Method for predicting pressure loss of radiant tube elbow
By combining experimental measurements and flow models, a pressure loss prediction formula was established, which solved the problem of inaccurate pressure loss prediction at bends in radial pipes, and achieved rapid and accurate pressure loss prediction, thereby improving the design efficiency and hydraulic balance of radial pipe networks.
Patent Information
- Application Number
- CN202511386670.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-26
- Publication Date
- 2025-12-23
AI Technical Summary
Existing technologies cannot accurately predict the pressure loss of radial tube bends under low flow rates and transitional flow conditions, leading to improper pump selection, system hydraulic imbalance, and increased energy consumption.
By experimentally measuring the relationship between pressure loss and flow velocity at the bend of the radiant tube, a physical model is constructed, a suitable flow model is selected, a pressure loss prediction formula is established, and pressure loss is predicted using the geometric parameters of the bend and the flow velocity.
It provides a fast and accurate method for predicting pressure loss, improves the efficiency and accuracy of hydraulic design for radial pipe networks, avoids pump selection errors, and ensures system hydraulic balance.
Smart Images
Figure CN121189018A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to a method for predicting pressure loss of a pipe. BACKGROUND
[0002] The pressure loss caused by local components (such as elbows, tees, etc.) in the radiation pipe is a key factor affecting the hydraulic balance of the system. For light radiation systems with small pipe spacing, a large number of elbows, and complex flow structure, the local resistance characteristics at the elbows are particularly significant. At present, the research in the field of heating, ventilation and air conditioning is mostly focused on the thermal performance and comfort of the radiation system, and the research on the hydraulic characteristics, especially the prediction of flow resistance and pressure loss at the elbow, is still insufficient.
[0003] In the prior art, the research on pipe elbow resistance is mostly for industrial pipes such as petroleum and chemical industry or special terrains (such as highland areas), and the empirical formula or numerical model used is often based on high Reynolds number or specific geometric conditions, which is difficult to directly apply to the radiation pipes in the radiation system under low flow rate and transition flow state. In addition, the traditional turbulence model has a large error in predicting such flow, which leads to inaccurate estimation of the local resistance coefficient of the elbow, and easily causes improper selection of water pump, thereby causing problems such as system hydraulic imbalance, increased energy consumption, and decreased refrigeration / heating performance. SUMMARY
[0004] In view of the above technical defects of the prior art, the task of the present application is to provide a method for predicting the pressure loss of a radiation pipe elbow, which solves the problem of large prediction error of the pressure loss under low flow rate and transition flow state by using existing empirical formula or numerical model.
[0005] The technical scheme of the present application is as follows: a method for predicting the pressure loss of a radiation pipe elbow, comprising the following steps:
[0006] Obtain the corresponding values of pressure loss and flow rate of a single radiation pipe elbow, and obtain the pressure loss-velocity experimental curve;
[0007] Construct a physical model of the radiation pipe elbow, calculate the pressure loss of the physical model of the radiation pipe elbow under different flow rates using different flow models, and obtain the pressure loss-velocity calculation curve corresponding to different flow models;
[0008] Compare the error of the pressure loss-velocity experimental curve and the pressure loss-velocity calculation curve, and select a matching flow model from the flow models for subsequent calculation;
[0009] Construct physical models of radiation pipe elbows with different geometric parameters and calculate the pressure loss under different flow rates based on the matching flow model, to obtain the corresponding data of different geometric parameters, flow rates, and elbow pressure loss;
[0010] The pressure loss prediction relationship is established, wherein the pressure loss is a proportional function of the elbow resistance coefficient and the fluid density, the pressure loss is a power function of the flow rate, the elbow resistance coefficient is a power function of the bend ratio R / d of the elbow, the elbow resistance coefficient is a power function of the bend angle θ / 180° of the elbow, R is the bend radius of the elbow, and d is the inner diameter of the elbow;
[0011] The pressure loss prediction relationship is determined based on the corresponding data fitting of the different geometric parameters, the flow rate, and the elbow pressure loss, and the elbow pressure loss of the radiant tube is predicted based on the determined pressure loss prediction relationship.
[0012] Further, when the corresponding values of the pressure loss and the flow rate of a single elbow of the radiant tube are obtained through experiments, an experimental pipeline including a plurality of elbows and straight pipe sections and an experimental pipeline including only straight pipe sections are constructed, respectively, and the pressure loss of each elbow is obtained based on the pressure loss difference of the two experimental pipelines.
[0013] Further, in the experimental pipeline, the number of elbows is not less than 20, and the length of the straight pipe section in a single experimental pipeline is not less than 60 meters.
[0014] Further, when the pressure loss of the elbow physical model of the radiant tube at different flow rates is calculated by using different flow models, the different flow models include RNG k-epsilon, Realizable k-epsilon, Transition SST, detached eddy DES, and large eddy model combined with sub-grid scale model, wherein the sub-grid scale model includes Smagorinsky, WALE, WALES, WALES S-Omega, and Kinetic-Energy Transport.
[0015] Further, when the corresponding relationship between the pressure loss and the flow rate of a single elbow of the radiant tube is obtained through experiments, the flow rate range is 0.25 m / s to 0.6 m / s.
[0016] Further, when the elbow physical models of the radiant tube with different geometric parameters are constructed, the selected range of the elbow geometric parameters is R: 50 mm to 100 mm, d: 7 mm to 16 mm, and θ: 180° to 270°.
[0017] Further, the matching flow model is a large eddy model combined with a Smagorinsky sub-grid scale model.
[0018] Further, the pressure loss prediction relationship is as follows:
[0019] ,
[0020] wherein, is the elbow resistance coefficient, For fluid density, Let n be the flow velocity and n be the flow velocity exponent.
[0021] Furthermore, the relationship between the bend resistance coefficient and the bend ratio and bend angle of the elbow is as follows:
[0022] ,
[0023] Where c is a coefficient, m1 is the bending ratio index, and m2 is the bending angle index.
[0024] Furthermore, n=1.67, c=0.52, m1=0.66, m2=0.92.
[0025] Compared with the prior art, the advantages of the technical solution of the present invention are as follows:
[0026] The predictive formula obtained by this invention is simple in form, and the required parameters are only the geometric parameters and flow velocity of the radiant pipe bend. It can quickly and accurately predict the pressure loss of a single bend without complex iteration or simulation calculations, which greatly improves the efficiency and accuracy of the hydraulic design of radiant pipe networks. It is particularly suitable for the optimization design of small-diameter pipe and multi-bend layout in light radiant systems.
[0027] This invention provides a precise basis for pump selection by accurately predicting the local resistance of elbows, avoiding problems of excessive or insufficient pump power caused by pressure drop estimation errors, thereby effectively ensuring the hydraulic balance of the system. Attached Figure Description
[0028] Figure 1 This is a schematic diagram of the first experimental system constructed for the method of predicting pressure loss in the radiant tube elbow of the present invention.
[0029] Figure 2 A schematic diagram of the physical model of the radiant tube elbow constructed for the prediction method of pressure loss of the radiant tube elbow of the present invention.
[0030] Figure 3 This is an example of the fitting curve between pressure loss and flow velocity in the method for predicting pressure loss in the radiant tube elbow of the present invention.
[0031] Figure 4 This presents representative data and a fitted surface showing the relationship between the resistance coefficient 'a' and geometric parameters in the method for predicting pressure loss in radiant tube elbows according to the present invention. Detailed Implementation
[0032] The present invention will be further described below with reference to embodiments, but these are not intended to limit the scope of the invention.
[0033] The method for predicting pressure loss at a radiant tube elbow according to embodiments of the present invention includes the following steps:
[0034] Step one: Measure the pressure loss of the elbow of the radiant tube.
[0035] Please refer to Figure 1 Fig. 1, the experimental system includes an experimental pipeline 1, a water pump 2, a water tank 3, a differential pressure transmitter 4, an electronic flowmeter 5 and necessary valves. The inlet of the water pump 2 is connected to the water tank 1, the outlet of the water pump 2 is connected to the inlet B of the experimental pipeline 1, the outlet A of the experimental pipeline 1 is provided with the electronic flowmeter 5 and is connected to the water tank 3. The differential pressure transmitter 4 is connected between the inlet B and the outlet A of the experimental pipeline 1 to obtain the pressure loss.
[0036] The experimental system is divided into two groups. In the first group of experimental system, the experimental pipeline includes an adiabatic bottom plate and a radiant tube embedded in the adiabatic bottom plate, the radiant tube contains N elbows and straight pipe sections, where N is not less than 20. The N elbows are connected in sequence by the straight pipe sections, the length of each straight pipe section between the elbows is the same, the length of each straight pipe section is the same, and a straight pipe section is connected to the first and last elbows as the inlet and outlet of the experimental pipeline respectively. In order to reduce the measurement error, the total length of all straight pipe sections is not less than 60 meters. In the second group of experimental system, the experimental pipeline is a simple straight pipe section, and the length of the straight pipe section is the same as the total length of the straight pipe sections in the first group of experimental system.
[0037] The fluid velocities of the two groups of experimental systems are set to obtain the pressure losses, different fluid velocities correspond to different working conditions, and the fluid velocity range is selected to be 0.25 m / s~0.6 m / s, and the working conditions are set at intervals of 0.02 m / s~0.03 m / s. Obtain the pressure loss ΔP1 of the first group of experimental systems and the pressure loss ΔP2 of the second group of experimental systems under each working condition.
[0038] The calculation method of the pressure loss of a single elbow is formula (1),
[0039] (1)
[0040] According to the results of the formula (1), the pressure loss-velocity experimental curve of a single elbow is obtained.
[0041] Step two: Construct a physical model of the elbow of the radiant tube with the same geometric parameters as the experiment.
[0042] In the numerical simulation calculation software, a physical model of the elbow of the radiant tube with the same structural parameters as the elbow in the first group of experimental systems is constructed, and the structured grid division is performed on the physical model of the elbow of the radiant tube, and the y+ of the near-wall region is kept close to 1.
[0043] Step three: Calculate the pressure loss of the elbow within the experimental flow velocity range.
[0044] Based on the constructed physical model of the elbow of the radiant tube, such as Figure 3As shown, the pressure loss at different operating points is calculated by using numerical simulation software, the operating points are selected as the same as the operating points when measuring the pressure loss of the radiant tube elbow, and the pressure loss-velocity calculation curve of the single elbow is obtained. When calculating the pressure loss at different operating points, a plurality of different flow models are selected for calculation, including RNG k-epsilon, Realizable k-epsilon, Transition SST, detached eddy (DES), large eddy model (LES) combined with sub-grid scale model, wherein the sub-grid scale model includes Smagorinsky, WALE, WALES, WALES S-Omega and Kinetic-Energy Transport. The pressure loss-velocity calculation curves corresponding to different flow models are obtained.
[0045] Step four: selecting a flow model according to the pressure loss-velocity experimental curve and the pressure loss-velocity calculation curve corresponding to different flow models.
[0046] According to the error between the pressure loss-velocity calculation curve corresponding to different flow models and the pressure loss-velocity experimental curve, the flow model corresponding to the pressure loss-velocity calculation curve with the minimum error is determined as the flow model used in subsequent calculation. In this embodiment, the determined flow model is large eddy model (LES) combined with Smagorinsky sub-grid scale model, and the error range is ±10%.
[0047] Step five: calculating the pressure loss of the elbow with different geometric parameters and flow rates.
[0048] The physical model of the radiant tube elbow is constructed according to different geometric parameters of the elbow, including the bending radius R, the inner diameter d and the bending angle θ, and the range of the bending radius R, the inner diameter d and the bending angle θ covers the elbow size of commonly used radiant modules, specifically: the range of the bending radius R is 50mm-100mm, the range of the inner diameter d is 7mm-16mm, and the range of the bending angle θ is 180°-270°. The flow model used in calculation is the model determined in step four, i.e. large eddy model-sub-grid scale model, and then the corresponding data of different geometric parameters, flow rates and elbow pressure loss are obtained.
[0049] Step six: constructing a pressure loss prediction relationship, the pressure loss is a proportional function of the elbow resistance coefficient and the fluid density, and the pressure loss is a power function of the flow rate, and in this embodiment, the prediction relationship is specifically:
[0050] (2)
[0051] In formula (2), is the pressure loss of the inlet and outlet of the elbow, the unit is Pa, ρ is the fluid density, unit kg / m 3 where ρ is the fluid density, unit kg / m
[0052] Step seven: based on the calculation results of step five, the pressure loss and velocity curve of different geometric structure elbow is drawn, the velocity exponent n and resistance coefficient a corresponding to the geometric parameters are obtained, Figure 3 is the fitting curve of R=75mm, d=9mm, θ=180° as an example, the calculation results of other geometric parameter combinations are similar to Figure 3 In this embodiment, the velocity exponent n is determined to be irrelevant to the geometric parameters, n is a constant 1.67, and the resistance coefficient a is related to the geometric parameters.
[0053] Step eight: based on the calculation results of step seven, the curve of resistance coefficient and geometric parameters is drawn, and the relationship between the resistance coefficient a and the geometric parameters is fitted, as shown in Figure 4 , wherein the resistance coefficient a is a power function of the bend ratio R / d of the elbow, and the resistance coefficient a is also a power function of the bend angle θ / 180°. The final resistance loss coefficient a and the prediction relationship of R / d and θ are formula (3):
[0054] (3)
[0055] For variable temperature flow, the resistance loss coefficient is affected by the physical property parameters, so a correction coefficient about the physical property parameters is added to formula (3).
[0056] Finally, according to the flow velocity and the geometric parameters of the radiant tube elbow, the pressure loss of the radiant tube elbow is predicted through the finally determined pressure loss prediction relationship.
[0057] The pressure loss prediction relationship obtained by the present application has a high determination coefficient R² of 0.9998, an average absolute error of only 0.22%, and a maximum error of not more than 0.64%, which is significantly better than the existing empirical formula or theoretical estimation method, and has extremely high precision in predicting the pressure loss of the radiant tube elbow. Therefore, by using the above-mentioned prediction method of the pressure loss of the radiant tube elbow, the geometric parameters (R, d and θ) of the radiant tube elbow and the fluid density are input, the flow resistance of the elbow can be quickly evaluated, the direct mapping from geometric data to resistance value is realized, and the prediction accuracy and efficiency are improved.
Claims
1. A method for predicting pressure loss in a radiant tube elbow, characterized in that, Includes the following steps: The experiment yielded the corresponding values of pressure loss and flow velocity at a single radiant tube bend, resulting in a pressure loss-velocity experimental curve. A physical model of the radiant tube elbow was constructed, and the pressure loss of the physical model of the radiant tube elbow at different flow velocities was calculated using different flow models to obtain the pressure loss-velocity calculation curves corresponding to different flow models. Compare the errors between the experimental pressure loss-velocity curve and the calculated pressure loss-velocity curve, and select the matching flow model from the flow models for subsequent calculations; Physical models of radial tube elbows with different geometric parameters were constructed, and pressure loss at different flow velocities was calculated based on the matched flow model to obtain corresponding data on pressure loss of elbows with different geometric parameters and flow velocities. Establish a pressure loss prediction formula, where pressure loss is a direct proportional function of the bend resistance coefficient and fluid density, pressure loss is a power function of flow velocity, bend resistance coefficient is a power function of the bend ratio R / d, bend resistance coefficient is a power function of the bend angle θ / 180°, R is the bend radius of the bend, and d is the inner diameter of the bend. The pressure loss prediction formula is determined by fitting the corresponding data of different geometric parameters, flow velocities and elbow pressure losses, and the pressure loss of the radiant tube elbow is predicted by the determined pressure loss prediction formula.
2. The method for predicting pressure loss at a radiant tube elbow according to claim 1, characterized in that, When the corresponding values of pressure loss and flow velocity of a single radiant tube bend were obtained in the experiment, experimental pipelines including several bends and straight pipe sections and experimental pipelines containing only straight pipe sections were constructed respectively. The pressure loss of each bend was obtained based on the pressure loss difference between the two experimental pipelines.
3. The method for predicting pressure loss at a radiant tube elbow according to claim 2, characterized in that, The number of elbows in the experimental pipeline shall not be less than 20, and the length of the straight pipe section in a single experimental pipeline shall not be less than 60 meters.
4. The method for predicting pressure loss at a radiant tube elbow according to claim 1, characterized in that, When calculating the pressure loss of the physical model of the radiant tube elbow at different flow velocities using different flow models, the different flow models include RNG k-epsilon, Realizable k-epsilon, Transition SST, Separated Eddy (DES), and large eddy model combined with subgrid-scale models, among which the subgrid-scale models include Smagorinsky, WALE, WALES, WALES S-Omega, and Kinetic-Energy Transport.
5. The method for predicting pressure loss at a radiant tube elbow according to claim 1, characterized in that, The experiment to obtain the relationship between pressure loss and flow velocity of a single radiant tube bend was conducted within the flow velocity range of 0.25 m / s to 0.6 m / s.
6. The method for predicting pressure loss at a radiant tube elbow according to claim 1, characterized in that, When constructing physical models of radiant tube elbows with different geometric parameters, the selected elbow geometric parameters range as follows: R: 50mm~100mm, d: 7mm~16mm, θ: 180°~270°.
7. The method for predicting pressure loss at a radiant tube elbow according to claim 1, characterized in that, The matched flow model is a combination of the large eddy model and the Smagorinsky subgrid-scale model.
8. The method for predicting pressure loss at a radiant tube elbow according to claim 1, characterized in that, The formula for predicting pressure loss is: ， in, This is the bend resistance coefficient. For fluid density, Let n be the flow velocity and n be the flow velocity exponent.
9. The method for predicting pressure loss at a radiant tube elbow according to claim 8, characterized in that, The relationship between the bend resistance coefficient and the bend ratio and bend angle of the bend is as follows: ， Where c is a coefficient, m1 is the bending ratio index, and m2 is the bending angle index.
10. The method for predicting pressure loss at a radiant tube elbow according to claim 9, characterized in that, n=1.67, c=0.52, m1=0.66, m2=0.92.