Method for Assessing Performance of Finned Tube Heat Exchanger under Non-uniform Face Velocity

Abstract

A method for assessing and improving the performance of a finned tube heat exchanger under non-uniform face velocity is disclosed. First, a mathematical analysis method of the finned tube heat exchanger under the non-uniform face velocity is established. Second, a heat exchange amount and the heat resistance of the heat exchanger are obtained. Third, a quantitative relation between the non-uniform face velocity distribution and the performance of the finned tube heat exchanger are obtained. Finally, the heat exchange amount and the heat resistance of the heat exchanger are drawn in a rectangular plane coordinate system; and the coordinate system is partitioned in accordance with change rules of the curves, so that a performance assessment diagram of the finned tube heat exchanger under the non-uniform face velocity condition is obtained.

Description

CROSS REFERENCE TO RELATED APPLICATION

This application is based upon and claims priority to Chinese Patent Application No. 201811551614.3, filed on Dec. 19, 2018. The entire disclosure of the above-identified application is incorporated herein by reference.

Some references, which may include patents, patent applications, and various publications, are cited and discussed in the description of the present disclosure. The citation and/or discussion of such references is provided merely to clarify the description of the present disclosure and is not an admission that any such reference is “prior art” to the disclosure described herein. All references cited and discussed in this specification are incorporated herein by reference in their entireties and to the same extent as if each reference was individually incorporated by reference.

TECHNICAL FIELD

The disclosure relates to the technical field of heat transfer optimization of heat exchangers, and particularly relates to a method for assessing and improving the performance of a finned tube heat exchanger under non-uniform face velocity.

BACKGROUND

Heat exchangers, as an important part in industrial production, are widely applied to various fields of production and life. In recent years, along with the development of society and the advancement of technology, production and life's requirements on the effectiveness, urgency and reliability of the heat exchanger are increasing; and novel enhanced heat exchange technologies and heat exchanger optimization design methods are continuously applied to the heat exchanger. Such approaches as fin optimization, channel design and the like, as conventional technical means, are mainly adopted in the development of novel efficient heat exchanger. However, the influence of face velocity distribution non-uniformity on the performance of the heat exchanger in design work is ignored in most researches, resulting in great differences between research results and actual effects of the heat exchanger. At present, due to few researches on face velocity non-uniformity of the finned tube heat exchanger, universal laws have not been made, causing small guiding significance to design work of the heat exchanger.

In practical work of the heat exchanger, air passes through the heat exchanger under the action of a fan, and face velocity is generally non-uniform, which is particularly obvious when the fan is perpendicular to the face side of the heat exchanger. In one aspect, non-uniformity of air side heat flow of the heat exchanger can be caused by the face velocity non-uniformity, and subsequently, the efficiency of fins can be reduced; and in the other aspect, flow rate of a refrigerant in a tube can become mismatched with flow velocity of air outside the tube due to the face velocity non-uniformity, and the overall heat exchange performance of the heat exchanger can greatly drop. At present, some shortcomings still exist in researches on the influence of the face velocity non-uniformity on the performance of the heat exchanger: firstly, instead of qualitative description on the degree of the face velocity non-uniformity, it merely takes influence of non-uniformity distribution in fixed forms on the performance of the heat exchanger into consideration, and regularity researches on influence of the non-uniformity degree on the performance are in lack; secondly, related calculation models are established on the basis of velocity one-dimensional non-uniformity distribution, and description and processing methods of multi-dimensional velocity are not adopted; and thirdly, related researches, which are conducted on the basis of complex modeling computation or experimental researches, are high in workload and cannot effectively assess the influence of non-uniform face velocity distribution on the performance of the heat exchanger. On the background, people urgently hope that the influence of the face velocity on the air side heat exchange performance of the heat exchanger can be proved from the view of theoretical derivation; and a method for assessing the influence of the face velocity non-uniformity on the performance of the finned tube heat exchanger is provided.

Therefore, a heretofore unaddressed need exists in the art to address the deficiencies and inadequacies.

SUMMARY

In order to overcome shortcomings of the prior art, the disclosure aims at providing a method for assessing and improving the performance of a finned tube heat exchanger under non-uniform face velocity; with the application of the method, the influence of an air side velocity distribution mode of the heat exchanger on the performance of the heat exchanger can be intuitively reflected; on the basis of quantitative calculation, a conventional heat exchanger optimization design method is corrected, so as to offer guidance to optimization design of the air side of the heat exchanger in one aspect and to provide reference for the optimization of the refrigerant side of the heat exchanger in the other aspect. Accordingly, the finned tube heat exchanger can be optimized and designed.

In order to achieve the purposes, the technical scheme provided by the embodiments is as follows.

A quantitative relation formula of the heat exchange coefficient loss factor, the heat exchange amount loss factor and the heat resistance increasing rate along with the velocity deviation factor of the finned tube heat exchanger under non-uniform velocity is obtained as the finned tube heat exchanger is equivalent to a multi-flow heat exchanger and based on theoretical derivation. Finally, the relation formula undergoes imaging processing, so that a performance assessment diagram under the non-uniform face velocity of the finned tube heat exchanger is obtained; therefore, the heat exchange performance of the entire heat exchanger under non-uniform velocity can be accurately assessed just depending on the performance of a single fin under various working conditions; and related performance parameters of the heat exchanger under the non-uniform velocity can be obtained by calculating the performance of the heat exchanger under uniform velocity.

In comparison with current research work on the performance of the heat exchanger under non-uniform face velocity, the method provided by the disclosure has the following advantages.

The performance assessment diagram under the non-uniform face velocity of the finned tube heat exchanger can fill a gap of description and processing methods on multi-dimensional velocity non-uniformity distribution and can be applied to researches on heat exchangers with the face velocity being in arbitrary distribution; related parameters of the performance of the heat exchanger under non-uniform face velocity can be obtained in the combination of the performance of the heat exchanger under a face velocity uniform distribution situation under a circumstance that the face velocity distribution is known, without assistance of complex modeling computation or experimental researches; and the performance assessment diagram under the non-uniform face velocity of the finned tube heat exchanger is concise and clear and is convenient to use, and the performance assessment diagram is significant for design and optimization guidance of the heat exchanger.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate one or more embodiments of the present disclosure and, together with the written description, explain the principles of the disclosure. Wherever possible, the same reference numbers are used throughout the drawings to refer to the same or like elements of an embodiment.

FIG. 1 is a schematic diagram of a simplified model of a finned tube heat exchanger, as a research object, of the disclosure;

FIG. 2 is a performance assessment diagram under the non-uniform face velocity of the finned tube heat exchanger of the disclosure;

FIG. 3 is a schematic diagram of velocity distribution forms in application cases of the disclosure;

FIG. 4 is a comparison diagram of the influence of uniform velocity distribution on the performance in application cases of the disclosure;

FIGS. 5(a)-5(e) are schematic diagrams of typical face velocity distribution types in upper triangular distribution, middle triangular distribution; lower triangular distribution; parabolic distribution and exponential distribution, respectively; and

FIG. 6 is a comparison diagram of the influence of various face velocity distribution types on the heat exchange performance of the heat exchanger of the disclosure.

DETAILED DESCRIPTION

The present disclosure will now be described more fully hereinafter with reference to the accompanying drawings, in which exemplary embodiments of the present disclosure are shown. The present disclosure may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure is thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Like reference numerals refer to like elements throughout.

The terms used in this specification generally have their ordinary meanings in the art, within the context of the disclosure, and in the specific context where each term is used. Certain terms that are used to describe the disclosure are discussed below, or elsewhere in the specification, to provide additional guidance to the practitioner regarding the description of the disclosure. For convenience, certain terms may be highlighted, for example using italics and/or quotation marks. The use of highlighting and/or capital letters has no influence on the scope and meaning of a term; the scope and meaning of a term are the same, in the same context, whether it is highlighted and/or in capital letters. It is appreciated that the same thing can be said in more than one way. Consequently, alternative language and synonyms may be used for any one or more of the terms discussed herein, nor is any special significance to be placed upon whether a term is elaborated or discussed herein. Synonyms for certain terms are provided. A recital of one or more synonyms does not exclude the use of other synonyms. The use of examples anywhere in this specification, including examples of any terms discussed herein, is illustrative only and in no way limits the scope and meaning of the disclosure or of any exemplified term. Likewise, the disclosure is not limited to various embodiments given in this specification.

It is understood that when an element is referred to as being “on” another element, it can be directly on the other element or intervening elements may be present therebetween. In contrast, when an element is referred to as being “directly on” another element, there are no intervening elements present. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

It is understood that, although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another element, component, region, layer or section. Thus, a first element, component, region, layer or section discussed below can be termed a second element, component, region, layer or section without departing from the teachings of the present disclosure.

It is understood that when an element is referred to as being “on,” “attached” to, “connected” to, “coupled” with, “contacting,” etc., another element, it can be directly on, attached to, connected to, coupled with or contacting the other element or intervening elements may also be present. In contrast, when an element is referred to as being, for example, “directly on,” “directly attached” to, “directly connected” to, “directly coupled” with or “directly contacting” another element, there are no intervening elements present. It is also appreciated by those of skill in the art that references to a structure or feature that is disposed “adjacent” to another feature may have portions that overlap or underlie the adjacent feature.

The terminology used herein is for the purpose of describing embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It is further understood that the terms “comprises” and/or “comprising,” or “includes” and/or “including” or “has” and/or “having” when used in this specification specify the presence of stated features, regions, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, regions, integers, steps, operations, elements, components, and/or groups thereof.

Furthermore, relative terms, such as “lower” or “bottom” and “upper” or “top,” may be used herein to describe one element's relationship to another element as illustrated in the figures. It is understood that relative terms are intended to encompass different orientations of the device in addition to the orientation shown in the figures. For example, if the device in one of the figures is turned over, elements described as being on the “lower” side of other elements would then be oriented on the “upper” sides of the other elements. The exemplary term “lower” can, therefore, encompass both an orientation of lower and upper, depending on the orientation of the figure. Similarly, if the device in one of the figures is turned over, elements described as “below” or “beneath” other elements would then be oriented “above” the other elements. The exemplary terms “below” or “beneath” can, therefore, encompass both an orientation of above and below.

Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present disclosure belongs. It is further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the present disclosure, and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

As used herein, “around,” “about,” “substantially” or “approximately” shall generally mean within 20 percent, preferably within 10 percent, and more preferably within 5 percent of a given value or range. Numerical quantities given herein are approximate, meaning that the terms “around,” “about,” “substantially” or “approximately” can be inferred if not expressly stated.

As used herein, the terms “comprise” or “comprising,” “include” or “including,” “carry” or “carrying,” “has/have” or “having,” “contain” or “containing,” “involve” or “involving” and the like are to be understood to be open-ended, i.e., to mean including but not limited to.

As used herein, the phrase “at least one of A, B, and C” should be construed to mean a logical (A or B or C), using a non-exclusive logical OR. One or more steps within a method may be executed in different order (or concurrently) without altering the principles of the disclosure.

Embodiments of the disclosure are illustrated in detail hereinafter with reference to accompanying drawings. Specific embodiments described herein are merely intended to explain the disclosure, but not intended to limit the disclosure.

The method for assessing and improving the performance under non-uniform face velocity of the finned tube heat exchanger provided by the disclosure is applied to optimization design of the finned tube heat exchanger under the non-uniform face velocity. Firstly, in order to solve the problem of air side air inlet non-uniformity of the finned tube heat exchanger under actual working conditions and to simplify a physical model, shown as FIG. 1, a mathematical analysis method of the finned tube heat exchanger under the non-uniform face velocity is established. On the basis, the influence on the heat exchange performance of the multi-channel finned tube heat exchanger under a face velocity multi-dimensional non-uniform distribution condition is taken into theoretical analysis, and rules of the influence of an air side velocity deviation factor on an average heat exchange coefficient, a heat exchange amount and the heat resistance of the heat exchanger are obtained; therefore, a quantitative relation between the non-uniform face velocity distribution and the performance of the finned tube heat exchanger is obtained. Finally, in accordance with results of the theoretical analysis, relation curves between the air side velocity deviation factor and the average heat exchange coefficient, the heat exchange amount and the heat resistance of the heat exchanger are drawn in a rectangular plane coordinate system; and the coordinate system is partitioned in accordance with change rules of the curves, so that a performance assessment diagram of the finned tube heat exchanger under the non-uniform face velocity condition is obtained, shown as FIG. 2.

Specifically, the method comprises the following steps:

1) determining a quantitative relation of face velocity non-uniformity to the air side average heat exchange coefficient of the finned tube heat exchanger;

(1) a quantitative relation between face velocity linear distribution and the air side average heat exchange coefficient of the finned tube heat exchanger; a relation between heat exchanger air side Nusselt number Nu and Reynolds number Re can be represented as:

Nu=cRe^m

wherein,

Nu=hD/λ

Re=uD/v

a relation between a heat exchanger coefficient h and a flow velocity u can be represented as:

h(u)=ku^m

a taylor expansion of the relation formula can be represented as:

$h\left(u\right)=h\left(u_0\right)+h^{\prime }\left(u_0\right)\left(u-u_0\right)+\frac{1}{2!}h^{″}\left(u_0\right){\left(u-u_0\right)}^2+\frac{1}{3!}h^{\mathrm{\prime \prime \prime }}\left(u_0\right){\left(u-u_0\right)}^3+\dots +\frac{1}{n!}h^{\left(n\right)}\left(u_0\right)+R_n\left(u\right)$

a basic relation formula of the influence of the non-uniform face velocity on the heat exchange performance is represented as:

h(u_a+Δu)+h(u_a−Δu)−2h(u_a)=h″(u_a)Δu²=m(m−1)ku^m-2Δu²

change in the heat exchange coefficient of the heat exchanger caused by face velocity non-uniformity is represented as:

$\Delta h=h_{\mathrm{uniform}}-h_{\mathrm{nonuniform}}=\frac{t\left(t+1\right)\left(2t+1\right)}{6n}m\left(1-m\right)k\Delta u^2u_a^{m-2}$

a heat exchange coefficient loss factor σ is represented as:

$\sigma =\frac{\Delta h}{h_{\mathrm{uniform}}}=\frac{n^2-1}{6n^2}m\left(-m\right){\omega }^2=\frac{1}{6}m\left(1-m\right){\omega }^2\left({\omega }_j\ne 0\right)$

wherein,

$\Delta u=\left(u_{\max }-u_{\min }\right)/n$ $u_a=\left(u_{\max }+u_{\min }\right)/2$ $\omega =\frac{u_{\max }-u_{\min }}{u_{\max }+u_{\min }}=\frac{\left(u_{\max }-u_{\min }\right)/2}{u_a}$ $n=2t+1$ $\frac{n^2-1}{n^2}\approx 1$

(2) a quantitative relation between arbitrary face velocity distribution and the air side average heat exchange coefficient of the finned tube heat exchanger;

when face velocity is in arbitrary distribution, the entire face side can be divided into a plurality of small blocks; provided that air velocity is in linear change in the plurality of small blocks, an overall heat exchange coefficient loss factor σ is obtained, represented as:

$\sigma =\frac{\Delta h}{h_{\mathrm{uniform}}}=1-\sum _j\frac{A_j}{A_f}\left(1-{\sigma }_j\right){\varepsilon }_{h\text{-}j}$

wherein,

${\sigma }_j==\frac{1}{6}m\left(1-m\right){\omega }_j^2$ ${\varepsilon }_{h\text{-}j}=\frac{h_{\mathrm{uniform}\text{-}j}}{h_{\mathrm{unform}}}={\left(\frac{u_{a\text{-}j}}{u_a}\right)}^m$

2) determining a quantitative relation of the face velocity non-uniformity to the heat exchange amount of the finned tube heat exchanger;

the heat exchange amount of a unit channel can be represented as:

q=h(u)AΔT

wherein, A stands for a heat exchange area in heat exchange channels, and ΔT is a heat exchange temperature difference. The various channels are the same in heat exchange area A. It is regarded that the various units of heat exchange channels are the same in heat exchange temperature difference ΔT when a velocity deviation amount is quite small, namely a velocity deviation factor ω is close to 0; and the heat exchange amount is mainly determined by the heat exchange coefficient h.

(1) a quantitative relation of face velocity linear distribution to the air side heat exchange amount of the finned tube heat exchanger;

when a velocity deviation amount is quite small under a face velocity linear change condition, the heat exchange amount can be represented as:

$Q_{\mathrm{nonuniform}}=A\Delta T\sum _1^tm\left(m-1\right){\mathrm{ki}}^2\Delta u^2u_a^{m\text{-}2}+\left(2t+1\right)h\left(u_a\right)A\Delta T$

under equivalent flow, the heat exchange amount of the overall machine (the heat exchanger) under uniform face velocity can be represented as:

Q_uniform=(2t+1)h(u_a)AΔT

under a face velocity linear distribution condition, a heat exchange amount loss factor η can be represented as:

$\eta =\frac{\Delta Q}{Q_{\mathrm{uniform}}}=\frac{t\left(t+1\right)}{6}m\left(m-1\right)u_a^{-2}\Delta u^2=\frac{n^2-1}{6n^2}m\left(m-1\right){\omega }^2$

the various channels are different in heat exchange temperature difference ΔT when velocity deviation is quite large, namely the velocity deviation factor ω is a relatively large value. The entire face side can be equally divided into nt pieces of cells, and a heat exchange amount loss factor ηj in each cell can be obtained as a velocity deviation factor ωj on the face side of each heat exchange cell is small enough; and furthermore, the heat exchange amount loss factor η of the entire heat exchanger under a face velocity linear distribution circumstance can be obtained in accordance with the relation of the heat exchange amount:

$\begin{array}{c}\eta =\frac{\Delta Q}{Q_{\mathrm{uniform}}}=\frac{\sum _j\Delta Q_j}{n_tQ_{\mathrm{uniform}\text{-}\mathrm{cell}}}\\ =\frac{A_j}{A_f}\sum _j\frac{Q_{\mathrm{uniform}\text{-}\mathrm{cell}}-Q_j}{Q_{\mathrm{uniform}\text{-}\mathrm{cell}}}\\ =\sum _j\frac{A_j}{A_f}\left[1-\left(1-{\eta }_j\right)\frac{Q_{\mathrm{uniform}\text{-}j}}{Q_{\mathrm{uniform}}}\right]\\ =1-\sum _j\frac{A_j}{A_f}\left(1-{\eta }_j\right){\varepsilon }_{Q\text{-}j}\end{array}$

wherein

${\eta }_j==\frac{1}{6}m\left(1-m\right){\omega }_j^2$ ${\varepsilon }_{Q\text{-}j}=\frac{Q_{\mathrm{uniform}\text{-}j}}{Q_{\mathrm{uniform}\text{-}\mathrm{cell}}}={\left(\frac{u_{a\text{-}j}}{u_a}\right)}^m\frac{\Delta T_{\mathrm{uniform}\text{-}j}}{\Delta T_{\mathrm{uniform}\text{-}\mathrm{cell}}}$

(2) a quantitative relation of face velocity arbitrary distribution to the air side heat exchange amount of the finned tube heat exchanger;

as a processing method of the heat exchange coefficient loss factor σ, the heat exchange amount loss factor η under a face velocity arbitrary distribution condition is represented as:

$\eta =\frac{\Delta Q}{Q_{\mathrm{uniform}}}=1-\sum _j\frac{A_j}{A_f}\left(1-{\eta }_j\right){\varepsilon }_{Q\text{-}j}$

3) determining a quantitative relation of the face velocity non-uniformity to the heat resistance of the finned tube heat exchanger; a heat-conduction control equation is represented as:

−∇·q=0

by multiplying temperature T by two sides of the control equation, a relation, which is shown as the follows, can be obtained:

q·∇T·∇·(qT)=0

in combination with a Gaussian divergence law, a relation, which is shown as the follows, can be obtained:

$\underset{V_1}{\int }\left[q·\nabla T-\nabla ·\left(\mathrm{qT}\right)\right]{\mathrm{dV}}_1=\underset{V_1}{\int }q·\nabla {\mathrm{TdV}}_1-\underset{A_1}{\int }\left(\mathrm{qT}\right)·n_1{\mathrm{dA}}_1=0$

entranspy dissipation of heat conduction can be represented as:

$G_{\mathrm{dis}\text{-}\mathrm{cond}}=\underset{V_1}{\int }{\lambda \left(\nabla T\right)}^2{\mathrm{dV}}_1=-\underset{A_1}{\int }\left(\mathrm{qT}\right)·n_1{\mathrm{dA}}_1$

a convective heat control equation can be represented as:

ρc(u·∇T)=−∇·q+ϕ

by multiplying temperature T by two sides of the control equation, a relation, which is shown as the follows, can be obtained:

$\frac{1}{2}\rho c\left[u·\nabla {\left(T\right)}^2\right]=-\nabla ·\left(\mathrm{qT}\right)+q·\nabla T$

by integrating an entire convective region, a relation, which is shown as the follows, can be obtained:

${\int }_{V_2}\frac{1}{2}\rho c\left[u·\nabla {\left(T\right)}^2\right]{\mathrm{dV}}_2=-{\int }_{V_2}\nabla ·\left(\mathrm{qT}\right){\mathrm{dV}}_2+{\int }_{V_2}q·\nabla {\mathrm{TdV}}_2$

in combination with a Gaussian divergence law, entranspy dissipation of a convective part, represented as the following formula, can be obtained:

$G_{\mathrm{dis}\text{-}\mathrm{conv}}={\int }_{V_2}{\lambda \left(\nabla T\right)}^2{\mathrm{dV}}_2=-{\int }_{A_2}\left(\frac{1}{2}\rho {\mathrm{cT}}^2\right)u·n_2{\mathrm{dA}}_2-{\int }_{A_2}\left(\mathrm{qT}\right)·n_2{\mathrm{dA}}_2$

total entranspy dissipation can be represented as:

$G_{\mathrm{dis}}=G_{\mathrm{dis}\text{-}\mathrm{cond}}+G_{\mathrm{dis}\text{-}\mathrm{conv}}=\sum _{i=1}^n\left(\frac{1}{2}c_im_iT_{\mathrm{in}\text{-}1}^2-\frac{1}{2}c_im_iT_{\mathrm{out}\text{-}i}^2\right)$

in accordance with definition of generalized heat resistance, the heat resistance of the multi-flow heat exchanger can be represented as:

$R=G_{\mathrm{dis}}/Q^2=\frac{1}{{\left(1-\eta \right)}^2Q_{\mathrm{uniform}}}\sum _{i=1}^n\frac{A_i}{A_f}\left(1-{\eta }_i\right){\varepsilon }_{Q-1}T_i$

wherein,

T_i=(T_in-i+T_out-i)/2

a non-uniform heat resistance increasing factor ψ is defined as:

$\psi =\frac{R_{\mathrm{nonuniform}}}{R_{\mathrm{uniform}}}=1+\left(\frac{1}{1-\eta }-1\right)\frac{T_{\mathrm{in}}}{T_{\mathrm{uniform}}}.$

Finally, a calculating relation formula, obtained from theoretical derivation, on the influence of the face velocity non-uniformity on the performance of the heat exchanger is reflected in a rectangular plane coordinate system. Based upon results, it is indicated that the influence of the non-uniform face velocity on the performance of the heat exchanger is quite small within a certain velocity deviation range; the heat exchange performance of the heat exchanger, under the influence of the non-uniform face velocity, drops along with increase in velocity deviation; and the heat exchange performance of the heat exchanger drops exponentially when velocity deviation reaches a certain degree. Based on the conclusion, the coordinate system is divided into three regions, so that a performance assessment diagram under the non-uniform face velocity of the finned tube heat exchange is formed; and in accordance with the diagram, the influence of various face velocity distribution on the performance of the heat exchanger can be assessed.

The disclosure will be described based upon two cases as follows.

Case I: the performance of a multi-loop multi-row-tube V-shaped heat exchanger of a 50 kW air source heat pump cold (hot) water set is assessed under a non-uniform face velocity condition.

Based upon numerical simulation, the performance of the multi-loop multi-row-tube V-shaped heat exchanger of the 50 kW air source heat pump cold (hot) water set under non-uniform face velocity is obtained: under such conditions that air side average air velocity is 2 m/s, velocity distribution is in linear distribution (shown as FIG. 3) and velocity deviations are respectively 0.25, 0.5 and 0.75, heat exchange amounts drop by 0.267%, 3.2% and 11.33% in comparison with the uniform face velocity condition.

The disclosure, in assessment of the case, specifically comprises the following implementation steps:

(1) in accordance with a relation formula of Nu number of air side fins as well as structural parameters of the fins, deducing out outlet temperatures of the fins under various face velocities of corresponding working conditions;

(2) in accordance with dimension parameters of the heat exchanger, calculating velocity distribution corresponding to various velocity deviations when average air velocity is 2 m/s;

(3) depending on velocity distribution situation of each group, reasonably blocking the heat exchanger;

(4) in accordance with quantitative calculating relation formula of the air side heat exchange amount loss of the finned tube heat exchanger under face velocity non-uniform distribution, and in combination with the steps (1), (2) and (3), calculating a loss proportion of heat exchange amounts of various velocity deviations;

(5) drawing a diagram in accordance with data obtained in the step (4); and

(6) plotting points in the diagram drawn in the step (5) in accordance with results of numerical simulation computation and conducting comparison.

Based on comparison results, it is indicated that heat exchange amount losses, which are calculated depending on the theory of the disclosure, are respectively 0.29%, 2.89% and 5.25% when velocity deviations are 0.25, 0.5 and 0.75, and in comparison with simulation results of the heat exchanger (taking a heat exchanger of the refrigerant side into consideration), errors are respectively 2.0%, 3.1% and 53.7%. It can be regarded that the assessment method provided by the disclosure is relatively high in reliability since non-uniform velocity distribution holds a dominant position in the influence on the heat exchange of the refrigerant side when the velocity deviations are overlarge. Based upon the case, it is indicated that with the application of the assessment method of the disclosure, the performance calculation of the heat exchanger under the non-uniform face velocity condition can be converted into the performance calculation under the uniform velocity condition; therefore, the precision of calculating actual working conditions of the heat exchanger is enhanced, and a calculating process is simplified.

Case II: in the actual work of the heat exchanger, distribution type of the face velocity depends on relative positions of the fan and the heat exchanger. For example, the face velocity generally appears as parabolic distribution when the fan faces the face side of the heat exchanger; the face velocity generally appears as upper triangular distribution when the action of a base (such as the ground) exists; and the face velocity appears as upper triangular distribution when the fan is arranged at the top. Common air velocity distribution types are shown as FIGS. 5(a), 5(b), 5(c), 5(d) and 5(e), wherein the upper triangular distribution, lower triangular distribution and middle triangular distribution result in different influences on the actual performance of the heat exchanger, which is mainly because the three arrangement modes can result in different influences on the flowing and heat exchange of the refrigerant side under a specific channel arrangement mode. Under a circumstance of not taking the heat exchange of the refrigerant side into consideration, influences of the three velocity distribution types on the air side heat exchange performance are consistent. In several typical face velocity distribution types shown as FIGS. 5(a), 5(b), 5(c), 5(d) and 5(e), exponential distribution velocity achieves the maximum dispersion degree, followed by triangular distribution, and then parabolic distribution velocity, referring to FIG. 6 for calculating results. Based upon the figures, the various face velocity distribution types keep great differences in influence on the heat exchange performance of the heat exchanger under a circumstance that an air volume is a defined value. In comparison with uniform face velocity distribution, parabolic velocity distribution causes the minimum heat exchange performance degradation degree, followed by triangular distribution, and then exponential distribution. Based upon results of theoretical calculation, under prescribed working conditions, heat exchange coefficient non-uniformity losses, which are caused by parabolic velocity distribution, triangular velocity distribution and exponential velocity distribution, are respectively 2.1%, 2.7% and 6.7%, heat exchange amount non-uniformity losses are respectively 5.6%, 7.4% and 13.3%, and heat resistance increasing rates are respectively 5.8%, 7.8% and 15.0%; therefore, it is indicated that the face velocity non-uniformity causes obvious influence on the actual heat exchange performance of the heat exchanger, and various face velocity distribution types keep great difference in influence on the performance of the heat exchanger; in actual performance calculation of the heat exchanger, calculation results are not accurate when the influence of the velocity non-uniformity distribution is not taken into consideration; and ignoring the influence of the heat exchange of the refrigerant side, the influence of the face velocity non-uniformity on the heat exchange performance of the heat exchanger is determined by the dispersion degree of the velocity, and the heat exchange performance loss becomes more obvious as the dispersion degree of the velocity is greater.

The foregoing description of the exemplary embodiments of the present disclosure has been presented only for the purposes of illustration and description and is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Many modifications and variations are possible in light of the above teaching.

The embodiments were chosen and described in order to explain the principles of the disclosure and their practical application so as to activate others skilled in the art to utilize the disclosure and various embodiments and with various modifications as are suited to the particular use contemplated. Alternative embodiments will become apparent to those skilled in the art to which the present disclosure pertains without departing from its spirit and scope. Accordingly, the scope of the present disclosure is defined by the appended claims rather than the foregoing description and the exemplary embodiments described therein.

Claims

1. A method for assessing and improving the performance of a finned tube heat exchanger under non-uniform face velocity, wherein the method comprises: σ = Δ   h h uniform = 1 6  m  ( 1 - m )  ω 2; Δ   h = h uniform - h nonuniform = t  ( t + 1 )  ( 2  t + 1 ) 6  n  m  ( 1 - m )   k   Δ   u 2  u a m - 2; ω = u max - u min u max + u min = ( u max - u min ) / 2 u a, wherein umax, umin and ua respectively stand for the maximum value, the minimum value and an average value of the corresponding air velocity of a researched face side, satisfying relations: Δ   u = ( u max - u min ) / n,  u a = ( u max + u min ) / 2,  n = 2  t + 1   and   n 2 - 1 n 1 ≈ 1; σ = Δ   h h uniform = 1 - ∑ j  A j A f  ( 1 - σ j )  ɛ h - j; ɛ h - j = h uniform  -  j h uniform = ( u a - j u a ) m; η = Δ   Q Q uniform = 1 - ∑ j  A j A f  ( 1 - η j )  ɛ Q - j; η j == 1 6  m  ( 1 - m )  ω j 2, ɛ Q - j = Q uniform  -  j Q uniform  -  cell = ( u a - j u a ) m  Δ   T uniform  -  j Δ   T uniform  -  cell; ψ = R nonuniform R uniform = 1 + ( 1 1 - η - 1 )  T in T uniform;

1) determining a quantitative relation of face velocity non-uniformity to an air side average heat exchange coefficient of the finned tube heat exchanger; (a) a quantitative relation between face velocity linear distribution and the air side average heat exchange coefficient of the finned tube heat exchanger is prescribed within an expression formula:

σ stands for a heat exchange coefficient loss factor, and Δh is change of the heat exchange coefficient of the heat exchanger caused by of face velocity non-uniformity, satisfying a formula:

wherein, huniform form distribution and hnonuniform distribution are heat exchange coefficients of the heat exchanger under uniform air velocity and non-uniform air velocity; m is a coefficient in a relation of Nu: Nu=cRem; n stands for the quantity of heat exchange channels; and k is a constant;

ω is a defined dimensionless parameter velocity deviation factor, satisfying a relation:

(b) a quantitative relation between face velocity arbitrary distribution and the air side average heat exchange coefficient of the finned tube heat exchanger is prescribed within an expression formula:

wherein, σj, ωj and huniform-j respectively stand for a heat exchange coefficient loss factor, a velocity deviation factor and a heat exchange factor corresponding to uniform velocity of the j<th> heat exchange unit (provided that the heat exchange units are in linear distribution);

εh-j is a heat exchange coefficient discrete factor, satisfying a relation:

2) determining a quantitative relation of the face velocity non-uniformity to heat exchange amount of the finned tube heat exchanger, prescribed within an expression formula:

wherein, η is a heat exchange amount loss factor, satisfying a relation:

εQ-j stands for a heat exchange amount deviation factor, satisfying a relation:

Quniform-j and ΔTuniform-j respectively stand for a heat exchange amount and a log mean temperature difference of the j<th> unit under a uniform velocity distribution condition; and Quniform-cell and ΔTuniform-cell respectively stand for a heat exchange amount and a log mean temperature difference corresponding to each cell under uniform velocity after the heat exchanger is equally divided;

3) determining a quantitative relation of the face velocity non-uniformity to the heat resistance of the finned tube heat exchanger, prescribed within an expression formula:

wherein, Ψ stands for an increasing rate of the heat resistance; Runiform and Rnonuniform respectively stand for air side heat resistance of the heat exchanger corresponding to uniform velocity and air side heat resistance of the heat exchanger corresponding to non-uniform velocity; and Tin and Tuniform respectively stand for air side inlet temperature of the heat exchanger and air side inlet/outlet arithmetic mean temperature under an average air velocity condition;

4) calculating relation formulas on the influence of the obtained face velocity non-uniformity on performance, namely the air side average heat exchange coefficient, the heat exchange amount and the heat resistance, of the finned tube heat exchanger, and reflecting the relation formulas in a rectangular plane coordinate system, wherein based upon results, it is indicated that the influence of the non-uniform face velocity on the performance of the heat exchanger is quite small within a certain velocity deviation range; the heat exchange performance of the heat exchanger, under the influence of the non-uniform face velocity, drops along with increase in velocity deviation; and the heat exchange performance of the heat exchanger drops exponentially when velocity deviation reaches a certain degree; and

5) dividing the coordinate system into three regions, namely a performance stable region, a performance degradation region and a performance serious degradation region based upon conclusion obtained in the step 4), so that a performance assessment diagram under the non-uniform face velocity of the finned tube heat exchanger is defined; and assessing influence of various face velocity distribution on the performance of the finned tube heat exchanger on the basis of the diagram.

2. The method for assessing and improving the performance of the finned tube heat exchanger under non-uniform face velocity of claim 1, wherein the rectangular plane coordinate system takes the velocity deviation factor ω as transverse coordinate, and the heat exchange coefficient loss factor σ, the heat exchange loss factor η and the heat resistance increasing rate Ψ as vertical coordinates.

3. The method for assessing and improving the performance of the finned tube heat exchanger under non-uniform face velocity of claim 2, wherein the influence of the face velocity non-uniformity on the performance of the heat exchanger is quite small when the velocity deviation is within 20-30%; the influence of the face velocity non-uniformity on the performance of the heat exchanger becomes obvious along with increase in velocity variation; and the performance of the heat exchanger is presented in exponential attenuation along with further increase in the velocity deviation.

4. The method for assessing and improving the performance of the finned tube heat exchanger under non-uniform face velocity of claim 3, wherein heat exchange performance of the entire heat exchanger under non-uniform velocity can be accurately assessed just depending on the performance of a single fin under various working conditions, so that related performance parameters of the heat exchanger under the non-uniform velocity can be obtained by calculating the performance of the heat exchanger under uniform velocity.

5. The method for assessing and improving the performance of the finned tube heat exchanger under non-uniform face velocity of claim 4, wherein the rationality of face velocity distribution can be inspected, so as to offer certain guiding suggestions for the velocity of the heat exchanger and the arrangement of internal parts, and to provide reference for the optimization of the shape of the heat exchanger.