Method for calculating Knoosel number of variable-pitch elliptical twisted heat exchange tube

Abstract

The invention relates to the field of heat exchangers, in particular to a variable-pitch elliptical twisted heat exchange tube and a Knoosel number calculation method. In order to improve the heat exchange performance of a tubular heat exchanger, reduce the occupied space of the heat exchanger and improve the defects of the traditional tubular heat exchanger, the invention provides a variable-pitch elliptical twisted heat exchange tube. The pipe is characterized in that on the basis of an elliptical spiral twisted pipe, the pipe is formed by combining segmented step type variable-pitch pipes, so that the flowing of fluid inside and outside the pipe is changed into pure countercurrent, the flowing speed and the flowing direction of the fluid can be changed in a staged manner, and the comprehensive performance is enhanced. Under the condition of the same pump power, more heat can be exchanged, and the purposes of saving energy and saving occupied space are achieved. Meanwhile, a Knoosel number calculation method is provided, the heat exchange coefficient of the twisted tube can be accurately calculated through the method, quantitative analysis of the heat exchange performance of the twisted tube is facilitated, and a theoretical basis is provided for comparison with a traditional heat exchange tube.

Description

Technical Field

[0001] The invention relates to the field of high-efficiency heat exchangers, and in particular to a variable-pitch elliptical twisted heat exchange tube and a Nusselt number calculation method thereof. Background Art

[0002] As low-carbon energy conservation is increasingly valued by people, improving energy utilization has become particularly important. For the manufacturing industry, more efficient, energy-saving and stable industrial equipment is needed. The twisted tube heat exchanger is a kind of high-efficiency heat exchanger with the characteristics of compact structure and high heat exchange efficiency. It has been widely used in chemical, power generation, air conditioning, waste heat recovery and other industrial fields. At present, tubular heat exchangers have many defects due to the limitations of baffles, such as: large pipeline vibration amplitude, flow dead zone, large shell side flow resistance, etc., which leads to large energy loss and low energy utilization in the heat exchanger. Therefore, the problem of developing new high-efficiency heat exchangers needs to be solved urgently. Among them, the overall heat exchange performance of the heat exchanger can be effectively improved by reasonably designing the heat exchange tube structure. Summary of the invention

[0003] In response to the problems of the prior art, the present invention provides a variable pitch elliptically twisted heat exchange tube, the purpose of which is to increase the comprehensive performance of the heat exchanger and improve energy utilization; at the same time, it provides a Nusselt number calculation method, which can accurately calculate the heat transfer coefficient of the heat exchange tube, making it convenient to compare the heat transfer performance with other heat exchange tubes.

[0004] In order to solve the above technical problems, the present invention is implemented through the following technical solutions:

[0005] A novel variable pitch elliptical twisted heat exchange tube comprises a smooth tube section, a transition section and a strong heat exchange tube section. The two ends of the heat exchange tube are smooth tube sections, the strong heat exchange tube section is a small pitch elliptical twisted tube in the middle part, a transition tube section is arranged between the smooth tube section and the strong heat exchange tube section, one end of the heat exchange tube is a cold fluid inlet, and the other end is a cold fluid outlet.

[0006] Preferably, the heat exchange tubes are arranged in a variable pitch, so that the flow of the fluid inside and outside the tubes is more turbulent.

[0007] The heat exchange tubes are made of copper tubes, stainless steel, aluminum alloy, etc. During the specific design, appropriate materials should be selected based on factors such as actual working pressure, ambient temperature, and medium corrosiveness.

[0008] A method for calculating the Nusselt number of a variable pitch elliptical twisted tube is provided, comprising the following steps:

[0009] S1, by volume flow The average fluid velocity u and mass flow rate at the inlet of the variable pitch elliptical twisted tube are calculated with the cross-sectional area A of the heat exchange tube. ;

[0010] S2. Assuming that the wall of the variable pitch elliptical twisted tube is kept at a constant temperature, calculate the logarithmic mean temperature difference of the pure countercurrent of the variable pitch elliptical twisted tube ;

[0011] S3, according to mass flow and log mean temperature difference Get the total heat transfer Q;

[0012] S4. Calculate the total inner surface area of ​​the variable pitch elliptical twisted tube : Divide the inner wall of the heat exchange tube into several parts along the elliptical perimeter of the two end faces, calculate the approximate area of ​​each microelement respectively, add up the accumulation of each surface to get the total area, and derive the calculation formula of this type of irregular area;

[0013] S5. Calculate the heat transfer coefficient h of the fluid in the variable pitch elliptical twisted tube;

[0014] S6. Based on all the above parameters and expressions, the Nusselt number Nu of the heat exchange tube is finally obtained.

[0015] The expression of the average flow velocity u in S1 is:

[0016]

[0017] The a is the length of the semi-major axis of the ellipse in the cross section of the twisted tube, and the b is the length of the semi-minor axis of the ellipse in the cross section of the twisted tube. The mass flow rate of the fluid in the tube is:

[0018]

[0019] Said is the density of the fluid at that temperature.

[0020] The pure countercurrent logarithmic mean temperature difference in S2 is:

[0021]

[0022] Said is the wall temperature of the heat exchange tube, is the cold fluid inlet temperature, is the outlet temperature of the cold fluid.

[0023] The total heat exchange Q in S3 is:

[0024]

[0025] Said is the specific heat of the fluid at constant pressure.

[0026] The total inner surface area of ​​the twisted tube in S4 :

[0027]

[0028] Said is the number of spiral turns of each heat exchange tube, is the length of each section of heat exchange tube, It is the angle of the arc length of the ellipse corresponding to the infinitesimal element of the split area.

[0029] The calculation formula of the fluid heat transfer coefficient h in S5 is:

[0030]

[0031] The calculation formula of Nusselt number Nu in S6 is:

[0032] Nu=\frac {{q}_{v}{c}_{p}ab({t}_{2}-{t}_{1})} {\rho \lambda ({T}_{w}-\frac {{t}_{1}-{t}_{2}} {ln\frac {{T}_{w}-{t}_{2}} {{T}_{2}-{t}_{1}}})\left [ {1.5(a+b)-\sqrt {ab}} \right ]\sum ^{n}_{i=1} {{\alpha}_{i}}\int ^{\frac {\pi} {2}}_{0} {\frac {ab\sqrt {4{\pi}^{2}{a}^{2}{b}^{2}+{P}^{2}_{i}({b}^{2}{cos}^{2}\theta +{a}^{2}{sin}^{2}\theta )}} {{b}^{2}{cos}^{2}\theta +{a}^{2}{sin}^{2}\theta}}d\theta}

[0033] Said is the thermal conductivity of the fluid.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present invention provides a method for calculating the Nusselt number of a variable pitch elliptical twisted tube, by dividing the inner surface of the twisted tube into an infinite number of area micro-elements along the wall, calculating the area of ​​each micro-element separately, and adding up the area accumulations of each micro-element to calculate the total heat exchange area of ​​the inner surface of the twisted tube; calculating the logarithmic mean temperature difference according to the heat exchanger and then using the surface heat transfer coefficient calculation formula to calculate the heat transfer coefficient of the twisted tube fluid, and then obtaining the average Nusselt number of the inner surface of the heat exchange tube, so as to quantitatively reflect the heat transfer performance of the heat exchange tube, and facilitate comparison with other heat exchange tubes. The calculation method of the present invention improves the accuracy of the calculation results, so that a relatively accurate heat transfer amount, fluid heat transfer coefficient and Nusselt number of the heat exchange tube can be obtained, providing a reference and comparison basis for heat transfer performance for subsequent exploration of new twisted heat exchange tubes. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of a three-dimensional model of a variable pitch elliptical twisted heat exchange tube related to the calculation method of the present invention.

[0037] Figure 2 It is a schematic diagram of the parameters of the variable pitch elliptical twisted heat exchange tube related to the calculation method of the present invention.

[0038] Figure 3 It is a schematic diagram of the calculation method flow of the present invention. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] like Figure 1As shown, the heat exchange tube includes a smooth tube section (1), a transition section (2), and a strong heat exchange tube section (3). The smooth tube section (1) and the transition section (2) are distributed in an axisymmetric form, and the tube sections are connected by welding. When the fluid passes through the twisted tube, under the action of the spiral tube, the boundary layer of the fluid is thinned, thereby enhancing the heat exchange effect between the fluid and the tube. The cold fluid in the heat exchange tube and the hot fluid outside the tube perform convective heat exchange in a pure countercurrent manner, thereby enhancing the overall heat exchange effect. Compared with the elliptical spiral twisted tube, the tube body between the smooth tube sections at both ends is arranged in sequence with elliptical cross-section spiral tube sections of different pitches and different lengths. The pitch of the spiral tube will change in a step-like manner, so that the fluid flow field also presents a staged and regular change with the twisted tube space. For the fluid in the tube, since the interior of the heat exchange tube is a three-dimensional variable space, the fluid has a variable flow direction and a variable flow velocity along the length of the tube. The fluid has radial and tangential velocity components, which makes the flow more turbulent and has a stronger destructive force on the boundary layer. From the outside of the tube, the unique geometric characteristics of the variable pitch twisted elliptical tube can make the adjacent tubes support each other at the long axis of the outer ellipse to form a tube bundle, thereby eliminating the baffles and achieving pure counterflow of the fluid outside the tube. A variable pitch spiral channel with a certain regularity is formed along the length of the tube. The fluid changes its flow rate periodically under the action of centrifugal force, which strengthens the turbulence of the fluid, helps to destroy the thermal boundary layer on the tube wall, and realizes enhanced heat transfer on the outside of the tube; in addition, there are no baffles on the shell side, and there is no dead zone. At the same flow rate, the flow resistance of the shell side fluid is reduced and it is not easy to scale.

[0041] like Figure 2 As shown, the semi-major axis length of the heat exchange tube cross-section ellipse is a, and the semi-minor axis length is b. Then the hydraulic diameter of the heat exchange tube is:

[0042] (1)

[0043] Keep the wall of the heat exchange tube at a constant temperature. The cold fluid passes through the heat exchange tube at a certain flow rate. Heat is exchanged between the fluid and the wall. After the temperature and flow rate are stable, the volume flow rate at the entrance of the twisted tube is actually measured to be , then the fluid velocity u at the inlet is:

[0044] (2)

[0045] Mass flow rate of fluid in heat exchange tube :

[0046]

[0047] In the formula, is the fluid density in the heat exchange tube, u is the average flow velocity in the tube, and A is the cross-sectional ellipse area.

[0048] The inlet temperature of the cold fluid in the twisted tube under the steady state is measured by the temperature sensor. , the outlet temperature of the cold fluid in the tube is , the inlet temperature of the hot fluid outside the tube is , the outlet temperature of the hot fluid outside the tube is The relative flow of the fluid inside and outside the heat exchange tube is pure countercurrent, so the temperature difference between the inlet and outlet of the twisted tube is , ,because and The difference between them is greater than 5%, so the logarithmic mean temperature difference is obtained. :

[0049]

[0050] In this example, for the convenience of calculation and analysis, the wall of the twisted tube is set as a constant temperature wall. , substituting into the formula we get:

[0051] (4)

[0052] Total heat transfer capacity of twisted tube Q:

[0053] (5)

[0054] In the formula, is the specific heat of the fluid at constant pressure.

[0055] Now derive the formula for the inner surface area of ​​the twisted tube wall:

[0056] As shown in the figure, the cross section of the variable pitch elliptical spiral twisted tube is an ellipse, the length of the major semi-axis of the ellipse is a, the length of the minor semi-axis is b, the center of the ellipse is point O, and the angle between the line OP from any point P on the ellipse to the center of the circle and the major semi-axis is , the value range is \left [ {0,\frac {\pi} {2}} \right ] , the length of OP is R. The number of spiral turns of each equal pitch spiral tube is , the corresponding helix length is . Then the coordinates of any point on the ellipse are:

[0057]

[0058] Combined with the ellipse equation:

[0059]

[0060] get

[0061]

[0062] Divide the inner wall of the twisted tube into several parts along the perimeter of the end face ellipse, then each infinitesimal element forms a closed figure with OP1, OP2 and the corresponding ellipse perimeter. Very small, OP1 OP2, the microelement figure can be approximated as a microelement sector, then the microelement angle Corresponding microelement arc length :

[0063]

[0064] The micro-angle The length of the corresponding spiral for:

[0065]

[0066] The micro-angle Corresponding microelement area :

[0067]

[0068] Integrate the left and right sides to obtain the inner surface area of ​​each section of the equal pitch tube :

[0069]

[0070] The total area of ​​heat exchange tubes for:

[0071]

[0072] Combining the above formula, the total area of ​​the inner wall of the twisted tube is:

[0073] (6)

[0074] According to Newton's cooling formula, when the fluid is heated, the convection heat transfer coefficient of the fluid in the tube is:

[0075] (7)

[0076] In heat transfer across a fluid surface, the Nusselt number is the ratio of the amount of convective heat to the amount of conductive heat across the boundary. The Nusselt number is calculated as:

[0077]

[0078] In the formula, is the thermal conductivity of the fluid.

[0079] By rearranging equations (1) to (8), we can obtain:

[0080] Nu=\frac {{q}_{v}{c}_{p}ab({t}_{2}-{t}_{1})} {\rho \lambda ({T}_{w}-\frac {{t}_{1}-{t}_{2}} {ln\frac {{T}_{w}-{t}_{2}} {{T}_{w}-{t}_{1}}})\left [ {1.5(a+b)-\sqrt {ab}} \right ]\sum ^{n}_{i=1} {{\alpha}_{i}}\int ^{\frac {\pi} {2}}_{0} {\frac {ab\sqrt {4{\pi}^{2}{a}^{2}{b}^{2}+{P}^{2}_{i}({b}^{2}{cos}^{2}\theta +{a}^{2}{sin}^{2}\theta )}} {{b}^{2}{cos}^{2}\theta +{a}^{2}{sin}^{2}\theta}}d\theta}

[0081] Only the preferred examples of the present invention are described in detail above, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the purpose of the present invention, and various changes should be included in the protection scope of the present invention.

Claims

1. A variable pitch elliptical twisted heat exchange tube, comprising a smooth tube section (1), a transition section (2), and an intensive heat exchange tube section (3), wherein both ends of the heat exchange tube are smooth tube sections (1), the intensive heat exchange tube section (3) is an elliptical twisted tube with a small pitch in the middle, a transition section (2) is provided between the smooth tube section (1) and the intensive heat exchange tube section (3), the smooth tube section (1) and the transition section (2) are arranged axially symmetrically along the intensive heat exchange tube section (3), one end of the heat exchange tube is a cold fluid inlet, and the other end is a cold fluid outlet.

2. A method for calculating the Nusselt number of a variable pitch elliptical twisted heat exchange tube, comprising the following steps: S1, by volume flow The average fluid velocity u and mass flow rate at the inlet of the variable pitch elliptical twisted tube are calculated with the cross-sectional area A of the heat exchange tube. ; S2. Assuming that the wall of the variable pitch elliptical twisted tube is kept at a constant temperature, calculate the logarithmic mean temperature difference of the pure countercurrent of the variable pitch elliptical twisted tube ; S3, according to mass flow and log mean temperature difference Get the total heat transfer Q; S4. Calculate the total inner surface area of ​​the variable pitch elliptical twisted tube : Divide the inner wall of the heat exchange tube into several parts along the elliptical perimeter of the two end faces, calculate the approximate area of ​​each microelement respectively, add up the accumulation of each surface to get the total area, and derive the calculation formula of this type of irregular area; S5. Calculate the heat transfer coefficient h of the fluid in the variable pitch elliptical twisted tube; S6. Based on all the above parameters and expressions, the Nusselt number Nu of the heat exchange tube is finally obtained.

3. The method for calculating the Nusselt number of a variable pitch elliptical twisted heat exchange tube according to claim 2, characterized in that: The expression of the average flow velocity u in S1 is: , a is the semi-major axis length of the ellipse in the cross section of the twisted tube, b is the semi-minor axis length of the ellipse in the cross section of the twisted tube, and the mass flow rate of the fluid in the tube is: , is the density of the fluid at that temperature.

4. The method for calculating the Nusselt number of a variable pitch elliptical twisted heat exchange tube according to claim 2, characterized in that: The pure countercurrent logarithmic mean temperature difference in S2 is: , is the wall temperature of the heat exchange tube, is the outlet temperature of the cold fluid.

5. The method for calculating the Nusselt number of a variable pitch elliptical twisted heat exchange tube according to claim 2, characterized in that: The total heat exchange in S3 is: , is the specific heat of the fluid at constant pressure.

6. The method for calculating the Nusselt number of a variable pitch elliptical twisted heat exchange tube according to claim 2, characterized in that: The total inner surface area of ​​the twisted tube in S4 : , is the number of spiral turns of each heat exchange tube, is the length of each section of heat exchange tube, It is the angle of the arc length of the ellipse corresponding to the infinitesimal element of the split area.

7. The method for calculating the Nusselt number of a variable pitch elliptical twisted heat exchange tube according to claim 2, characterized in that: The calculation formula of the fluid heat transfer coefficient h in S5 is: .

8. The method for calculating the Nusselt number of a variable pitch elliptical twisted heat exchange tube according to claim 2, characterized in that: The calculation formula of the Nusselt number Nu in S6 is: Nu=\frac {{q}_{v}{c}_{p}ab\left ( {{t}_{2}-{t}_{1}} \right )} {\rho \lambda \left ( {{T}_{w}-\frac {{t}_{1}-{t}_{2}} {ln\frac {{T}_{w}-{t}_{2}} {{T}_{w}-{t}_{1}}}} \right )\left [ {1.5\left ( {a+b} \right )-\sqrt {ab}} \right ]\sum ^{n}_{i=1} {{\alpha}_{i}\int ^{\frac {\pi} {2}}_{0} {\frac {ab\sqrt {4{\pi}^{2}{a}^{2}{b}^{2}+{P}^{2}_{i}\left ( {{b}^{2}{cos}^{2}\theta +{a}^{2}{sin}^{2}\theta} \right )}} {{b}^{2}{cos}^{2}\theta +{a}^{2}{sin}^{2}\theta}}d\theta}} , is the thermal conductivity of the fluid.

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