Tube bundles are standard equipment in heat exchanger design. Typically, when passing the bundle the process flow is subject to several flow re-directions which in consequence, lead to an uneven process side flow profile in parallel tubes. This may be harmless if speed differences are on a low scale. If, however a certain level of maldistribution is exceeded the operator may be confronted with severe consequences.
Orifice design to ensure even flow rates in pre-heater applications are well-known in boiler design. Specific equations to assess maldistribution and to design orifices in different flow arrangements have been developed for that purpose.
Less attention so far, has been paid to the field of air-cooled steam condensers (“ACCs”) although, occasionally some plants encounter problems of steam side maldistribution. This is visible by excessive sub-cooling of border areas (“cold spot” formation) at some condenser bundles caused by premature termination of steam condensation. As a result, the plant performance is badly affected. Moreover, in cold climates these cold spots are a potential risk of frost formation which must be definitely prevented.
Well-known calculation procedures of maldistribution will be summarized in PART ONE of this report by creating a unified theory applicable to all types of flow arrangement (single-phase) based on matrix algebra. It is shown how this method can be successfully applied to geometry variations.
In PART TWO, the procedure is extended to flow maldistribution of condensing steam in a typical ACC street (two-phase). The basics physics are diligently explained. The procedure enables proper design of ducting geometry. Conclusions for safe everyday operation – especially at variation of ambient conditions - are drawn.
Table of Contents
1 Introduction
2 Tube Bundle Model
3 Basic Flow Arrangements
3.1 ‘Z’ Flow
3.2 ‘U’ Flow
3.3 ‘L’ Flow
3.4 ‘T’ Flow
3.5 Arbitrary Flow Arrangements
4 Header Geometry and Orifice Variation
5 Steam Flow Variation in ACC Streets
6 Cold Spot in ACC Primary Condenser
6.1 Condensate Collection Line
6.2 Separate Bottom Header in Primary Condenser
7 Cold Spot in ACC Secondary Condenser
8 Steam Mass Flow Limit
9 Complete ACC Street Model
10 Dephlegmator Heat Duty Shift
Research Objectives & Key Topics
The report aims to provide a unified mathematical framework using matrix algebra to analyze and assess flow maldistribution in heat exchanger tube bundles, with a specific focus on the complex two-phase flow conditions found in air-cooled steam condensers (ACCs).
- Mathematical modeling of planar flow arrangements via matrix algebra.
- Assessment of steam-side flow maldistribution in ACC streets.
- Mechanisms of "cold spot" formation and their prevention in condenser bundles.
- Impact of header geometry and dephlegmator duty fractions on flow stability.
- Strategies for optimizing steam ducting and condensate collection line (CCL) design.
Extract from the Book
1 Introduction
Process side maldistribution is a typical feature of flow in tube bundles used for heat exchange. Maldistribution is not only detrimental to exchanger efficiency but, in some cases - endangers the structural stability of the equipment. Methods to counteract maldistribution effects have been developed over the years and successfully used in exchanger design. Primarily, these methods are used for pre-heater design of boilers where the fluid is single-phase liquid. However so far, a general method to deal with two-phase condensing steam is missing. This will be made up for in the following report.
We start from well-known, proven calculation procedures by developing a unified calculation model applicable to all types of planar flow arrangement. To cope with phase change effects the basic theory is extended by some terms which are not needed in classical single-phase flow. It is shown that all standard flow arrangements can by covered by one set of equations. Furthermore, the procedure is applied to flow maldistribution of condensing steam in a typical air-cooled condenser (“ACC”) street.
Summary of Chapters
1 Introduction: This chapter identifies the issue of flow maldistribution in heat exchanger tube bundles and proposes a new, unified calculation method for two-phase condensing steam.
2 Tube Bundle Model: The chapter establishes the mathematical foundation using matrix algebra to describe flow in idealized tube bundles with phase changes.
3 Basic Flow Arrangements: Different planar flow types ('Z', 'U', 'L', 'T') are analyzed to derive governing equations for boundary mass fluxes.
4 Header Geometry and Orifice Variation: This section extends the model to accommodate non-constant header geometries through stepwise profiles and boundary matrices.
5 Steam Flow Variation in ACC Streets: The procedure is adapted for two-phase flow in ACC streets, incorporating physical properties of steam-liquid mixtures.
6 Cold Spot in ACC Primary Condenser: The model is applied to identify critical conditions for cold spot development in primary condenser modules.
7 Cold Spot in ACC Secondary Condenser: This chapter analyzes flow maldistribution in the dephlegmator (secondary condenser), focusing on reflux flow conditions.
8 Steam Mass Flow Limit: The report defines criteria for minimum mass flow to prevent cold spot formation under varying operational conditions.
9 Complete ACC Street Model: A comprehensive system model is proposed to link adjacent module groups using boundary condition matrices.
10 Dephlegmator Heat Duty Shift: This attachment analyzes the impact of ambient temperature variations on the condensation heat duty distribution.
Keywords
Flow Maldistribution, Single Phase, Two Phase, Air-Cooled Condenser, ACC, Steam Duct Design, Cold Spot, Tube Bundle, Heat Exchanger, Matrix Algebra, Dephlegmator, Condensate, Manifold, Steam Cycle, Thermodynamic Modeling
Frequently Asked Questions
What is the primary scope of this work?
The work focuses on analyzing flow maldistribution in tube bundles, providing a universal mathematical method for both single-phase and two-phase condensing steam applications.
What are the main thematic areas addressed?
Key themes include heat exchanger efficiency, the physical causes of cold spot formation in ACCs, mathematical matrix modeling of flow, and design recommendations for condensers.
What is the research goal?
The primary goal is to close the gap in existing literature by providing a general, unified calculation method for two-phase steam maldistribution, which facilitates safer and more efficient ACC design.
Which scientific method is employed?
The author uses matrix calculus and linear differential equations to define and solve for mass flux distributions within varied flow arrangements.
What is covered in the main body?
The main body details the transition from single-phase to two-phase modeling, evaluates different flow arrangements, and provides practical criteria for avoiding cold spots under various geometric constraints.
Which keywords define this paper?
Essential keywords include Flow Maldistribution, Air-Cooled Condenser (ACC), Cold Spot, Two-Phase Flow, Heat Duty Fraction, and Matrix Algebra.
How does ambient air temperature affect cold spot formation?
The attachment section demonstrates that changes in ambient air temperature shift heat duty between primary and secondary condensers, which can significantly alter the risk of cold spot formation and requires specific design considerations.
Why is the "dephlegmator split" significant in multi-row designs?
Splitting the dephlegmator into multiple fractions reduces steam velocities in the Condensate Collection Line (CCL), which is highly effective in straightening flow profiles and minimizing pressure losses, thereby reducing the risk of maldistribution.
- Arbeit zitieren
- Dipl.-Ing. Hans Georg Schrey (Autor:in), 2018, Flow Maldistribution in Tube Bundles. Application on Air-Cooled Steam Condensers, München, GRIN Verlag, https://www.grin.com/document/432886
