}{\pi T_b^{2}kNu}$

$\frac{\delta \left({({\dot{S}}_{gen})}_{\mathrm{\Delta }T}\right)}{{({\dot{S}}_{gen})}_{\mathrm{\Delta }T}}={\left[{\left(\frac{\delta q}{q}\right)}^2+{\left(\frac{\delta T_b}{T_b}\right)}^2+{\left(\frac{\delta k}{k}\right)}^2+{\left(\frac{\delta Nu}{Nu}\right)}^2\right]}^{0.5}$

$\frac{\delta \left({({\dot{S}}_{gen})}_{\mathrm{\Delta }T}\right)}{{({\dot{S}}_{gen})}_{\mathrm{\Delta }T}}={\left[{\left(0.0277\right)}^2+{\left(0.00526\right)}^2+{\left(0.00526\right)}^2+{\left(0.0289\right)}^2\right]}^{0.5}$

$\frac{\delta \left({({\dot{S}}_{gen})}_{\mathrm{\Delta }T}\right)}{{({\dot{S}}_{gen})}_{\mathrm{\Delta }T}}=0.0407$

Hence, uncertainty in entropy generation due to temperature difference is 4.07%.

5. Entropy generation due to pressure drop

$({\dot{S}}_{gen}{)}_{\mathrm{\Delta }P}=\frac{32{\dot{m}}^{3}f}{{\pi }^2{\rho }^2{T}_b{D}_h^5}$

$\frac{\delta \left({({\dot{S}}_{gen})}_{\mathrm{\Delta }P}\right)}{{({\dot{S}}_{gen})}_{\mathrm{\Delta }P}}={\left[{\left(\frac{\delta \dot{m}}{\dot{m}}\right)}^2+{\left(\frac{\delta f}{f}\right)}^2+{\left(\frac{\delta \rho }{\rho }\right)}^2+{\left(\frac{\delta T_b}{T_b}\right)}^2+{\left(\frac{\delta D_h}{D_h}\right)}^2\right]}^{0.5}$

$\frac{\delta \left({({\dot{S}}_{gen})}_{\mathrm{\Delta }P}\right)}{{({\dot{S}}_{gen})}_{\mathrm{\Delta }P}}={\left[{\left(0.0257\right)}^2+(0.0744\right)}^2+{\left(0.000816\right)}^2+{\left(0.00526\right)}^2+{\left(0.000936\right)}^2{]}^{0.5}$

$\frac{\delta \left({({\dot{S}}_{gen})}_{\mathrm{\Delta }P}\right)}{{({\dot{S}}_{gen})}_{\mathrm{\Delta }P}}=0.0789$

Hence, uncertainty in entropy generation due to pressure drop is 7.89%.