# Preliminary Design of Compact Condenser in an Organic Rankine Cycle System for the Low Grade Waste Heat Recovery

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^{†}

## Abstract

**:**

^{TM}software. The cycles are generated starting from the same heat source: the exhaust gas of a typical 2.0 L Diesel engine (or from a small size turbine engine). The design of the condenser has been performed to obtain a very compact component, evaluating the heat exchanger tube and fins type design. Through empirical formulas, the area of heat exchange, the heat required to exchange and the pressure drop in the element have been calculated. A commercial software package is used to build the model of the condenser, then a thermal and mechanical analysis and a CFD analysis are realized to estimate the heat exchange. Finally the evaluations, the possible future studies and possible improvements of the system are shown.

## 1. Introduction

## 2. The ORC Recovery Energy System

- biomass incineration with heat recovery;
- geothermal sources;
- thermal recovery from ICE engines;
- high-T solar panels.

## 3. ORC Thermodynamic Analysis

#### 3.1. Simulation

Data | Value |
---|---|

Mass flow rate (kg/s): | 0.15 |

Exhaust temperature (K): | 845.15 |

Pressure (kPa): | 202.6 |

Average Composition (per cent by volume): | CO = 0.041; |

CO_{2} = 2.74; | |

O_{2} = 17.14; | |

C_{x}H_{y} ≤ 0.03 |

Data | R134a | R245fa |
---|---|---|

Mass flow rate (kg/s) | 1 | 0.7 |

Temperature (K) | 288.15 | 288.15 |

Pressure (kPa) | 150 | 150 |

- R134a: 1,1,1,2-Tetrafluoroethane, R-134a, Florasol 134a, or HFC-134a, is a haloalkane refrigerant, it has the formula CH
_{2}FCF_{3}and a boiling point of 246.85 K at atmospheric pressure. 1,1,1,2-Tetrafluoroethane is an inert gas used primarily as a “high-temperature” refrigerant for domestic refrigeration and automobile air conditioners. - R245fa: HFC-245fa is also known as pentafluoropropane and by its chemical name 1,1,1,3,3-pentafluoropropane. Unlike the CFC and HCFC blowing agents formerly used for this purpose, it has no ozone depletion potential and is nearly non-toxic.

#### 3.2. Process Simulation with CAMEL-Pro^{TM}

^{TM}Process Simulator [6,7]. The computer code for the modular simulation of energy conversion processes was developed as part of the research conducted by the “CIRCUS” group (International Centre for Research and Scientific Computing University Department of Mechanics and Aeronautics) at University of Roma “Sapienza”. The code developed (in C++ and C#), called CAMELPro

^{TM}(an acronym for Modular CAlculation for ELements) is characterized by being designed from the outset as an Object Oriented program; and it is composed by two parts: a central body that only perform the common operations in any simulator (reading input, graphical interaction with the user, assembly of a power plant, presentation of the results), and a library of “elements” (expandable) containing independents structures. The elements can be represented by an object or component, that are modularly interfaced with other components.

## 4. The Plant Layout and Simulation Results

- turbine inlet pressure;
- turbine inlet temperature;
- turbine pressure outlet;
- condenser outlet temperature.

- evaporation phase (7–8),
- expansion in the turbine (8–9),
- condensation (9–10),
- increased fluid pressure (10–7).

- exhaust gas inlet (2),
- exhaust gas exit (3),
- cooling water inlet (6),
- cooling water outlet (5),
- mechanical power absorbed by the pump (4),
- power output produced (1).

Data | Unit | Value |
---|---|---|

R134a mass flow rate | (kg/s) | 0.38 |

R134a boiler inlet temperature (7) | (K) | 307.48 |

R134a boiler outlet temperature (8) | (K) | 334.20 |

R134a condenser inlet temperature (9) | (K) | 315.29 |

R134a condenser outlet temperature (10) | (K) | 306.80 |

R134a boiler inlet pressure (7) | (kPa) | 1670 |

R134a boiler outlet pressure (8) | (kPa) | 1500 |

R134a condenser inlet pressure (9) | (kPa) | 950 |

R134a condenser outlet pressure (10) | (kPa) | 874 |

Outlet gas temperature (3) | (K) | 402.16 |

Outlet cooling water temperature (5) | (K) | 304.48 |

Power output (1) | (kW) | 3.526 |

Power absorbed by pump (4) | (kW) | 0.302 |

Data | Unit | Value |
---|---|---|

R245fa mass flow rate | (kg/s) | 0.35 |

R245fa boiler inlet temperature (7) | (K) | 315.21 |

R245fa boiler outlet temperature (8) | (K) | 345 |

R245fa condenser inlet temperature (9) | (K) | 326.23 |

R245fa condenser outlet temperature (10) | (K) | 315 |

R245fa boiler inlet pressure (7) | (kPa) | 680 |

R245fa boiler outlet pressure (8) | (kPa) | 612 |

R245fa condenser inlet pressure (9) | (kPa) | 300 |

R245fa condenser outlet pressure (10) | (kPa) | 270 |

Outlet gas temperature (3) | (K) | 403.59 |

Outlet cooling water temperature (5) | (K) | 311 |

Power output (1) | (kW) | 4.463 |

Power absorbed by pump (4) | (kW) | 0.124 |

Data | R134a | R245fa | Water cycle |
---|---|---|---|

Net power product (kW) | 3.224 | 4.329 | 2.084 |

Evaporator (kW) | 71.53 | 71.31 | 72.77 |

Condenser (kW) | 68.23 | 66.88 | 70.68 |

Efficiency | 4.5% | 6% | 2.9% |

Carnot efficiency | 8.2% | 8.7% | 9% |

## 5. Thermodynamic Model of the Condenser

#### 5.1. Selection of Tube-Fin Heat Exchanger

#### 5.2. “LMTD Method” and “Heat Exchanger Effectiveness Method”

_{1}and ΔT

_{2}are the temperature drops between two fluids at each end of a counter flow exchanger. For a counter flow exchanger, in our case, ΔT

_{h,i}and ΔT

_{h,o}indicate the inlet and outlet temperatures of condensing fluid, and the inlet and outlet temperatures of cooling fluid, respectively. The heat transfer equation is given by:

#### 5.3. Heat Transfer Coefficient

_{i}” and “A

_{o}” represent the inside and outside areas of the inner tube. To decrease the number of unknowns of the problem, the calculation of heat transfer coefficient “U” is only limited to the inner area “A

_{i}”, and the term “A

_{i}/A

_{o}” is replaced by the equation:

#### 5.4. Mono-Phase Heat Transfer and Pressure Drop Correlations

_{h}). The above equations offer simplicity in computation, but uncertainties on the order of ±25% are not uncommon, as described in the studies of Allen and Eckert [14]. Then the convective coefficient is evaluated by Nusselt Number as (inside and outside):

_{e}” is the equivalent length of the pipe, “ρ” is the density of the gas inside tube, “u

_{m}” is the fluid velocity in the pipe and “d

_{i}” is the internal pipe diameter.

#### 5.5. Two-Phase Heat Transfer and Pressure Drop Correlations

- condensation of R134a in smooth horizontal tubes,
- tube inner diameter of 8 mm,
- tube length of 2.5 m,
- the mass flux between 200 and 700 kg/s,
- the number of data point of the study is 280 [17].

_{tt}):

_{e}”. The total mass velocity “G”, and the properties for the two-phase friction factor “f

_{N}” are evaluated at a linearly averaged refrigerant temperature. The new two-phase friction factor is:

## 6. Preliminary Design of the Condenser

#### 6.1. Tube and Fins Geometry

_{t}” tubes, as follows:

- “N
_{s}” is the number of tubes where the mass to condense is distributed, and they are arranged in parallel mode, - “N
_{r}” is the number of turns of tubes.

_{i}”, a length “L

_{1}”, and an thickness “T

_{h}”. For the study of heat exchange on finned side, the Briggs and Young correlation [22] has been used, that is based on regression analysis:

**Figure 3.**Tube fin details. Individually finned tube staggered arrangment. (

**a**) Geometry; (

**b**) unit cell and (

**c**) tube fin details.

_{p}”, is the tube surface minus the area blocked by the fins. It is given by:

_{f}” is the fin thickness, “N

_{f}” is the number of fins per unit length. Furthemore the area of the side plates is added to the heat exchange one. The fin surface area, “A

_{f}”, is given by:

_{o}is equal to ${A}_{p}+{A}_{f}$.

#### 6.2. The Problem Approach and the Iterative Calculation

- The thermodynamic data of three phases have been calculated using the software CAMEL-Pro;
- In the same software the temperature drop and thermal power of exchange have been detected;
- A starting geometry of study is defined, in terms of tubes numbers “N
_{s}” and “N_{r}”, their internal diameter, and characteristics of fins; - The hydraulic diameters and the velocity of fluids are calculated, so the values of the convective coefficients of heat exchange and then the global heat exchange coefficient “U”;
- The necessary area of heat exchange “A” is calculated, then the component size and its efficiency;
- Pressure drops are calculated in the individual phases, which correspond to a new inlet and outlet condensation temperatures;
- The problem is set again to get the smallest values of the area “A”, and reduce the overall dimensions of the component.

## 7. Condenser Design Results for the R134a System

- Low price of the fluid;
- Technology already widely studied and well-established, and with verified formulas for condensation studies;
- Efficient and economic turbine for the expansion already present on the market.

_{s}” and number of turns “N

_{r}”, then the tubes total number “N

_{t}” have been identified.

Characteristics | Value | Unit |
---|---|---|

Inner tube diameter | 6 | mm |

Tube thickness | 1 | mm |

Fins distance | 2 | mm |

Fins height | 3 | mm |

Fins thickness | 0.3 | nm |

Tube distance “P_{t}” | 17 | mm |

Tube distance “P_{l}” | 17 | mm |

Tubes number “N_{s}” | 15 | - |

Tubes number “N_{r}” | 17 | - |

Total tubes number | 255 | - |

_{i}”, to better distribute the steam quality from the liquid phase to the vapor phase [15,16]. In Table 7, Table 8 and Table 9 the results of our assumptions are reported.

Dimensions | Value | Unit |
---|---|---|

Component length “L_{1}” | 320 | mm |

Component width “L_{2}” | 265 | mm |

Component height “L_{3}” | 300 | mm |

Thermal power | Value | Unit |
---|---|---|

Q “Sub-cooling” | 232.8349 | W |

Q “Condensing” | 66222.436 | W |

Q “Superheated” | 1774.1024 | W |

Q “Total” | 68229.374 | W |

Area | Value | Unit |
---|---|---|

Area “Sub-cooling” | 0.005947 | m^{2} |

Area “Condensing” | 1.362625 | m^{2} |

Area “Superheated” | 0.098094 | m^{2} |

Area “Total” | 1.466666 | m^{2} |

#### 7.1. Condenser Design

^{®}(Dassault Systèmes SolidWorks Corp., Waltham, MA, USA) has been used. The software allows one to create both the 3D model and the dimensional drawings of the parts, to characterize the elements in each part. Then all single mechanical parts of the condenser have been assembled. The elements realized are: the model of the finned tube for the heat exchange, the shell equipped with baffles to guide the cooling water, and two side bulkheads. The next step is the component assembly, where the correct design of all parts and the correct mounting, without interference, have been verified.

_{s}” indicates the number of tubes), is introduced into the next group of parallel pipes. All the sections of passage for fluids are designed to respect the following velocity limits:

- Maximum cooling water speed is 5 m/s,
- Maximum speed of R134a liquid phase is 5 m/s,
- Maximum speed of R134a vapor phase is 30 m/s.

#### 7.2. Superheated Zone CFD Analysis

- 913,568 elements,
- Result resolution of initial mesh level 5,
- Heat conduction in solid is set on,
- Gravitational effect is set on.

Boundary conditions | Inlet R134a | Outlet R134a | Inlet water | Outlet water |
---|---|---|---|---|

Pressure (Pa) | 950,000 | - | 147,000 | - |

Temperature (°K) | 315.29 | - | 304.05 | - |

Mass flow rate (kg/s) | - | 0.0253 | - | 1 |

**Figure 12.**Section side view of temperature plot with the scale of measurement optimize for R134a internal trend.

**Figure 13.**Section side view of pressure plot, with the scale of measurement optimize for R134a internal trends.

^{2}remains approximately constant along almost the totality of the fin, but with a significant decrease of 50% in the outer part. The integral calculations carried out on the internal and external areas of the element, are necessary for evaluation of the heat transfer rate in Watts. Theoretical values and the simulation values are very close to each other (Table 11), this shows a good element design, and, often, the theoretical calculations provide a safety margin in the operation.

Variables | Theoretical value | Simulation value |
---|---|---|

Outlet R134a temperature (°K) | 310.66 | 311 |

Pressure drop R134a (Pa) | 7215 | 6402 |

Thermal power exchanged (W) | 109.04 | 109.42 |

#### 7.3. Simulation of Mechanical Stress

- 24,987 elements,
- Mesh based on curvature ( the mesh tool creates more elements in higher-curvature areas automatically),
- Four Jacobian points (the number of integration points to be used in checking the distortion level of tetrahedral elements).

- Inlet pressure = 950,000 Pa,
- Maximum temperature = 305 K (for the inner tube surface),
- Maximum stress = 40 × 10
^{6}N/m^{2}, - Yield strength = 258,646,000 N/m
^{2}.

_{1}, σ

_{2}and σ

_{3}the Von Mises stress is expressed as [23]:

## 8. Condenser Design Results for the R245fa System

Characteristics | Value | Unit |
---|---|---|

Inner tube diameter | 8 | mm |

Tube thickness | 1 | mm |

Fins distance | 2 | mm |

Fins height | 3 | mm |

Fins thickness | 0.3 | nm |

Tube distance “P_{t}” | 19 | mm |

Tube distance “P_{l}” | 19 | mm |

Tubes number “N_{s}” | 17 | - |

Tubes number “N_{r}” | 15 | - |

Total tubes number | 255 | - |

Dimensions | Value | Unit |
---|---|---|

Component length “L_{1}” | 290 | mm |

Component width “L_{2}” | 335 | mm |

Component height “L_{3}” | 300 | mm |

Thermal power | Value | Unit |
---|---|---|

Q “Sub-cooling” | 197.78738 | W |

Q “Condensing” | 64105.018 | W |

Q “Superheated” | 2579.2371 | W |

Q “Total” | 66882.042 | W |

Area | Value | Unit |
---|---|---|

Area “Sub-cooling” | 0.008925 | m^{2} |

Area “Condensing” | 1.53173 | m^{2} |

Area “Superheated” | 0.205966 | m^{2} |

Area “Total” | 1.746621 | m^{2} |

## 9. Conclusions

## Nomenclature

A | area (m ^{2}) |

C_{p} | specific heat capacity (J/kg·K) |

CFD | Computational Fluid Dynamics |

D | diameter (m) |

f | Fanning friction factor |

F | LMTD correction factor |

FEM | Finite Element Method |

Fr | Froude number |

g | gravitational acceleration (m/s ^{2}) |

G | Mass velocity (kg/m ^{2}·s) |

H | convection heat t. coefficient (W/m ^{2}·K) |

HRVG | Heat Recovery Steam Generator |

K | thermal conductivity (W/m·K) |

K_{f} | constant |

L | characteristics length (m) |

l_{f} | fin length (m) |

LMTD | Logarithmic Mean Temp. Diff. |

$\dot{m}$ | mass flow rate (kg/s) |

N | tubes number |

NTU | Number of Transfer Unit |

Nu | Nusselt number |

r | radius (m) |

R | thermal resistance (K/W) |

P | pressure (Pa) |

Pr | Prandtl number |

P_{t}, P_{l} | tubes distance |

$\dot{Q}$ | heat transfer rate (W) |

Re | Reynolds number |

S | fin distance (m) |

T | temperature (K) |

t_{f} | fin thickness (m) |

u | velocity (m/s) |

U | heat transfer coefficient (W/m ^{2}·K) |

v | specific volume (m ^{3}/kg) |

x | vapor title |

ΔX | distance (m) |

X_{tt} | Martinelli parameter |

## Greek letters

α | latent heat (J/kg) |

β | condenser area density |

ε | effectiveness |

µ | viscosity (kg/s m) |

ρ | density (kg/m ^{3}) |

σ | internal tension (Pa) |

## Subscripts

c | cold fluid |

e, eq | equivalent |

f | fin |

g | gas |

h | hot fluid, hydraulic |

i | inlet |

l | liquid |

lm | long mean |

m | medium |

min | minimum |

o | outlet |

p | primary |

r | parallel |

s | serial |

t | total |

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Capata, R.; Zangrillo, E.
Preliminary Design of Compact Condenser in an Organic Rankine Cycle System for the Low Grade Waste Heat Recovery. *Energies* **2014**, *7*, 8008-8035.
https://doi.org/10.3390/en7128008

**AMA Style**

Capata R, Zangrillo E.
Preliminary Design of Compact Condenser in an Organic Rankine Cycle System for the Low Grade Waste Heat Recovery. *Energies*. 2014; 7(12):8008-8035.
https://doi.org/10.3390/en7128008

**Chicago/Turabian Style**

Capata, Roberto, and Erasmo Zangrillo.
2014. "Preliminary Design of Compact Condenser in an Organic Rankine Cycle System for the Low Grade Waste Heat Recovery" *Energies* 7, no. 12: 8008-8035.
https://doi.org/10.3390/en7128008