CHALLENGE

The main challenge is the application of Flownex to model simple recuperator designs that are based on bare tubes in cross flow.

BENEFITS

One of the main strengths of Flownex is its ability to model heat transfer to and from piping systems. As a result, it is relatively straightforward to create a Flownex model for a recuperator which performs the relevant heat transfer and fluid mechanics calculations.

SOLUTION

A Flownex recuperator compound component was developed and is presented in this case study. The model is based on single pass bare tubes in cross flow to a rectangular shell. Components can be connected in series (or parallel) to model multi-pass recuperators. The model presented utilizes Flownex’s gas mixture capabilities to model the shell side fluid which is typically a flue gas. As such, the shell side fluid is only valid for low-pressure applications.

INTRODUCTION

A recuperator is a specific application of a heat exchanger used to recover heat from a hot fluid. Perhaps the most frequent application of a recuperator is to recover heat from hot flue gas before it is discharged into the atmosphere. Several different recuperator designs are used in industry; however, one of the simplest and most cost effective designs is a bundle of bare tubes positioned in cross flow to the flue gas. The tubes may be a single pass or multi-pass design. Figure 1 shows a schematic of a six-pass recuperator for a gas turbine. 

FLOWNEX MODEL

A compound component was developed in Flownex to model a single tube pass recuperator based on bare tubes in cross flow to a rectangular shell. The component is set up such that a minimum of inputs are required to assess the performance of the design. Figure 2 shows a simple recuperator model for a single tube pass design. The process inputs are specified at the boundary conditions while the recuperator geometry is specified on the recuperator element itself. The blue rectangle shows most of the available inputs for the recuperator. 

Figure 3 shows five recuperator bundles in series for the exhaust gas while there are two independent sections; one heating CO2 and the other heating air. As shown, bundles can easily be connected in series for the exhaust gas, as is usually the case, but they can also be connected in parallel. Combinations of series and parallel bundles can also be specified with ease. Similarly, the connection of the tube-side flow paths can be as simple or complex as the user wants. Figure 3 shows the air outlet bundle consisting of two bundles in parallel.

RECUPERATOR COMPOUND COMPONENT INPUTS AND RESULTS

The recuperator compound component inputs property page was laid out to simplify the input data requirements as much as possible and is shown in Figure 4.

In the Fluids & Material group, the shell-side and tube-side fluids and the tube material are specified. The Tube Geometry group specifies data relating to the tube geometry, most of which are self-explanatory. The following items may require further clarification:

• Length: this is the tube length per single pass, i.e. it is the length of a single tube visible to the flue gas stream in the shell.

• No of tubes per row: this is the number of tubes in the transverse direction, perpendicular to the flow.

• Figure 4: Input data property page   No of tube rows in bundle: this is the number of tube rows in the longitudinal direction, i.e. parallel to the flow. The product of the No of tubes per row and the No of tube rows in bundle represents the total number of tubes in the bundle.

• Bundle divided into sections: the model allows for a single bundle (single tube pass section) to be split into more than one Flownex component to allow for more accurate calculations. The tube bundle in the compound component consists of a single Flownex pipe element. Although the pipe element is sub-divided into ten increments, which allows for temperature variations along the tube, no variation in the direction of the flue gas flow is allowed for. Of specific importance is the variation of tube wall temperatures in the direction of flue gas flow. The first few tube rows often referred to as the shock or shield tubes, are usually of a different material capable of withstanding higher temperatures. It is convenient therefore to be able to divide a bundle into two or more sections to obtain better estimates of the tube wall temperatures in the first few tube rows. Therefore, when a bundle is divided as is shown in Figure 3 above, the sub-divided bundle Flownex components are connected in parallel for the tube-side and in series for the shell side. Furthermore, the No of tube rows in bundle for all the subdivided sections must be the same, i.e. 11 in the case shown. The entry field No of tube rows in this section, which will appear when a bundle is sub-divided, must be completed so that the totals for all the sub-divided sections will equal the total number of tubes in the bundle. For example, if the bundle consists of eleven rows as shown, and the bundle is subdivided into two sections with the first shield tube section comprised of 4 rows, then the second section must have seven rows.

• The longitudinal and transverse pitches are shown in Figure 7.

• The next two fields, Shell-tube clearance, are used to calculate the rectangular shell width and height. The shell width is calculated from the number of tubes per row and the transverse tube pitch, and then the clearance in the tube pitch direction is added. The shell height is simply taken as the tube length plus the Shell-tube clearance (tube direction).

• The user has five options when specifying tube fouling: No fouling, Resistance only, Resistance based on thickness, Resistance based on conductivity and Thickness and conductivity. For the second option, the user only needs to specify the fouling factor. For the third to fifth options, the user must provide a combination of two variables from the Resistance (fouling factor), Thermal conductivity of the foulant (fouling material) and the Thickness of the fouling layer.

• The Thermal design margin of safety is a safety factor used in design. To ensure the design is 10% over-surface, enter a factor of 10%.

• The model also assists in the mechanical design aspects of the tubes. Design parameters are entered which allows the model to verify the sufficiency of tube wall thicknesses and required flange ratings for tube connections.

The results page is similarly laid out with simplicity in mind. The results groups are briefly as follows:

• The Performance Results provides a short summary of the most important heat transfer performance results.

• The Geometry Results provides the user with the total number of tubes in the bundle, the heated tube length, shell dimensions and more.

• The Tube-Side Results provides Heat Transfer results for the tube inside and outside surface as well as Flow Results, Mean Fluid Variables and Upstream and Downstream flow element results that are similar to those of a standard Flownex pipe element.

• Shell-Side Results offer the results of mass flow, velocity, pressures, temperature and fluid properties for the shell-side fluid.

• Mechanical Design Results – Tube present the user with the results of tube design strength calculations.

• Mechanical Design Results – Flange presents the user with the results of flange design strength and rating calculations.

RECUPERATOR COMPOUND COMPONENT

The recuperator compound component design is discussed in the following sections. When double-clicking on any of the bundle compound components shown in Figure 2 or Figure 3, the internals of the component is shown in a separate window (Figure 6) which allows the user to view and edit any of the inputs and results of any of the elements that form part of the compound component.

Although the compound component’s network may look rather busy, it is essentially comprised of just three standard Flownex elements; a pipe element representing the shell side flow, a pipe element representing the tube side flow, and a Composite Heat Transfer (CHT) element representing the heat transfer between the two flow streams. The remaining icons are scripts that perform the necessary calculations for the outside convection coefficient, the shell-side pressure loss, fouling factor calculations, fluid properties, pipe and flange rating calculations and some post-processing calculations. Some of these calculations are discussed in more depth below.

Tube Geometry Extractor (Geom Extr Script)

A script was developed to enable the correct tube diameter and wall thickness to be obtained regardless of whether the user specified the tube geometry in terms of a nominal diameter and a schedule or a simple internal diameter and a wall thickness.

Pressure Pipe & Flange Rating Script (Pressure Rating Script)

This script may be used to perform mechanical strength calculations for the coil pipe and associated flanges. The development of this script is discussed in detail in the following case study available from [1]: CS-051: Pressure Piping Thickness and Flange Rating Calculation

Outside Convection Script (h_o Script)

This script reads the tube and shell geometries from the tube and shell pipe elements as well as the Tube Geometry Extractor. It then calculates the outside tube convection coefficient using methods developed by Zukauskas [2] which are discussed in more detail below. This convection coefficient is then assigned to the shell-side of the CHT element.
 

Fouling Factor Script (Fouling F Script)

The script implements fouling factor calculations by modeling the internal and external tube fouling factors as actual layers specified in the CHT element. The user may specify:

• No fouling: When selected, Flownex will set the layer thickness to a negligibly small value (1E-6 mm) and the layer conductivity shall be fixed to a very high value (1000 W/m.K). This will result in a fouling layer that is negligibly small with a negligible temperature difference across it.

• Resistance only: When selected, the user may specify a value for fouling resistance (m2.K/W). Since the actual fouling layers are modeled, Flownex assumes a hard-coded layer thickness of 0.1 mm. The fouling layer thermal conductivity is then calculated based on these two values.

• Resistance – based on thickness: When selected, the user may specify both the fouling resistance and the fouling layer thickness. As with the previous option, the fouling layer thermal conductivity is then calculated based on these two values.

• Resistance – based on conductivity: When selected, the user may specify both the fouling resistance and the fouling layer thermal conductivity. Similar to the previous two options, these two values are then used to calculate the fouling layer thickness.

A previous case study by this author on the modeling of fouling factors, titled Fouling Factors in Flownex Heat Transfer Models [3] may be found here: CS-044: Fouling Factors in Fownex Heat Transfer Models

Mixed Fluid Props at T_s Script (Mix Props at T_s Script)

This script is a copy of script in the Master Database script repository and is used to obtain the shell-side fluid properties at tube surface temperatures.

Pressure Loss Script (dP Script)

This script calculates the shell-side fluid pressure loss. This represents the flue gas flow pressure loss across the tube bank. The script implements a method by Gaddis [4] as published in the VDI Heat Atlas (2010) [4] which is discussed in more detail below. The script allows for both inline and staggered tube arrangements and the specification of transverse and longitudinal tube pitches.

Gnielinski Temperature Correction Script (Gnielinski Script)

The model uses the Gnielinski [5] correlation to calculate the tube inside Nusselt number. The CHT element allows for several correction factors, amongst others for effects where large differences between the tube wall temperature and bulk fluid temperature exist.

Design Margin Script (Des Margin Script)

It is convenient to be able to specify a design margin F (safety factor) when sizing equipment. This script allows for the specification of a design margin which is then assigned to the CHT element as a Heat transfer grading factor. This factor F, between 0 and 1, decreases the heat transfer as follows:

(1)

Postprocessing Script (Postproc Script)

This script is used to determine some valuable performance parameters for reporting purposes. These include the LMTD, the corrected LMTD, the tube total outside surface area, the heat flux and the overall heat transfer coefficient U_o.

CORRELATIONS USED IN THE RECUPERATOR MODEL

Several different empirical models are available for the calculation of heat transfer coefficients and pressure losses across tube banks. The tube outside convection coefficient used in this model is based on the Zukauskas [2] correlations. The shell side pressure loss across the tube bundle is based on the method of Gaddis [4]. The fouling factor calculation methods are based on equations presented by this author.

External Convection Coefficients of Tube Banks in Cross Flow

The model implements the updated correlations by Zukauskas [2] as presented by Cengel [6]. The correlations are presented in the following two tables:

(2)

where:

Nu_D is the Nusselt number based on the tube outside diameter.

h is the tube outside surface convection coefficient, W/m².K.

D is the tube outside diameter, m.

k is the outside fluid thermal conductivity, W/m.K.

F is a correction factor for a bundle with fewer rows than 16 (N_L) as given in Table 2.

C, m and n are constants given in Table 1.

Re_D is the Reynolds number based on the outside tube diameter, m.

Pr is the Prandtl number based on fluid properties at the mean bulk fluid temperature.

Pr_s is the Prandtl number based on fluid properties at the tube surface temperature.

Table 1: Nusselt Number correlations for cross flow over tube banks for NL >= 16 (from Zukauskas, 1987) (NL is the number of tube rows in the shell flow direction).

Table 2: Correction Factor F for NL < 16.

Pressure Loss of Flow Across Tube Banks

The pressure loss of the external flow across the tube bank is calculated according to a method by Gaddis [4]. The equations are based on a superposition of equations of Bergelin et al. [7] for laminar flow in a modified form and the equations of Gaddis and Gnielinski [8] for turbulent flows. It is a flexible method which allows for inline and staggered tube configurations as well as variations in the transverse and longitudinal tube pitches. It calculates the ideal flow drag coefficients for the configuration and then corrects these coefficients for variations in temperature and number of rows. Tube bank arrangements and geometric parameters are shown in Figure 7.

The pressure loss across a tube bank is calculated as follows:

(3)

where:

C_d   is the drag coefficient.

N_L   is the number of tube rows in the external flow direction.

𝜌    is the mean density of the external fluid, kg/m³.

V_max   is the maximum fluid velocity between the tubes, i.e. the velocity between the narrowest cross section of the tubes. Note that this could be either A_T or A_D in Figure 7 above, m/s.

All properties are taken at mean conditions, for example, 𝜌 = (𝜌𝑖𝑛 + 𝜌𝑜𝑢𝑡)/2, except where properties are to be taken at the tube outside surface temperature T_s , for example 𝜇𝑠.

The drag coefficient is a function of the Reynolds number, Re, the transverse pitch ratio a and the longitudinal pitch ratio b, where:

(4)

(5)

(6)

𝑆𝑇, 𝑆𝐿 and 𝑆𝐷 are the transverse, longitudinal and diagonal tube pitches respectively, in m. To calculate the maximum velocity between the tubes, the minimum cross sectional flow area must be determined:

For inline tube banks: 

(7)

where V_shell.in is the shell-side fluid velocity upstream of the tube bank, in m/s.

For staggered tube banks the minimum flow area could be either A_T or A_D as shown in Figure 7. When A_D presents the smallest cross-sectional flow area:

(8)

 Minimum flow area is A_D

When A_T presents the smallest cross-sectional flow area (similar to an inline tube arrangement):

(9)

Minimum flow area is A_T

(10)

The shell-side upstream velocity is calculated as follows:

where:

𝑚̇  is the shell side fluid mass flow rate, kg/s.

𝐴𝑠ℎ𝑒𝑙𝑙   is the shell side cross sectional area upstream of the tube bank, m².

Definition of an Ideal Tube Bundle

An ideal tube bundle is defined arbitrarily as follows: Physical properties of the fluid is independent of temperature, number of tube rows 𝑁𝐿 ≥ 10, number of tubes per row ≥ 10, ratio of tube length to tube diameter ≥ 10, fluid velocity in the free cross section at inlet of tube bundle is uniform and perpendicular to the free cross section and smooth tube surface. Deviations from the ideal situation can be taken into account by means of correction factors.

The drag coefficient C_d for an ideal tube bundle consists of laminar and turbulent components:

(11)

where:

C_d.l  is the laminar component of the drag coefficient

C_d.t  is the turbulent component of the drag coefficient

F  is a Reynolds number dependent correction factor for the turbulent component of the drag coefficient.

For inline tube banks, F  C_d.l  and C_d.t  are calculated as follows [8]:

		(12)
		(13)
		(14)
		(15)
		(16)

For staggered tube banks, F  C_d.l  and C_d.t  are calculated as follows [8]:

		(17)
		(18)
		(19)
		(20)
		(21)
		(22)

For Eq.(20) and (21) respectively:

Temperature correction for non-isothermal (non-ideal) flow is applied to the drag coefficients calculated above, as heating or cooling of the tube bundle will lead to changes of the fluid properties in the thermal layer near the tube surface. The drag coefficients are multiplied by these temperature correction factors to account for the temperature influence. For the laminar drag coefficient, the non-isothermal correction factor is [7]:

(23)

where:

(24)

For the turbulent drag coefficient, the non-isothermal correction factor may be calculated according to Sieder and Tate [9]:

(25)

Correction factors for small number of tube rows (less than ten rows) for the drag coefficients are required according to Bergelin et al. [7]. For the laminar drag coefficient, the correction factor is very similar to the correction factor for temperature correction as given above.

Therefore, the laminar temperature correction and small number of rows correction factors may be combined, and hence:

(26)

where:
 

(27)

where:

f_zn.l is the laminar component of the correction factor for the combined effect of the number of tubes rows less than ten as well as correction for temperature.

Note that Eq. 26 and Eq. 27 effectively replace Eq. 23 and Eq. 24.

In the turbulent flow range, the change in the drag coefficient C_d.t for a tube bundle with change in the number of tube rows between 5 and 10 is small [10] and may be ignored. However, sudden expansion of the flow area from that of the last tube row to the total available free area in the tube bundle leads to an additional pressure drop, which is negligible for a tube bundle with a large number of tube rows but may be significant in a tube bundle with a small number of tube rows. This may be compensated for by adding a correction factor f_n.t to the drag coefficient C_d.t in case of an isothermal flow, or to the corrected drag coefficient f_z.t C_d.t in the case of a non-isothermal flow [8]:

		(28)
		(29)

General Equation for the Drag Coefficient

The general equation for the drag coefficient for a non-isothermal (non-ideal) tube bundle, as is the case in a heat exchanger, must incorporate the temperature correction factor as well as the correction factor for the number of tube rows. Therefore, Eq. 11 is adapted as follows:

(30)

Note that Eq. 30 applies to both inline and staggered tube bank configurations. As such, for inline tube banks Eq. 30 should be written using the variables C_d.i , C_d.l.i , C_d.t.i and F_i . Similarly, for a staggered arrangement the variables are C_d.s , C_d.l.s , C_d.t.s and F_i .

The Modelling of Fouling Factors

In an earlier case study by this author, the modeling of fouling factors was discussed in detail. In this section, only a brief discussion on this topic is repeated in the interest of its implementation in this case study.

Heat transfer is often calculated in terms of a thermal resistance and a temperature difference as follows:

(31)

where:

R is the thermal resistance [K/W].

Fouling factors are commonly written in terms of thermal resistances and are simply added in series to the other thermal resistance components in the heat transfer problem. The following equation represents the total thermal resistance for heat transfer between two fluids separated by a tube where fouling exists on the inside and outside surfaces:

(32)

where:

h_i and h_o are the inside and outside surface convection coefficients [W/m².K].

A_i and A_o are the inside and outside surface areas subjected to convection heat transfer [m²].

R_fi and R_fo are the inside and outside surface fouling factors respectively [m².K/W].

D_i and D_o are the inside and outside pipe diameters [m].

k is the pipe material thermal conductivity [W/m.K].

L is the length of the pipe [m].

As mentioned earlier in this document, the user can specify fouling in terms of a resistance, the conductivity of the foulant (fouling material) if it is known and the thickness of the foulant if known. Flownex, however, does not offer the capacity to specify fouling in these terms, and as was discussed in the earlier case study, one way to implement fouling is to model a Flownex pipe element with three layers in the Composite Heat Transfer (CHT) element. The first layer represents the tube outside surface fouling layer, the second layer represents the tube wall material while the third layer represents the tube inside surface fouling layer. To enable this layered model to work, the fouling layer thermal conductivity, thermal capacitance and layer thickness must be specified. Under steady state modeling, the thermal capacitance has no influence, thus the required Flownex inputs may be obtained from rearranging Eq. 32.

With a known fouling factor as specified, together with a known foulant, and thus a known or estimated thermal conductivity for the fouling layer, the fouling layer thickness can be calculated. This can be done by equating the fouling resistance in Eq. 32 to the resistance presented by an equivalent solid cylindrical fouling layer:

(33)

Noting that the diameters in the equation above relate to fouling layer and not the pipe or tube wall in this instance, they may be written in terms of the fouling laying thickness t. Inside and outside fouling thickness may then be written as:

(34)

and similarly:

(35)

where:

t_i is the inside fouling layer thickness.

t_o is the outside fouling layer thickness.

Solving for the fouling thicknesses when the thermal conductivities are known, it can be shown that:

(36)

(37)

Similarly, solving for the foulant thermal conductivities when the fouling layer thicknesses are known, it can be shown that:

(38)

(39)

For typical fouling factors used in industry, please refer to the previous case study on fouling factors.

Calculating the Corrected Log-Mean-Temperature-Difference (LMTD)

The heat transfer achieved by a shell-and-tube or cross-flow heat exchanger is often expressed in terms of the following:

(40)

where:

U_o is the overall heat transfer coefficient, [W/m².K].

A_o is the total tube outside surface area, [m²].

∆𝑇𝑙𝑛 is the log-mean temperature difference [LMTD], [K].

F is the LMTD correction factor to correct for the difference between the actual heat exchanger configuration (cross-flow) to an ideal theoretical counter-flow heat exchanger.

The LMTD for a heat exchanger is calculated as:

(41)

where:

(42)

(43)

T is the shell-side temperature, t is the tube-side temperature, and the subscripts 1 and 2 refer to inlet and outlet conditions respectively.

In determining the correction factor F, the following temperature ratios are commonly used in heat exchanger design:

(44)

(45)

These two parameters are typically used to read the correction factor F  from sets of curves that may be found in most heat transfer textbooks. For the single-pass cross-flow heat exchanger presented in this case study however, the following equations (obtained from the CHE Guide, [11]) may be used to determine the correction factor F :

(46)

Transposing this equation:

(47)

The number of transfer units NTU is used in the well-known effectiveness-NTU calculation method and is related to the factor K above as follows:

(48)

Transposing this equation:

(49)

The correction factor F for a single-pass cross-flow heat exchanger may then be calculated from the following:

(50)

(51)

CASE STUDIES

This section compares the results of three case studies using the Flownex model to equivalent calculations using Aspen EDR. The cases are:

• A single pass air-air recuperator with no fouling.

• The same model as above, but with fouling specified and the bundle divided into two sections.

• A multi-pass multi-fluid recuperator extracting heat from flue gas, heating two tube-side streams; air and CO2.

Case Study 1: A Single Pass Flue-Gas-To-Air Recuperator With No Fouling 

The Flownex model of a single pass flue-gas- to-air recuperator is shown in Figure 8. The Flownex compound component offers four fluid connections, two for the flue gas stream and two for the air stream. In the case presented, the pressures are specified at the outlet boundaries while the temperatures and flow rates are specified at the inlet boundaries. For this case study, the input data is presented in Table 3 below.

Table 3: Case Study 1 Input Data.

The Flownex results of this case are shown in Figure 5 and are compared with results from a calculation using Aspen Exchanger Design & Rating (EDR) V9 and summarized in the following table. Good agreement is shown between the Flownex and Aspen results.

Table 4: Case Study 1 Results and Comparison with Aspen EDR.

Case Study 2: A Single Pass Flue-Gas-To-Air Recuperator Split Into Two Sections and with Fouling  

The model presented in Figure 9 below is essentially the same as presented in Case Study 1 in Figure 8. For this case however, the tube bundle is split into two sections; the first section representing the first four tube rows, and the second section representing the remaining seven tube rows. This allows the maximum tube wall temperatures for the shield tube rows to be calculated more accurately by not averaging them with all the tubes in the bundle. Furthermore, inside and outside fouling factors of 0.0002 m2.K/W have also been applied to this case. 

The Flownex results for this case are shown in Table 5 and are compared with results from Case Study 1.

Table 5: Case Study 2 Results and Comparison with Case Study 1 and Aspen EDR.

• The total heat load for Case Study 2 will be lower than for Case Study 1 due to the fouling added to the tubes. This is also reflected in the slightly lower overall heat transfer coefficient for Case Study 2. It is curious, however, that with the application of the inside and outside fouling factors Aspen EDR did not reflect any significant reduction in heat load. The Flownex model shows an 25 kW heat load reduction.

• The effective LMTD is higher for the shield tubes and lower for the remaining seven rows than was calculated in Case Study 1. For the non-shield tubes, the calculated effective LMTD is in close agreement with the results obtained for Aspen EDR.

• The maximum and average tube temperatures are better differentiated in this case study and results are still in good agreement with Aspen EDR.

   

Case Study 3: A Multi-Pass Multi-Fluid Recuperator

The first two components of the model presented in Figure 10 below is essentially the same as presented in Case Study 2 in Figure 9. The third component represents the inlet pass of a U-bundle (refer to Figure 1) flue-gas-to-air recuperator. The last two components represent a separate U-bundle for a flue-gas-to-CO₂ recuperator.  The model shows the flexibility of the Cross-Flow Bare Tube Recuperator compound component presented in this case study where the compound components may be connected in series on the flue gas side and where multiple tube-side fluids are accommodated logically and straightforwardly. Since the outlet of each bundle serves as the inlet for the next, changes in the design of upstream bundles are automatically reflected in the performance of downstream bundles.

Figure 10 also presents most of the bundle inputs and results on the canvas in a convenient layout. This offers the design engineer a single overview of all significant results side-by-side and enables immediate visual feedback of any design changes. The flexibility of the Flownex model to configure a results layout on the canvas goes beyond the capabilities of most other commercial software such as Aspen EDR.

When modeling of a four-pass recuperator is required, for example, four bundles are simply connected in series for both the shell (flue gas) side as well as the tube side. Furthermore, connections between the tube passes can be accurately modeled, whether return bends or manifold headers or any other configuration. As shown in Figure 10 below, each U-bundle employs return bends for each U-tube. Note that the return bend element used is of the same dimensions as the tubes it connects and is specified as being the same number in parallel as the total tube count of the bundle.

For a similar model in Aspen EDR, two separate projects, each modeling one bundle with its own tube-side fluid, will have to be created. The design process will then become very iterative as any changes in the upstream bundle’s design or operating conditions will result in a different flue gas temperature for the downstream bundle. This temperature must then be manually transferred between the two separate projects.

SUMMARY

Using a relatively straightforward Flownex compound component, a comprehensive flue gas recuperator model could be constructed. It was shown that the results are in close agreement with other commercial software such as Aspen EDR. However, its flexibility goes beyond the capabilities of most commercial software. It was shown that any number of bundles could be connected in virtually any configuration, such as complex combinations of parallel and series, while flowing multiple fluids tube-side. Furthermore, the model could be extended by the user with relative ease to incorporate more capabilities such as finned surfaces or two-phase fluids.

REFERENCES

[1] “Pressure Pipe Wall Thickness and Flange Rating Calculation Using a Script and a Generic 4D Chart”, case study available on the Flownex website at:

https://flownex.com/case-studies/pressure-piping-thickness-and-flange-rating-calculation/

[2] Zukauskas, A (1987), “Heat Transfer from Tubes in Cross Flow.” In Handbook of Single Phase Convective Heat Transfer, Eds. S. Kakac, R.K. Shah, and Win Aung. New York: Wiley Interscience.

[3] “Fouling Factors in Flownex Heat Transfer Models”, case study available on the Flownex website at:

https://flownex.com/case-studies/fouling-factors-in-flownex-heat-transfer-models/

[4] Gaddis E.S. (2010), “Pressure Drop of Tube Bundles in Cross Flow”, VDI Heat Atlas (2010), section L1.4.

[5] Gnielinski, V. (1976), “New Equations for Heat and Mass Transfer in Turbulent Pipe and Channel Flow”, International Chemical Engineering 16, 1976, pp. 359-368.

[6] Cengel, Y.A. (2006), “Heat and Mass Transfer, A Practical Approach”, Third Ed, McGraw Hill, p.419.

[7] Bergelin O.P., Colburn A.P. and Hull H.L. (1950), “Heat transfer and Pressure Drop During Viscous Flow Across Unbaffled Tube Banks.”, University of Delaware, Engineering Experimental Station, Bulletin No. 2, Newark, Delaware.

[8] Gaddis E.S. and Gnielinski V. (1983) Druckverlust in Querdurchstroemten Rohrbuendeln. vt “Verfahrenstechnik” 17(7):410–418.

[9] Sieder E.N. and Tate G.E. (1936) Heat Transfer and Pressure Drop of Liquids in Tubes. Indl Engg Chem 28(12):1429–1435.

[10] Scholz F (1968) Einfluss der Rohrreihenzahl auf den Druckverlust und Waermeuebergang von Rohrbuendeln bei hohen Reynoldszahlen. Chemie-Ing.-Tech. 40(20):988–995.

[11] CHE Guide (Chemical Engineer’s Guide). https://cheguide.com/2016/09/lmtd-correction-factor-charts/