Effect of surface roughness on the performance of heat exchanger

Abstract

In this research work, double-pipe counter flow heat exchanger has been analyzed with various roughnesses of steel, aluminum and copper pipes and also with two different cold fluids: water and ammonia at same flow rates. Dimensions of the heat exchanger are inner and outer diameters of inner pipe being 0.034 and 0.042 m, whereas diameters of outer pipe are 0.054 and 0.06 m, respectively, and length of heat exchanger is 1.8 m. In K-ℇ modeling, computational fluid dynamics tool has been used for performance analyses and this computational work has been validated by entropy, exergy and entransy analyses. After computational numerical analyses, this investigation has concluded that maximum rate of heat transfer through heat exchanger has been found with copper–ammonia combination with smooth surface. Minimum rates of entropy generation, exergy destruction, entransy dissipation-based thermal resistance and entransy dissipation number have been obtained with copper–water combination, and minimum entropy generation number and maximum effectiveness have been obtained with copper–ammonia combination. Percentage changes in the parameters/properties have also been calculated at different operating conditions. Copper as inner pipe material with smooth surface and ammonia as cold fluid have been recommended for counter flow double-pipe heat exchanger. Computer software has been developed for hassle-free analyses of heat exchanger.

Introduction

In a heat exchanger, heat is transferred from hot fluid to cold fluid by conductive and convective heat transfer mechanisms. The hot or cold fluid is separated through solid walls called pipes to avoid mixing of fluid or direct contact. Shell- and tube-type heat exchanger, double-pipe heat exchanger and plate- or fin-type heat exchanger are different types of heat exchangers mainly used in various industries like power plants, chemical plants, refrigeration and air-conditioning systems [1,2,3,4]. Double-pipe counter flow heat exchanger (as shown in Fig. 1) has been chosen for CFD analyses and found effectiveness, overall heat transfer coefficient and outlet temperatures of the flowing fluids for different cases [5], and then numerical validation has been done by analyzing the rates of entropy generation, exergy destruction and entransy dissipation. The dimensions of double-pipe counter flow heat exchanger chosen in this research are shown in Table 1. Double-pipe counter flow heat exchanger has been analyzed with steel, aluminum and copper as inner pipe materials with water and ammonia as cold fluids. This work has been done with different roughnesses of pipes but same mass flow rates for hot and cold fluids, i.e., 0.08 kg/s.

Fig. 1

Double-pipe counter flow heat exchanger

Table 1 Dimensions of double-pipe heat exchanger

Roughness which is extremely important for mechanical point of view is the component of surface texture and can be determined through deviations in normal vector’s direction where large deviation indicates rough, whereas small deviation indicates smooth surfaces. High value of roughness is objectionable due to complexity in manufacturing, and manufacturing cost increases by decreasing the surface roughness. Surface roughness can be measured by surface roughness comparator manually, but generally it is measured by profilometer. Roughness is denoted by ε_r. There are two types of roughnesses: one is absolute roughness, and other is relative roughness. Absolute roughness is the measure of surface roughness of a material and this roughness is important for calculating pressure drop particularly in turbulent flow regime, but relative roughness is the ratio of roughness to diameter of pipe and it is used to measure the roughness of inner surface of the pipe. The value of friction factor can be found from moody chart by relative roughness [6]. If ɛ_r is roughness of pipe (mm) and D is the diameter of pipe (mm), then relative roughness can be expressed as:

$${\text{Relative}}\;{\text{roughness}} = \varepsilon_{r} /D$$

(1)

Chen et al. have done work on entropy generation concepts on various thermodynamic systems; irreversible engine, pin fin heat sinks and also isothermal crystallization processes. After analyses, they suggested minimum entropy generation principle for better performance/operation of thermodynamic systems [7,8,9,10,11]. Exergy analyses at different conditions have been performed on heat exchangers and power plants by Geete et al. and Ibrahim et al., and after analyses they found minimum exergy destruction is good for better outputs from thermal systems [12,13,14,15,16]. Chen et al., Feng et al., Guo et al. and other researchers have worked on entransy concepts for heat exchanging devices, and they applied entransy dissipation, entransy dissipation-based thermal resistance and entransy dissipation number on thermodynamic systems for comparative performance analyses and concluded that these parameters should be minimum [17,18,19,20,21,22,23,24,25,26,27,28]. In this research work, rates of entropy generation, exergy destruction, entransy dissipation, entransy dissipation-based thermal resistance, entransy dissipation numbers, effectiveness and entropy generation numbers have been calculated at different operating conditions to get better conditions at which performance of counter flow double-pipe heat exchanger will be the best.

Methodology

Outlet temperatures for double-pipe counter flow heat exchanger have been investigated with water and ammonia as cold fluids and steel, aluminum and copper as inner pipe materials at the different roughnesses of the inner surfaces of the inner pipes by CFD tools. In this research work, commercial code has been used for analyses in ANSYS Fluent 15.0 software. K-ℇ modeling has been used for performance analyses and taken from the literature. It is well established fact that K-ℇ model has been used in RANS. For validation, rates of entropy generation, exergy destruction and entransy dissipation have been found with entransy dissipation-based thermal resistances, entropy generation numbers and entransy dissipation numbers for the same conditions, and the following methodology has been adopted for this research work. The first law of thermodynamics for cyclic process states that the cyclic integration of heat is equal to the cyclic integration of work, but when the first law is applied for a process, then a thermodynamic property comes out which is internal energy. Similarly, the second law of thermodynamics for cyclic process gives information about systems: heat engine, heat pump and refrigerator, but when this law is applied for a process, then a new property appears which is entropy (S). It has been found that for a closed system, change in entropy for irreversible process is more than the integration of dQ/T for that process; it means some entropy is generated which indicates losses in the process. Internal irreversibility or dissipative work is the main cause for entropy generation, and it is always positive or zero (for reversible process). Irreversibility or losses can be calculated by entropy generation for heat exchangers, and it is calculated as [7,8,9,10,11]:

$$TdS_{{\text{gen}}} = \, m_{h} C_{ph} \int {(T_{h} ) + m_{c} C_{pc} \int {(T_{c} )} }$$

(2)

$$TdS_{{\text{gen}}} = \, m_{h} C_{ph} \int_{Thi}^{Tho} {Th + m_{c} C_{pc} \int_{Tci}^{Tco} {T_{c} } }$$

(3)

$$dS_{{\text{gen}}} = m_{h} C_{ph} \ln \left( {T_{ho} /T_{hi} } \right) + m_{c} C_{pc} \ln \left( {T_{co} /T_{ci} } \right)$$

(4)

where dS_gen is the rate of entropy generation in kW/K. The exergy or available energy of a system can be defined as maximum possible work which is extracted from that system when system approaches the thermodynamic equilibrium state with its surrounding called dead state (i.e., P_a and T_a). Exergy is that kind of property which depends on state of system and surrounding, and when system reaches dead state, exergy of system becomes zero. Reversible work transfer from the system is always greater than actual work transfer, and the difference between these works is known as irreversibility of the system; the term T_aS_gen is the decrease in exergy of the system because of irreversibility. This concept was given by Gouy-Stodola, and he said the rate of exergy losses or exergy destruction rate in a process is proportional to the rate of entropy generation and ambient temperature. Exergy destruction rates for double-pipe counter flow heat exchanger have been calculated at various conditions by the following equation [12,13,14,15,16]:

$$0 = \left[ {m_{h} C_{ph} \{ (T_{hi} {-} \, T_{ho} ){-}T_{a} \ln (T_{hi} - \, T_{ho} )\} } \right]{-}\left[ {m_{c} C_{pc} \{ (T_{co} {-} \, T_{ci} ){-}T_{a} \ln (T_{co} - \, T_{ci} )\} } \right]{-}\varphi_{{\text{des}}}$$

(5)

$${\text{Exergy}}\;{\text{destruction}}\;{\text{rate}}\;\left( {\varphi_{{\text{des}}} } \right) = \left[ {m_{h} C_{ph} \{ (T_{hi} {-} \, T_{ho} ){-}T_{a} \ln (T_{hi} - \, T_{ho} )\} } \right]{-}\left[ {m_{c} C_{pc} \{ (T_{co} {-} \, T_{ci} ){-}T_{a} \ln (T_{co} - \, T_{ci} )\} } \right]$$

(6)

where m_h and m_c are flow rates (kg/s), C_ph and C_pc are specific heats (kJ/kg-K) of hot and cold fluids, respectively, T_hi and T_ci are inlet temperatures (Kelvin), T_ho and T_co are outlet temperatures (Kelvin) of hot and cold fluids, T_a is ambient temperature and φ_des is exergy destruction rate (kW) [12,13,14,15,16]. The performance of heat exchanger can be analyzed by entransy which is the ability of heat transfer through heat exchanger, and it can be clarified by analogy between electrical and thermal parameters. If electrical and thermal potentials are V and T, and electrical and heat fluxes are I and Q, respectively, then electrical resistance will be (V/I) and thermal resistance will be (T/Q). Electricity and heat transfer rates are I and Q, Ohm’s law is I = K_e A (dV/dn), Fourier’s law is Q = K A (dT/dn), electrical charge stored is Q, and heat stored is Q(U)= m C_v T. Electric capacitance is Q/V, and thermal capacitance is U/T. Similarly, electrical potential energy stored in a capacitor is QV/2, and thermal potential energy stored in a system is UT/2. Thus, entransy (G) is defined as the half of the product of internal energy (U) and temperature (T) and expressed as [17,18,19,20,21,22,23,24,25,26,27];

$$G = \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} UT$$

(7)

Rate of entransy dissipation which is losses can be calculated by mass flow rates, specific heats and inlet/outlet temperatures of the hot and cold fluids, and it can be expressed as:

$$G_{d} = \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \left[ { \, m_{h} C_{ph} \{ (T_{hi} )^{2} - (T_{ho} )^{2} \} } \right]{-}\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} [m_{c} C_{pc} \left\{ {(T_{co} )^{2} - (T_{ci} )^{2} } \right\}$$

(8)

where G is entransy (kW-K), G_d is rate of entransy dissipation (kW-K) and U is internal energy (kW). For performance analysis, entransy dissipation-based thermal resistance for heat exchanger is also found which is related to rate of entransy dissipation and heat transfer through heat exchanger and can be expressed as:

$$R_{t} = G_{d} /Q^{2}$$

(9)

where R_t is entransy dissipation-based thermal resistance (K/kW) and Q is rate of heat transfer through heat exchanger (kW). A dimensionless number called entransy dissipation number is introduced by researchers for performance analysis of heat exchanger, and this term can be found by rate of entransy dissipation, heat transfer through heat exchanger and maximum temperature difference in heat exchanger (i.e., T_hi and T_ci). Entransy dissipation number (EDN) can be expressed as [28]:

$$EDN = G_{d} /[Q \, (T_{hi} - T_{ci} )]$$

(10)

This EDN equation can be modified with effectiveness (ɛ) which is the ratio of actual heat transfer (Q) to maximum heat transfer (Q_max) through heat exchanger and can be written as [1,2,3,4];

$$\varepsilon = \left( Q \right)/\left( {Q_{{\text{max}}} } \right)$$

(11)

$$\varepsilon = [(m_{h} C_{ph} )_{{\text{max}}} (T_{hi} - T_{ho} )]/[(m_{f} C_{pf} )_{{\text{min}}} (T_{hi} {-}T_{ci} )]_{{\text{max}}}$$

(12)

$${\text{or}}\;\varepsilon = [(m_{c} C_{pc} )_{{\text{max}}} (T_{co} {-}T_{ci} )]/[(m_{f} C_{pf} )_{{\text{min}}} (T_{hi} {-}T_{ci} )]_{{\text{max}}}$$

(13)

So, EDN can be modified as;

$$EDN = G_{d} /[\varepsilon Q_{{\text{max}}} (T_{hi} - T_{ci} )]$$

(14)

$$EDN = G_{d} /[\varepsilon \{ (m_{f} C_{pf} )_{{\text{min}}} (T_{hi} {-}T_{ci} )\} (T_{hi} - T_{ci} )]$$

(15)

$${\text{or}}\;EDN = G_{d} /[\varepsilon (m_{f} C_{pf} )_{{\text{min}}} (T_{hi} - T_{ci} )^{2} ]$$

(16)

In this research work, entropy generation number has been calculated for the heat exchanger and it should be as minimum as possible for the better performance of the heat exchanger. It is the ratio of entropy generation during irreversible heat transfer through the heat exchanger to the minimum heat capacity of the flowing fluid [29].

$$N_{eg} = dS_{{\text{gen}}} /(mC_{p} )_{{\text{min}}}$$

(17)

In the present work, CFD analyses of double-pipe heat exchanger for counter flow have been performed where water is used as hot fluid while water or ammonia is used as cold fluids (which flow through heat exchanger) with steel, aluminum and copper as inner pipe materials with different roughnesses of pipes. After simulation, numerical validation has been done and compared all results and proved which pipe material (with surface roughness) and cold fluid give best effectiveness or rate of heat transfer but lowest rates of entropy generation, exergy and entransy dissipation and entransy dissipation number. Geometry of double-pipe heat exchanger is shown in Fig. 2, and four different meshes are given in Table 2 [5]. A method has been done to decide mesh for CFD analysis. For example, outlet temperatures of cold and hot fluids for mesh 3 and mesh 4 do not vary significantly (as in Table 2), so mesh 3 has been chosen for research work which has 485,831 elements and 507,656 nodes.

Fig. 2

Geometry of double-pipe counter flow heat exchanger

Table 2 Outlet temperatures of four meshes

Results

Temperature counters have been found by CFD analyses at different operating conditions as shown in Figs. 3 and 4, and the conditions are: (a) inlet temperature of hot fluid (water) is 350 K, inlet temperature of cold fluid (water) is 300 K, mass flow rates of hot and cold fluids are 0.08 kg/s, specific heat of water is 4.186 kJ/kg-K, inner pipe materials are steel, aluminum and copper, and outer pipe material is steel; and (b) inlet temperature of cold fluid (ammonia) is 210 K, inlet temperature of hot fluid (water) is 300 K, and specific heat of ammonia is 4.744 kJ/kg-K. Results which have been obtained from CFD analyses for all three materials for all three cases of different cold fluids and roughnesses of inner pipes are mentioned in Tables 3, 4 and 5. Outlet temperatures and rates of heat transfer for each condition have been tabulated.

Fig. 3

Temperature contours for steel, aluminum and copper at conditions (a)

Fig. 4

Temperature contours for steel, aluminum and copper at conditions (b)

Table 3 Results with steel pipe and change in pipe’s roughness with different cold fluids

Table 4 Results with aluminum pipe and change in pipe’s roughness with different cold fluids

Table 5 Results with copper pipe and change in pipe’s roughness with different cold fluids

Results from analyses show that maximum heat transfer between hot and cold fluids can be achieved if thermal conductivity of the inner pipe of double-pipe heat exchanger is higher. Rate of heat transfer and effectiveness increases with the thermal conductivity of the material, and these parameters also change with the change in cold fluid and roughness of the pipe. Rates of entropy generation, exergy destruction and entransy dissipation with entransy dissipation-based thermal resistances, entransy dissipation numbers and entropy generation numbers are shown in Tables 6 and 7.

Table 6 Entropy, exergy and entransy analyses for water as hot and cold fluids

Table 7 Entropy, exergy and entransy analyses for water as hot and ammonia as cold fluids

Comparative curves have also been plotted for different inner pipe materials and different roughnesses of pipes between the rates of heat transfer through heat exchanger, entropy generation, exergy destruction, entransy dissipation, entransy dissipation-based thermal resistances, entransy dissipation numbers and entropy generation numbers as shown in Figs. 5, 6, 7, 8, 9, 10 and 11. These curves indicate: (1) maximum percentage decrements in the rate of heat transfer between flowing fluids (i.e., 48.075, 31.372 and 28.705%) were found for Cu–water, steel–ammonia and Al–water combinations as inner pipe materials and cold fluids when surface roughnesses were highest but maximum percentage increment (i.e., 114.162%) achieved with Cu–water combination when surface was smooth. (2) Maximum percentage changes for entropy generation, exergy destruction, entransy dissipation, entransy dissipation-based thermal resistance, entransy dissipation number, effectiveness and entropy generation number were found (2.531, 1.159, 0.776, 4.796, 2.127, 3.125 and 2.744%, respectively) for steel–water, (18.041, 7.6, 29.221, 50.273, 3.148, 31.25 and 18.053%, respectively) for steel–ammonia, (37.623, 71.424, 8.112, 112.753, 51.612, 28.629 and 37.442%, respectively) for Al–water, (18.118, 14.747, 2.316, 32.818, 16.436, 12.274 and 18.102%, respectively) for Al–ammonia, (49.787, 90.502, 8.682, 238.561, 75.93, 48.093 and 49.595%, respectively) for Cu–water and (58.73, 18.644, 26.221, 14.913, 7.928, 19.893 and 58.443%, respectively) for Cu–ammonia combinations at highest surface roughness, but comparatively less percentage changes for these parameters were found (1.265, 0.562, 0.381, 2.358, 1.063, 1.875 and 1.372%, respectively) for steel–water, (8.35, 3.73, 14.128, 21.643, 2.248, 15.441 and 8.284%, respectively) for steel–ammonia, (11.881, 4.966, 11.201, 27.638, 6.451, 16.532 and 12.112%, respectively) for Al–water, (6.106, 3.432, 6.797, 14.165, 3.072, 9.386 and 6.101%, respectively) for Al–ammonia, (31.489, 38.636, 5.689, 119.43, 43.982, 34.604 and 31.742%, respectively) for Cu–water and (37.037, 10.375, 15.551, 8.489, 4.261, 11.671 and 36.87%, respectively) for Cu–ammonia combinations for smoother surfaces of inner pipes of double-pipe counter flow heat exchanger.

Fig. 5

Percentage decrement in heat transfer with steel pipe at different roughnesses

Fig. 6

Percentage decrement in heat transfer with aluminum pipe at different roughnesses

Fig. 7

Percentage decrement in heat transfer with copper pipe at different roughnesses

Fig. 8

Percentage increment in heat transfer with different inner pipe materials

Fig. 9

a, b Percentage change in properties with steel pipe at different roughnesses: a water and b ammonia as cold fluids

Fig. 10

a, b Percentage change in properties with aluminum pipe at different roughnesses: a water and b ammonia as cold fluids

Fig. 11

a, b Percentage change in properties with copper pipe at different roughnesses: a water and b ammonia as cold fluids

Computer software has also been developed in this research work called effect of surface roughness on the performance of heat exchanger (ESRPHEx) as shown in Fig. 12, and this computer software is useful to eliminate human errors during mathematical calculations and also helpful to reduce time consumption during the analyses [30].

Fig. 12

Developed computer software for performance analyses

Conclusion

In this research work, comparative analyses of heat exchanger with steel, aluminum and copper as inner pipe materials and with water and ammonia as cold fluids have been done and observed that the maximum amount of heat transfer between flowing fluids and effectiveness of heat exchanger is 12.895 kW and 0.377, which have been found when copper was used as inner pipe with smooth surface finish and ammonia as cold fluid. It has also been concluded that the following conditions are required for best performance from a heat exchanger: entropy generation rate, entropy generation number, exergy destruction rate, entransy dissipation rate, entransy dissipation-based thermal resistance and entransy dissipation number should be minimum. So, minimum rate of entropy generation is 0.00118 kW/K, entropy generation number is 1.131, exergy destruction rate is 0.280 kW, entransy dissipation-based thermal resistance is 4.004 K/kW, and entransy dissipation number is 0.457 which have been found with copper pipe. Maximum percentage increment has been found when copper was used as inner pipe material with smooth surface. It has also been observed that when water was used as cold fluid, the percentage changes in entropy generation, exergy destruction, entransy dissipation, entransy dissipation-based thermal resistance, entransy dissipation number, effectiveness and entropy generation number increase with thermal conductivity of inner pipe, and percentage changes in these parameters were less with ammonia as compared to water at same operating conditions. After analyses, high heat capacity of fluid (i.e., ammonia as cold fluid) and high conductive material (copper as inner pipe) with smooth surface have been recommended to get best performance from heat exchanger.