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外文翻譯
英文原文：
A SCREENING METHOD FOR THE OPTIMAL SELECTION OF PLATE HEAT EXCHANGER CONFIGURATIONS
J.M.Pinto and J.A.W.Gut
Department of Chemical Engineering,University of S?o Paulo, USP
Abstract - An optimization method for determining the best configuration(s) of gasketed plate heat exchangers is presented. The objective is to select the configuration(s) with the minimum heat transfer area that still satisfies constraints on the number of channels, the pressure drop of both fluids, the channel flow velocities and the exchanger thermal effectiveness. The configuration of the exchanger is defined by six parameters, which are as follows: the number of channels, the numbers of passes on each side, the fluid locations, the feed positions and the type of flow in the channels. The resulting configuration optimization problem is formulated as the minimization of the exchanger heat transfer area and a screening procedure is proposed for its solution. In this procedure, subsets of constraints are successively applied to eliminate infeasible and nonoptimal solutions. Examples show that the optimization method is able to successfully determine a set of optimal configurations with a minimum number of exchanger evaluations. Approximately 5 % of the pressure drop and channel velocity calculations and 1 % of the thermal simulations are required for the solution.
Keywords: plate heat exchanger, heat exchanger configuration, optimization, screening method.
INTRODUCTION
The plate heat exchanger (PHE) consists of a pack of gasketed corrugated metal plates, pressed together in a frame. The fluids flow through a series of parallel flow channels and exchange heat through the thin corrugated metal plates. The gasket design and the closed ports of the plates determine the fluid flow arrangement, which can be parallel, in series or one of several possible combinations of the two. The flow distribution, number of plates, type of gaskets and feed locations characterize the exchanger configuration.
CONFIGURATION CHARACTERIZATION
To characterize the PHE configuration, six distinct parameters are used: NC, PI, PII, f , Yh and Yf, which are described as follows:
NC : Number of Channels
PI and PII : Number of Passes on Sides I and II
f : Feed Connection Relative Location
Yh : Hot Fluid Location
Yf : Type of Flow in Channels.
This binary parameter defines the type of flow inside the channels, which can be straight or crossed depending on the gasket type (Fig. 1). The crossed flow avoids the formation of stagnation areas, but the straight flow type is easier to assemble. It is not possible to use both types together. If Yf = 1, then the flow is crossed in all channels. If Yf = 0, the flow is straight in all channels.
The six parameters can represent any regular configuration and an example of configurations for a nine-plate PHE is shown in Fig. (2). For any given number of channels, NC, the five remaining parameters have a finite set of allowable values, which limits the number of possible configurations, as shown in Fig. (3). The disperse pattern is due to the variation in the number of integer factors of NCI and NCII. For the range of number of channels between 2 and 500 there are 284,976 different configurations.
Equivalent Configurations
For a given value of number of channels and a fixed type of flow, the existence of equivalent configurations (that have the same thermal effectiveness and pressure drops) is possible. Identification of equivalent configurations is important to avoid unnecessary exchanger evaluations. The equivalence of two or more configurations occurs due to the property of flow reversibility (Pignotti & Tamborenea, 1988), to the presence of single pass or to geometrical similarity (the configuration can be freely rotated or mirrored).
A methodology to detect equivalent configurations is shown in Tab. (1). For each set of NC, PI, PII and Yf there are groups of values for parameter f that result in equivalent configurations. In the case of even-numbered NC, there may be equivalency between Yh = 0 and Yh = 1 because sides I and II have the same number of channels and therefore can have the same numbers of passes. Consider for instance the exchanger shown in Fig. (2), which is arranged for f = 1 and Yh = 1; according to Tab. (1), changing the sides of the fluids (Yh = 1 ? Yh = 0) will yield a different although equivalent configuration.
CONFIGURATION OPTIMIZATION
The configuration optimization problem is formulated as the minimization of the number of channels, NC, which is equivalent to minimizing the exchanger heat transfer area or its fixed cost (Eq. 1). There are constraints on the number of channels (NC), fluid pressure drops (DPhot, DPcold), channel flow velocities (vhot, vcold) and exchanger effectiveness (E), as shown in Constraints (2a) to (2f). The optimization model is also subject to the PHE model, necessary for calculation of the aforementioned variables (Constraint 3).
subject to
Constraint (2a) on the number of channels is related to the available number of plates and exchanger capacity. The minimum values for fluid pressure drop avoid large variations between the average fluid pressures that can bend the plates. Lower bounds on channel flow velocities avoid the formation of preferential paths or stagnation areas inside the channels.
The thermal and hydraulic modeling of the PHE (Constraint 3) was developed by Gut and Pinto (2001). The rigorous thermal model accounts for the variation in the overall heat transfer coefficient in the exchanger and consists of a system of differential and algebraic nonlinear equations, which can be solved by numerical methods. Assuming the heat transfer coefficient invariable, the rigorous model can be reduced to the so-called simplified thermal model, which consists of a system of linear ordinary differential equations and has an analytical solution. Since there is little difference between the main simulation results achieved by rigorous and simplified thermal models, the latter will be used for the optimization, keeping the former for final verification of the results.
The Screening Method
The proposed optimization procedure is based on the screening method, also employed by Daichendt and Grossmann (1994) for heat exchanger network optimization. In this procedure, constraints are successively used to remove infeasible and nonoptimal solutions of a MINLP problem, thus reducing its size and complexity.
In the optimization of a PHE configuration, the Constraint on the number of channels (2a) defines the initial set, IS, of possible configurations, formed by combinations of the five remaining parameters. An exhaustive enumeration procedure could be used to obtain the optimal configurations within this set; however, this procedure requires a large computational effort due to the large number of thermal simulations needed.
Since it is possible to calculate (DP, v) prior to the thermal simulation using average values for the fluid temperatures, the constraints on pressure drops and channel velocities (Constraints 2b to 2e) can be used to eliminate all infeasible elements in set IS. Therefore, a reduced set of configurations, RS, is generated. It is important to note that to obtain set RS it is not necessary to calculate (DP, v) for all the configurations in IS because of the following:
A1) parameter f has no influence over (DP, v),
A2) (DP, v) is independent for sides I and II. Thus, for a given NC, the calculations are made only once for each allowable number of passes,
A3) for a given NC, DP is proportional to the number of passes; therefore, if DP > DPmax is verified, any configuration with a larger number of passes also results in an infeasible solution,
A4) for an even-numbered NC, sides I and II have the same number of channels and therefore the same allowable numbers of passes. In this case, (DP, v) will have the same value for Yh = 1 and Yh = 0.
Once set RS is obtained, the effectiveness Constraint (2f) is used to select the optimal set of configurations, OS. However, it is not necessary to thermally simulate all elements in RS because of the following:
B1) there are equivalent configurations with the same effectiveness; thus only one needs to be simulated,
B2) if a search is conducted in increasing order of NC, when the optimal set is found, all remaining configurations with higher values of NC can be neglected.
Since the influence of parameter Yf on the convective coefficients and friction factor is usually unknown, this parameter may be fixed prior to optimization, thus reducing the number of possible configurations by 50 %. Moreover, it is not possible to change the type of flow in an existing exchanger.
Based on these principles, a screening algorithm is developed for the solution of the PHE configuration problem. The steps of the screening algorithm are as follows. For this algorithm, Yf must have a given value (Yf = 0 or 1). If there is available data on the influence of Yf on the heat exchange and friction correlations, this algorithm can be used once for each case and the results compared.
1. The required data for plate (corrugation pattern, dimensions, area enlargement factor and thermal conductivity), hot and cold fluids (flow rate, inlet temperature, fouling factor and correlations for friction factor, convective heat transfer coefficients and physical properties) and constraints (lower and upper bounds for Constraints (2a) to (2f)) are read.
2. Initialization: RS = ? , NC(k) = NCmin , k = 1.
3. All allowable numbers of passes for sides I and II (PIi, PIIj) are obtained for NCk.
4. Verification of constraints on pressure drop and channel flow velocities:
4.1 The (DP, v) pair is calculated for the cold fluid located on side I for each one of the numbers of passes PIi (in increasing order). If the constraints of (DP, v) are satisfied, the cold-fluid/sideI-pass pair is selected. If DPmax is exceeded, there is no need to evaluate larger numbers of passes. This procedure is applied to the cold fluid located on side II for all the numbers of passes, PIIj, thereby selecting the cold-fluid/sideII-pass pairs.
4.2 The same procedure as that in step 4.1 is applied to the hot fluid, obtaining the hot-fluid/sideI-pass and hot-fluid/sideII-pass pairs.
5. The selected pairs of cold-fluid/sideI-pass and hot-fluid/sideII-pass are combined to generate all possible configurations with Yh = 0. Each combination results in four configurations since f has four values equivalent to (DP, v). The same procedure is applied to the selected hot-fluid/sideI-pass and cold-fluid/sideII-pass pairs, yielding configurations with Yh = 1. All generated configurations are stored in RS.
6. If NC(k) = NCmax, then proceed to step 7. Otherwise, NC(k+1) = NC(k) + 1, k = k + 1 and return to step 3.
7. Set RS is now complete. It contains all the configurations that satisfy the constraints on pressure drop and channel velocity for both sides. Now the optimal set, OS, must be obtained.
8. The configurations in RS with the minimum value of NC are selected.
9. The equivalent configurations are detected and grouped using the methodology shown in Tab. (1).
10. The simplified thermal model (the overall heat transfer coefficient is constant) is used to simulate one of the configurations in each group, obtaining the corresponding thermal effectiveness.
11. If one or more groups of equivalent configurations satisfy the effectiveness constraint, they are stored in set OS and there is no need to simulate other elements of RS. Otherwise, proceed to the next value of NC in set RS and return to step 9.
12. The rigorous thermal model is used to simulate the nonequivalent elements in OS to verify the effectiveness results. In case of discrepancy (|Esimplified ? Erigorous| / Erigorous ￡ e ), the rigorous model should be used in the previous simulations after step 8. Otherwise, the optimal solution is achieved.
OPTIMIZATION RESULTS
It was verified that the number of channels per pass has a strong effect on the pressure drop, and consequently, about 98 % of the elements in IS are eliminated in the first part of the screening (steps 1 through 8). Compared to an exhaustive enumeration procedure, the screening method demands approximately 5 % of the required evaluations of (DP, v). Further, to obtain set OS only a few elements are thermally simulated (approximately 1 % of the elements in IS or 20 % of the elements in RS).
As an example to show the efficiency of the screening method, consider the selection of a configuration for a process-water (26.0 kg/s, 67 °C) / cooling-water (62.5 kg/s, 22 °C) PHE with 1.4 m chevron plates with crossed channel flow (Yf = 1). The constraint bounds are shown in Constraints (4a) to (4f).
In this problem, IS has 26,240 elements and only 1.8 % of the (DP, v) calculations and 0.06 % of the simulations were necessary for the solution of the problem by the screening method. The comparative performance of the screening and enumeration methods is shown in Fig. (4). The set RS obtained contains 84 configurations, ranging from NC = 43 to NC = 144, with pass arrangements of 1/2, 2/3 and 2/4 for hot fluid/cold fluid. The problem solution consists of two pairs of equivalent configurations, all with 120 channels, two passes for the hot fluid and three passes for the cold fluid, as shown in Tab. (2). The required CPU time in a DEC-Unix workstation for the simulations of the simplified model was under 1 min, and 5 min were necessary to validate the results using the rigorous model (the deviations in E were under 1 %).
CONCLUSIONS
The configuration of a gasketed plate heat exchanger (PHE) was represented by a set of six distinct parameters and a methodology to detect equivalent configurations was presented. The problem of optimizing the PHE configuration was formulated as the minimization of the heat transfer area, subject to constraints on the number of channels, the pressure drop and channel flow velocities for hot and cold fluids and the exchanger thermal effectiveness as well as the PHE simulation model. Since it is not possible to derive a mathematical model of the PHE that is explicitly a function of the configuration parameters, a mixed-integer nonlinear programming (MINLP) approach could not be used. A screening procedure was then proposed to solve the optimization problem. In this procedure, subsets of the constraints were successively used to eliminate infeasible and nonoptimal elements from the set defined by the bounds on the number of channels. An algorithm was developed to perform the screening with minimum computational effort. Examples show that this algorithm can successfully select a group of optimal configurations (rather than a single solution) for a given application using a very reduced number of thermal simulations.
中文翻譯：
板式換熱器構(gòu)型的最佳選擇的篩選方法
J.M.Pinto和J.A.W.Gut
USP圣保羅大學(xué)化學(xué)工程系
摘要：一種確定墊片式板式換熱器的最佳配置的優(yōu)化方法。目標(biāo)是選擇仍然滿足約束條件的信道數(shù)目的最小傳熱面積的配置，兩種流體的壓力降，該通道的流速和換熱器的熱效率。熱交換器的結(jié)構(gòu)由6個(gè)參數(shù)，如下定義的信道數(shù)目，通行證的每一側(cè)的流體的位置，進(jìn)給位置和不同的流中的信道的數(shù)目。生成的配置優(yōu)化問題轉(zhuǎn)化為盡量減少換熱面積，并提出了其解決方案的篩選程序。在此過程中，依次施加約束的子集，以消除不可行的和非最佳的解決方案。實(shí)施例表明，該優(yōu)化方法能夠成功地確定一組最優(yōu)的配置與最小數(shù)量的熱交換器評估。約5％的壓力降和信道的速度計(jì)算和1％的熱模擬所需的解決方案。
關(guān)鍵詞：板式熱交換器，熱交換器的配置，優(yōu)化，篩選方法。
簡介
板式換熱器（PHE）由一包墊圈的金屬波紋板，在一個(gè)框架中壓合在一起。通過一系列的平行流動(dòng)通道進(jìn)行熱交換，通過薄金屬波紋板構(gòu)成的流體。板的墊圈設(shè)計(jì)和關(guān)閉的端口確定的流體流動(dòng)裝置，它可以是平行的，串聯(lián)或幾種可能的組合的兩個(gè)。流板，分布，數(shù)量型墊片和進(jìn)料位置交換配置的特點(diǎn)。
構(gòu)型表征
為了表征的PHE配置，六個(gè)不同的參數(shù)用于NC，PI，PII，F(xiàn)，YH，YF，描述如下：
NC：通道數(shù)
PI和PII：兩側(cè)的傳球數(shù)I和II
F：進(jìn)給連接的相對位置
YH：熱流體地點(diǎn)
YF：通道中的流量類型。
這個(gè)二進(jìn)制參數(shù)定義了不同的內(nèi)部流動(dòng)通道，它可以是直鏈或劃線根據(jù)對墊片的類型（圖1）。交叉流可避免形成的停滯區(qū)，但直路的流類型是更容易組裝。一起使用這兩種類型，這是不可能的。如果Yf的=1，則流程的所有通道中的交叉。如果Yf的=0時(shí)，流程是直鏈的所有通道中。
6個(gè)參數(shù)可以表示任何常規(guī)配置和九板的板式換熱器的配置的一個(gè)例子示于圖。 （2）。對于任何給定的信道數(shù)，NC，五個(gè)其它參數(shù)允許值的有限集合，這限制了可能的配置數(shù)，在圖所示。 （3）。分散模式是由于NCI和NCII數(shù)量的整數(shù)因子的變化。如果在2和500之間的信道數(shù)的范圍內(nèi)，有284976個(gè)不同的組態(tài)。
圖3：通道數(shù)可能出現(xiàn)的常規(guī)組態(tài)的函數(shù)
等效配置
對于一個(gè)給定的信道和一個(gè)固定的不同的流數(shù)的值，等效的構(gòu)型（即具有相同的熱效率和壓力下降）的存在是可能的。相當(dāng)于配置的識(shí)別是很重要的，以避免不必要的熱交換器評價(jià)。兩個(gè)或兩個(gè)以上的配置等價(jià)的發(fā)生是由于流量可逆性的財(cái)產(chǎn)（Pignotti Tamborenea，1988），單通的存在或幾何相似（構(gòu)型可以自由旋轉(zhuǎn)或鏡像）。
一種方法來檢測同等構(gòu)型標(biāo)簽。 （1）。對于每一組的NC，PI，PII和Yf各組的值，結(jié)果在相當(dāng)于構(gòu)型參數(shù)f。在偶數(shù)NC的情況下，有可能是YH= 0和YH=1之間的適合的，因?yàn)镮和II兩側(cè)具有相同的信道數(shù)，因此可以有相同的遍數(shù)?？紤]例如圖中所示的熱交換器。 （2），它被設(shè)置為f= 1，YH= 1;為制表。 （1），改變流體的兩側(cè)（YH= 1（R）YH= 0）將產(chǎn)生不同雖然等效的構(gòu)型。
構(gòu)型優(yōu)化
配制成的信道的數(shù)目，NC，這相當(dāng)于最小化的換熱面積或者其固定費(fèi)用（式1）的最小化的構(gòu)型的最優(yōu)化問題。通道（NC），流體壓力的的下降（DPhot DPcold），通道的流速（vhot，vcold）和換熱效率（E）的數(shù)量上有限制，如圖以約束（2A）（2F）。優(yōu)化模型也受到PHE模型，計(jì)算上述變量（約束3）所必需的。
得到
（2a）中的信道數(shù)目的約束有關(guān)的可利用的數(shù)字板和交換容量。流體壓力降的最低值，避免了大的變化，可以彎曲板之間的平均流體壓力。下界通道的流速避免的優(yōu)先路徑或通道內(nèi)的停滯區(qū)的形成。
篩選方法
建議優(yōu)化程序是基于的篩選方法，Daichendt之外，格羅斯曼（1994）也采用換熱網(wǎng)絡(luò)優(yōu)化。在此過程中，依次使用約束除去不可行的和非最佳的MINLP問題的解決方案，從而降低了它的大小和復(fù)雜性。
在板式換熱器的構(gòu)型的最優(yōu)化，約束的數(shù)量的信道（2a）中定義的初始設(shè)置，IS，可能的構(gòu)型，形成的5個(gè)其它參數(shù)組合。窮舉程序，可以被用來獲得該組合內(nèi)的最佳構(gòu)型，但是，此過程需要一個(gè)大的計(jì)算工作量，由于需要大量的熱模擬。
因?yàn)樗强梢杂?jì)算（DP，v）的前熱模擬使用的流體溫度的平均值，壓力下降，信道速度（2b中的約束到2e）上的約束可以被用來消除所有不可行元素在套IS。因此，一組簡化的構(gòu)型，RS，生成的。重要的是要注意，要獲得設(shè)置的RS（DP，v）的計(jì)算中的所有構(gòu)型為由于下述原因，這是沒有必要的：
A1）參數(shù)f有沒有影響（DP，V），
A2）（DP，v）的獨(dú)立的I和II兩側(cè)。因此，對于一個(gè)給定的NC，是由計(jì)算只有一次，每個(gè)允許的遍數(shù)，
A3）對于一個(gè)給定NC，DP是遍數(shù)成比例，因此，，如果DP> DPMAX驗(yàn)證，也通過與更大數(shù)量的任何構(gòu)型的查詢結(jié)果在一個(gè)不可行的解決方案，
A4）的偶數(shù)NC，側(cè)面I和II具有相同數(shù)量的信道，因此，相同的允許的遍數(shù)。在這種情況下，（DP，v）的YH = 1和YH = 0具有相同的值。
一旦設(shè)置RS獲得的有效性約束（2f）的用于選擇最佳的一組構(gòu)型，操作系統(tǒng)。然而，這是沒有必要的熱模擬RS因?yàn)橄铝幸蛩刂械乃性兀?
B1）是等價(jià)的配置具有相同的有效性，因此只有一個(gè)需要被模擬
B2），如果搜索進(jìn)行數(shù)值越高，數(shù)控?cái)?shù)控遞增的順序，找到最優(yōu)集時(shí)，所有剩余的構(gòu)型可以忽略不計(jì)。
由于參數(shù)Yf的對流系數(shù)和摩擦系數(shù)的影響通常是未知的，是固定的，這個(gè)參數(shù)可能在優(yōu)化之前，從而減少了50％，可能的構(gòu)型。此外，它是不可能改變現(xiàn)有的熱交換器中的流動(dòng)不同的。
基于這些原則，篩選算法開發(fā)的解決方案，的PHE構(gòu)型問題。篩選算法的步驟如下所示。對于此算法，Yf的必須有一個(gè)給定的值（Yf的= 0或1）。 Yf的熱交換和摩擦的相關(guān)性的影響，如果有可用的數(shù)據(jù)，這種算法可以使用一次，每一種情況下的結(jié)果進(jìn)行了比較。
1。所需的數(shù)據(jù)，板（波紋圖案，尺寸，面積的擴(kuò)大系數(shù)和熱導(dǎo)率），熱流體和冷流體（流量，進(jìn)口溫度，污垢系數(shù)和摩擦系數(shù)的相關(guān)性，對流傳熱系數(shù)和物理性質(zhì)），和約束（低級和上界約束（2A）到（2F））被讀取。
2。初始化：RS = AE，NC（K）= NCmin，K = 1。
3。所有允許的遍數(shù)，得到了雙方I和II（PII，PIIj）NCK。
4。驗(yàn)證約束壓降和渠道流速：
4.1（DP，V）對坐落在身邊，我的每一個(gè)傳球的數(shù)字PII（順序遞增）冷流體計(jì)算。如果約束的（DP，v）的得到滿足，cold-fluid/sideI-pass的一對被選中。如果超過DPMAX，不需要計(jì)算大量的通行證。此過程中被施加到位于第二側(cè)的冷流體，可用于所有的數(shù)字通行證，PIIj，從而選擇cold-fluid/sideII-pass對。
4.2相同的步驟，在步驟4.1中被施加到熱流體，，獲得hot-fluid/sideI-pass和hot-fluid/sideII-pass對。
5。對cold-fluid/sideI-pass和hot-fluid/sideII-pass的選擇相結(jié)合，產(chǎn)生YH = 0的所有可能的構(gòu)型。由于f（DP，v）的有四個(gè)值的每一種組合的結(jié)果在四個(gè)構(gòu)型。被施加到所選擇的hot-fluid/sideI-pass和cold-fluid/sideII-pass對相同的程序，得到Y(jié)H = 1的構(gòu)型。所有生成的構(gòu)型存儲(chǔ)在RS。
6。如果NC（K）= NCmax中，然后進(jìn)行第7步。否則，NC（K +1）= NC（K）+ 1，K = K + 1，返回到步驟3。
7。集RS現(xiàn)已完成。它包含的所有組合滿足壓降和通道速度為雙方的約束。載入的最佳設(shè)置，操作系統(tǒng)，必須獲得。
8。構(gòu)型在RS與NC的最小值都被選中。
9。被檢測到的等效構(gòu)型，并使用選項(xiàng)卡中所示的方法進(jìn)行分組。 （1）。
10。的簡化熱模型（總傳熱系數(shù)是恒定的）是用來模擬一個(gè)在各組的配置，獲得相應(yīng)的熱效力。
11。如果一個(gè)或多個(gè)組的等效構(gòu)型滿足有效性約束，它們被存儲(chǔ)在套OS，就沒有必要模擬的RS的其他元素。否則，進(jìn)行NC集RS的下一個(gè)值并返回到第9步。
12。的嚴(yán)格的熱模型是用來模擬在操作系統(tǒng)的非對等元素的有效性驗(yàn)證的結(jié)果。嚴(yán)格的模型差異（| Esimplified?Erigorous | / Erigorous￡E）的情況下，應(yīng)使用第8步后，在以前的模擬。否則，最佳的解決方案來實(shí)現(xiàn)。
優(yōu)化結(jié)果
據(jù)證實(shí)，每道次的信道的數(shù)目上的壓力降，具有很強(qiáng)的影響，因此，約98％的中的元素IS篩選的第一部分（步驟1到8）在消除。的篩選方法相比窮舉程序，要求所需的評價(jià)（DP，v）的約5％。此外，為了獲得一套OS僅有幾個(gè)元素的熱模擬（IS中的元素，或約1％，在RS中的元素的20％）。
作為一個(gè)例子，說明效率的篩選方法，可考慮選擇的構(gòu)型過程（26.0公斤/秒，67℃）水/冷卻水（62.5公斤/秒，22°C）1.4 PHE米字形交叉通道流板（YF = 1）。約束邊界約束為（4a）到（4f）.
在這個(gè)問題中，IS有26240個(gè)元素，為解決這一問題的篩選方法（DP，v）的計(jì)算和0.06％的模擬中只有1.8％是必要的。篩選和計(jì)數(shù)方法的性能比較示于圖中。（4）。集RS得到的包含84個(gè)構(gòu)型，取值范圍從NC= 43，NC= 144，通安排為1/2，2/3和2/4為熱流體/冷流體。問題的解決方案，包括兩對相同構(gòu)型，所有的120個(gè)通道，熱流體和冷流體的三張通行證兩遍，所示的標(biāo)簽。 （2）。一個(gè)DEC-UNIX工作站的簡化模型模擬所需的CPU時(shí)間是下1分鐘，5分鐘是必要的使用嚴(yán)格模式（在E的偏差在1％以下）以驗(yàn)證結(jié)果。
表2：得到最佳構(gòu)型優(yōu)化的例子
結(jié)論
墊片式板式熱交換器（PHE）的構(gòu)型所表示的一組6個(gè)不同的參數(shù)和方法，提出了檢測等同構(gòu)型。優(yōu)化板式換熱器的結(jié)構(gòu)的問題是配制成的傳熱面積的最小化，受約束的信道數(shù)，壓降和熱流體和冷流體的通道的流速和換熱器的熱效力以及板式換熱器的模擬模型。 ，因?yàn)樗遣豢赡塬@得的板式換熱器的數(shù)學(xué)模型是顯式的構(gòu)型參數(shù)的函數(shù)的，混合整數(shù)非線性規(guī)劃（MINLP）的方法不能使用。篩選程序，然后提出解決優(yōu)化問題。在此過程中，依次用約束條件的子集，消除不可行的和非最佳的信道數(shù)的范圍所定義的集合的元素。開發(fā)一種算法以最小的計(jì)算努力進(jìn)行篩選。實(shí)例表明，該算法能夠成功地選擇一組最佳構(gòu)型（而不是一個(gè)單一的解決方案），對于一個(gè)給定的應(yīng)用程序使用數(shù)量的減少熱模擬。
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