MIDTERM PROJECT: HEAT EXCHANGER DESIGN 3D Computational Modeling Techniques

Brian Tovar

Christopher Phaneuf ME407: Computational Fluid Dynamics

Professor Scott Bondi 14 Apr 2008

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Table of Contents

1 Introduction 2 1.1 Objective 1.2 Underlying Thermodynamics 1.3 Heat Exchangers 2 Design 4 2.1 Assumptions 2.2 Concepts 2.3 Geometry 3 Computational Fluid Dynamics 6 3.1 Preliminary Concept Validation 3.2 Working Fluid -- Air 3.2.1 Preprocessing 3.2.2 Solver Setup 3.3 Working Fluid -- Refrigerant 4 Results 11 5 Discussion 14 Appendix I: Thermodynamics Hand Calculations 15 Appendix II: Heat Transfer Hand Calculations 16 Appendix III: Dimensioned Schematic 17

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1 INTRODUCTION

1.1 Objective

To design and evaluate an evaporator for a refrigeration unit capable of cooling air from 100 ˚F to 50 ˚F while maintaining a flow velocity less than 500 ft/min. The overall capacity shall be one ton (12,000 Btu/hr) and the maximum aspect ratio of the heat exchanger is 2:3. The working fluids shall not incur “excessive” pressure drop. Estimated cost, dry weight, and efficiency also guide the design of this heat exchanger. 1.2 Underlying Thermodynamics

The device to be designed is one of four elements in the basic vapor-compression cycle. The diagram below illustrated the flow of the cycle:

Figure 1 Vapor compression cycle

The evaporator creates a cold reservoir by transferring heat from the air passing through / over it

to the refrigerant. This heat transfer into the refrigerant is called inQ� and is known as the capacity

of the refrigeration unit. Refrigerant temperature through the evaporator is often considered constant to simplify thermodynamic analyses.

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1.3 Heat Exchangers

Several heat exchangers configurations exist, each lending itself to a different application. The most common type for the purposes discussed in this study are crossflow exchangers that feature a coil of copper tubing and an array of fins. Another type is the shell-and-tube heat exchanger, which send flow through a baffled shell containing a number of parallel tubes of refrigerant.

Figure 2 Heat exchangers – Standard crossflow (top) and shell-and-tube (bottom)

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2 DESIGN

2.1 Assumptions

� Refrigerant temperature is constant over length of evaporator

� The convection coefficient for the annular fins is 20 Km

W⋅

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� Outer shell of heat exchanger is insulated from surroundings

2.2 Concept

We decided to model a shell-and-tube heat exchanger. This design is effective for its ability to promote a high level of mixing (and in turn heat transfer) by moving the flow with baffles. The configuration presented here uses counter-flow paired with annular fins, all encased in a compact enclosure. For the sake of meshing, our design consolidates the bank of tubes within the shell into a single, one-inch pipe running axially through the center. The inlet and outlet locations were a topic of debate. One simple but less realistic approach is to run air through the annulus axially. The physical realization of the design would present issues with interference with the refrigerant tube, which would have to obstruct part of the inlet section or run through the center of the fan (…a future consideration for the next phase of this study). Instead, the design is based on flow sent into the shell through perpendicular ducts as the CAD drawings demonstrate.

Figure 3 Illustration demonstrating the simplified design

The entire exchanger is made of aluminum allow with a thermal conductivity 117 Ffthr

Btu°⋅⋅

and an approximate dry weight of 1 kg (2.2 lbs). The exposed surface area is around 275 in2.

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2.3 Geometry

The dimensions of the outer shell are four inches by twelve inches. This does not include a pair of one inch offset rectangular ducts, which are themselves one and a half inches by two inches. These serve as the inlet and outlet for airflow through the heat exchanger, and therefore must be positioned diagonally across the volume. There are three annular fins and two annular rings that obstruct flow and induce proper mixing. They are spaced axially two inches apart from each other and the walls while also being a tenth of an inch thick. The outer diameter of the fins match the inner diameter of the rings, which are both a one and a half inch radius. The pipe carrying refrigerant runs axially parallel to the enclosure for the length of the enclosure. The total mass of the aluminum needed for this heat exchanger is about 2.2 lbs, as determined using Solidworks.

Figure 4 Overall design geometry (modeled in Solidworks)

(see appendix for dimensioned schematic)

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3 COMPUTATIONAL FLUID DYNAMICS

3.1 Preliminary Concept Validation Following a suggestion to perform a simple preliminary simulation to verify the potential for adequate performance, a 2D-axisymmetric analysis was evaluated. A straightforward quad mesh (52875 cells, 106665 faces, 53791 nodes) was generated and run using a k-e turbulence model. The geometry is exactly that a cross-section of the three-dimensional model, except the boundary conditions had to be altered since the device is necessarily a three-dimensional case. This difference should not stray too far from realistic results since only the orientation of the inlet and outlet have changed. As expected, the stream encounters a series of baffles that stirs up the flow, a catalyst for improved heat transfer.

3.2 Working Fluid – Air

3.2.1 Preprocessing The space for airflow through the model was designed in Solidworks and its geometry was exported to STEP format. IGES, when imported into Gambit leaves more residual points that are tedious to clean up; hence STEP was the better option. The mesh was created first using addition and subtraction of automatically generated volumes; such as cylinders and bricks. Then, when the overall geometry was only the space that the air would flow through the heat exchanger, each face was meshed. Some faces had to have different, or rather, finer mesh settings but they all had meshing scheme of quad paved. The volume was successfully meshed using a Hex Core scheme with a T Grid setting. The mesh, though large, was the only reasonable geometry that we were able to volume mesh. It had on upward of a half-million elements: 597,984 cells 1,258,467 edges 121,374 nodes

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Figure 5 4 View Drawing of Mesh in Gambit

Figure 6 Detail of Face Mesh along the Inner Fin and Refrigerant Tube

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3.2.2 Solver Setup

Figures 7 & 8 Viscous Model and Velocity Inlet Settings

Figures 9 & 10 Fin and Refrigerant Pipe Thermal Properties

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3.3 Working Fluid -- Refrigerant In order to confirm reasonable refrigerant flow, a 2D simulation was run for simple pipe flow. The mesh consists of 3,120 cells and features a successive spacing toward the walls. With the material properties of R-134a manually entered into FLUENT, the simulation was run with a k-epsilon Realizable turbulence model. The negligible pressure drop is illustrated in the pressure distribution plot below.

Figure 11 Pressure distribution of R-134a

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Figure 12 Temperature distribution of R-134a

Figure 13 Velocity distribution of R-134a

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4 RESULTS

Outlet temperature: 49.8 °F Pressure drop: 0.0016 psi

Figure 14 Residuals history

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Figure 15 Contour Plot of Temperature along the vertical mid-plane

Figure16 Pressure Drop from Inlet to Outlet

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Figure 17 Streamlines colored by Velocity Magnitude

Figure 18 Contour Plot of Velocity along the vertical mid-plane

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5 DISCUSSION

Taking the unconventional approach of modeling an experimental shell-and-tube heat exchanger yielded surprisingly successful performance. Once the settings for the boundary conditions were tweaked to correspond to realistic flow parameters based on hand calculations and common sense, our heat exchanger was able to meets the requirements. Benefits of our design include flexibility of implementation. The current perpendicular ducting for the inlet and outlet serves as one of many options for the flow orientation. Sending the warm air into the shell axially may require some alteration of geometry but will still likely demonstrate the effectiveness and modularity of the design. One aspect of the design that sets it apart from typical evaporators is the single, straight section of refrigerant pipe. Without the numerous bends observed with most exchangers, the flow encounters fewer sources of head loss and therefore maintains its pressure. The compact size makes for a light and relatively inexpensive device. For a cost estimate based on materials and labor (at $11.00/hour), a one-off version of our design would cost about $520.00. That is obviously not representative of the actual cost of this component for large-scale production but would be an attractive price for an employer looking for an innovative and thoroughly analyzed heat exchanger concept.

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APPENDIX I: Thermodynamics Hand Calculations

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APPENDIX II: Heat Transfer Hand Calculations

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APPENDIX III: Dimensioned Schematic