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換熱器的優(yōu)化選型
W. Lub 和 S.A. Tassoub
英國(guó)米德?tīng)柸怂?,布魯?nèi)爾大學(xué)機(jī)械設(shè)計(jì)工程部
【摘要】板式換熱器的優(yōu)化選型是根據(jù)換熱器的用途和工藝過(guò)程中的參數(shù)和NTU=KA/MC=△t/△tm,即傳熱單元數(shù)NTU和溫差比(對(duì)數(shù)平均溫差—換熱的動(dòng)力)選擇板片形狀、板式換熱器的類型和結(jié)構(gòu)。
【關(guān)鍵詞】平均溫差 NTU 板式蒸發(fā)器 冷凝器
1 平均溫差△tm
從公式Q=K△tmA,△tm=1/A∫A(t1-t2)dA中可知,平均溫差△tm是傳熱的驅(qū)動(dòng)力,對(duì)于各種流動(dòng)形式,如能求出平均溫差,即板面兩側(cè)流體間溫差對(duì)面積的平均值,就能出換熱器的傳熱量。平均溫差是一個(gè)較為直觀的概念,也是評(píng)價(jià)板式換熱器性能的一項(xiàng)重要指標(biāo)。
1.1 對(duì)數(shù)平均溫差的計(jì)算
當(dāng)換熱器傳熱量為dQ,溫度上升為dt時(shí),則C=dQ/dt,將C定義為熱容量,它表示單位時(shí)間通過(guò)單位面積交換的熱量,即dQ=K(th-tc)dA=K△tdA,兩種流體產(chǎn)生的溫度變化分別為dth=-dQ/Ch,dtc=-dQ/Cc,d△t=d(th-tc)=dQ(1/Cc-1/Ch),則dA=[1/k(1/Cc-1/Ch)]·(d△t/△t),當(dāng)從A=0積分至A=A0時(shí),A0=[1/k(1/Cc-1/Ch)]·㏑[(tho-tci)/(thi-tco)],由于兩種流體間交換的熱量相等,即Q=Ch(thi-tho)=Cc(tco-tci),經(jīng)簡(jiǎn)化后可知,Q=KA0{[(tho-tci)-(thi-tco)]/㏑[(tho-tci)/(thi-tco)]},若△t1=thi-tco,△t2=tho-tci,則Q=KA0[(△t1-△t2)/㏑(△t1/△t2)]=KA0△tm,式中的△tm=(△t1-△t2)/㏑(△t1/△t2)。
順流 △tm=[(thi-tci)-(tho-tco)] /㏑[(thi-tci)/(tho-tci)]
逆流 △tm=[(thi-tco)-(tho-tci)] /㏑[(thi-tco)/(tho-tci)]
對(duì)于各種流動(dòng)型式,在相同的進(jìn)口、出口溫度條件下,逆流的平均溫差最大。
當(dāng)板式換熱器入口和出口兩流體的溫差△t1和△t2之間的差不大時(shí),可采用算術(shù)平均溫差(△t1+△t2)/2,一般△t1/△t2小于1.5時(shí),可采用,若△t/△t2為3時(shí),則誤差約為10%。
1.2 傳熱單元數(shù)法
在傳熱單元數(shù)法中引入一個(gè)無(wú)量綱參數(shù)NTU,稱為傳熱單元數(shù),它表示板式換熱器的總熱導(dǎo)(即換熱器傳熱熱阻的倒數(shù))與流體熱容量的比值NTU=KA/MC,它表示相對(duì)于流體熱容流量,該換熱器傳熱能力的大小,即換熱器的無(wú)量綱“傳熱能力”。對(duì)于板式換熱器來(lái)說(shuō),KA/MC=△t/△tm,式中△t/△tm稱為溫差比,上式中的右邊的工藝過(guò)程用NTUp表示,左邊的換熱設(shè)備的條件用NTUE表示。NTUp是流體溫度的變化與平均溫差的比值,表示的是用1℃△tm的變化引起幾度流體溫度變化的值,當(dāng)△tm大時(shí),NTUp則小;當(dāng)△tm小時(shí),它有變大的傾向。相反,在NTUp變大的過(guò)程中,△tm的溫度變化較大,NTUp較小時(shí),其△tm的溫度變化較小(見(jiàn)表1)。
表1 △tm,NTUp的關(guān)系
△tm大
△tm小
NTUp小
NTUp大
NTUp大
NTUp小
△tm的溫度變化大
△tm的溫度變化小
板式換熱器的優(yōu)化設(shè)計(jì)計(jì)算,就是在已知溫差比NTUE的條件下,合理地確定其型號(hào)、流程和傳熱面積,使NTUp等于NTUE。
1.3 換熱過(guò)程和NTU
與供熱空調(diào)相關(guān)的換熱過(guò)程如下如示:
?、?用蒸汽加熱水 ⑵ 水—水換熱
a. 蒸汽 133→133℃ c. 一次水 65→60℃
水 5→65℃(生活熱水) 二次水 45←40℃(采暖)
b. 蒸汽 133→133℃ d. 一次水 14→9℃
水 55→65℃(采暖) 二次水 13←7℃(制冷)
e. 一次水 29→24℃
二次水 26←21℃(制冷機(jī)的冷卻)
以上5例工藝過(guò)程的NTUp(見(jiàn)表2)
表2 供熱空調(diào)工藝過(guò)程的NTUp
過(guò)程
△tm
NTUp
a
133→133℃
5→65℃
94.86
(65-5)/94.86=0.632
b
133→133℃
55→65℃
72.88
(65-55)/72.88=0.13
c
65→60℃
45←40℃
20.00
(45-40)/20=0.25
d
14→9℃
13←7℃
1.44
(13-7)/1.44=4.17
e
29→24℃
26←21℃
3.00
(26-21)/3=1.67
1.4 板式換熱器和NTUE
NTUE表示板式換熱器的能力,換熱器的面積是具有一定傳熱長(zhǎng)度的單位傳熱體的組合,總傳熱長(zhǎng)度是單位長(zhǎng)度和流程數(shù)的乘積。當(dāng)NTUE是總數(shù)時(shí),若每1流程數(shù)為NTUe時(shí),則NTUE=n·NTUe(其中n是流程數(shù))。
當(dāng)NTUe=NTUE=NTUp時(shí),換熱器為單程。若NTUe﹤NTUp時(shí),則換熱器應(yīng)為多流程,故設(shè)計(jì)時(shí)應(yīng)先預(yù)定n。由于每種板片單程的NTUe值基本上是定值,如適合表2中e的流量為25m3/h的單程板式換熱器的NTUe為17㎡。從NTUe=A·K/MC可知,當(dāng)NTUe為定值時(shí),A·K成反比,仍以e為例,當(dāng)K=500kcal/㎡·h·℃時(shí),A=1.67×25000/500=83.5㎡,流程數(shù)n=83.5/17≈5。當(dāng)K=2500kcal/㎡·h·℃時(shí),A=16.7㎡,流程數(shù)n=1。每一流程的NTUe如下所示:K=500,NTUe=NTUE/n=0.33,K=2500時(shí),NTUe=1.67。由此可知,根據(jù)NTUe即可求出換熱器的流程數(shù),傳熱系數(shù)和傳熱面積。從以上可知,若板式換熱器設(shè)計(jì)不合理,可能使換熱面積過(guò)大,也可能使板間流速太高,阻力過(guò)大。
1.5 板式換熱器制造技術(shù)的進(jìn)步,板片種類的增加,提高了板式換熱器對(duì)各種工藝過(guò)程的適應(yīng)性。
?、?大NTU(∽8),小△tm(∽1~2)的板式換熱器滿足了區(qū)域供冷和熱泵機(jī)組蒸發(fā)器、冷凝器的要求。從以上分析可知,△tm是換熱的驅(qū)動(dòng)力,若△tm小,即意味著驅(qū)動(dòng)力小,要實(shí)現(xiàn)兩種流體之間的換熱,必須增大傳熱系數(shù),增大傳熱面積,為了使傳熱面積不至過(guò)大,唯一的是增大傳熱系數(shù)K。
① 淺密波紋板片是北京市京海換熱設(shè)備制造有限責(zé)任公司開(kāi)發(fā)的新型板片,它的傳熱系數(shù)約為7000W/㎡·K,是水平平直波紋板的2倍,是人字形波紋板的1.5倍,在區(qū)域供冷中時(shí),檢測(cè)的△tm約為1.2。在作為冰蓄冷的乙二醇和冷凍水的換熱器使用中,△tm約為1.5。
② 板式蒸發(fā)器、板式冷凝器也是北京市京海換熱設(shè)備制造有限責(zé)任公司開(kāi)發(fā)的適應(yīng)于熱泵機(jī)組的新型換熱器。與管殼式蒸發(fā)器、冷凝器相比,它具有如下優(yōu)點(diǎn):?jiǎn)挝惑w積內(nèi)板式蒸發(fā)器、板式冷凝器的傳熱面積約是管殼式換熱器的3倍;板式蒸發(fā)器的傳熱系數(shù)約為1000~1200 W/㎡·K,板式冷凝器的傳熱系數(shù)約為1500~2000 W/㎡·K均為管殼式換熱器的2~3倍;在板式蒸發(fā)器上采用了使制冷劑液體分布均勻的分配器裝置,當(dāng)蒸發(fā)器板片數(shù)較多時(shí),可能會(huì)出現(xiàn)制冷劑液體分配不均的,不能充分利用所有蒸發(fā)傳熱面積,使蒸發(fā)溫度低于設(shè)計(jì)計(jì)算溫度。采用分配器后即能克服上述問(wèn)題。有關(guān)單位檢測(cè)數(shù)據(jù)說(shuō)明,板式蒸發(fā)器、板式冷凝器的傳熱系數(shù)在△tm約為2.5~3℃時(shí),在1500~2000 W/㎡·K之間,且阻力小,滿足了熱泵機(jī)組的要求。
?、?小NTU(∽0.3~2),大△tm(∽40~90℃)的板式換熱器滿足了熱回收工藝和工藝加熱、冷卻的要求。當(dāng)工藝過(guò)程在大△tm的條件下進(jìn)行換熱時(shí),說(shuō)明驅(qū)動(dòng)力大,所需的傳熱面積較小,對(duì)傳熱系數(shù)要求也不高,但,這種工藝過(guò)程或者工作壓力高,或者工作溫度高,或者工藝加熱、冷卻過(guò)程的液體中含有纖維或直徑較大的顆粒,對(duì)板式換熱器的承壓、耐溫能力提出了要求,對(duì)換熱器的板間距提出了要求。
① 排(煙)氣—水板殼式換熱器(省能器),排(煙)氣—空氣板殼式換熱器(空氣預(yù)熱器)是北京市京海換熱設(shè)備制造有限責(zé)任公司和蘭石化共同開(kāi)發(fā)出來(lái)的新型板式換熱器,全焊接板式換熱器中介質(zhì)的換熱是通過(guò)板管束來(lái)實(shí)現(xiàn)的,組成板管束的板片由專用模具壓制成型,全焊接式板束裝在壓力殼內(nèi)。波紋板片具有靜攪拌作用,能在很低的雷諾數(shù)下形成湍流,且污垢系數(shù)低,傳熱系數(shù)是管殼式換熱器的2~3倍。為了適應(yīng)換熱量大,流體壓降小的要求,板間距大,當(dāng)量直徑約為28㎜。為了滿足工藝的要求板束工作壓力(反壓)P≤4.5Mpa,板束工作壓力(正壓)同殼體工作壓力,不受限制;工作溫度t≤550℃。烏魯木齊石化分公司40萬(wàn)噸/年連續(xù)重整采用了進(jìn)料(冷介質(zhì))和出料(熱介質(zhì))的板殼式換熱器,進(jìn)料流量50t/h,進(jìn)、出口溫渡88℃,470℃。出料流量50t/h,進(jìn)、出口溫度100℃,500℃,對(duì)數(shù)平均溫差約38℃,總傳熱系數(shù)約為380kcal/㎡·h·℃,熱負(fù)荷達(dá)23×106kcal/h,進(jìn)料壓降20Kpa,出料壓降50Kpa。
② 多效蒸發(fā)板式加熱器(換熱器),這種換熱器既是工藝加熱裝置,又是重要的熱回收裝置。以前由于板式換熱器的流道?。ò彘g距1.5~5.0㎜),不適宜于氣—?dú)鈸Q熱和蒸氣冷凝;且易堵塞,故不宜用于含懸浮物的流體。為了盡量地發(fā)揮板式換熱器的長(zhǎng)處,克服存在問(wèn)題,適應(yīng)工藝的要求,北京市京海換熱設(shè)備制造有限責(zé)任公司開(kāi)發(fā)出了新型的多效蒸發(fā)板式換熱器,這種板式換熱器屬寬流道型,其板間距為8.0㎜,適合于蒸氣冷凝,適合于含懸浮物的流體,且不易堵塞,最大處理量達(dá)1200m3/h。
New plate heat exchanger optimization Selection
W. Lub and S.A. Tassoub
Department of Mechanical Engineering, School of Engineering and Design, Brunel University, Uxbridge, Middlesex, UK .
Abstract: The plate heat exchanger Selection is based on the optimization of the use of heat exchangers and in the process of the parameters and NTU = KA / MC = △ t / △ tm, that is, transfer units of NTU and the temperature difference than (the average temperature difference -- Heat transfer in power) choose plate shapes, plate heat exchanger and the type of structure.
Key words: the average temperature difference between NTU plate evaporator condenser
1 average temperature difference △ tm
When the heat exchanger to heat-dQ, when the temperature rose to dt, C = dQ / dt, C will be defined as heat capacity, it said units of time through the exchange of heat per unit area, dQ = K (th-tc) dA = K △ tdA, two of the fluid temperature changes were dth =- dQ / Ch, dtc =- dQ / Cc, d △ t = d (th-tc) = dQ (1/Cc-1/Ch), while dA = [1 / k (1/Cc-1/Ch)] ? (d △ t / △ t), when the A = 0 points to A = A0 when, A0 = [1 / k (1/Cc-1 / Ch)] ? ㏑ [(tho-tci) / (thi-tco)], because of two fluid exchange between the heat equivalent, that is, Q = Ch (thi-tho) = Cc (tco-tci), the simplified Know, Q = KA0 ([(tho-tci) - (thi-tco)] / ㏑ [(tho-tci) / (thi-tco)]), if △ t1 = thi-tco, △ t2 = tho-tci , Q = KA0 [(△ t1-△ t2) / ㏑ (△ t1 / △ t2)] = KA0 △ tm, in-△ tm = (△ t1-△ t2) / ㏑ (△ t1 / △ t2) .
Down △ tm = [(thi-tci) - (tho-tco)] / ㏑ [(thi-tci) / (tho-tci)]
Countercurrent △ tm = [(thi-tco) - (tho-tci)] / ㏑ [(thi-tco) / (tho-tci)]
For various flow patterns in the same import, export under the conditions of temperature, the average temperature difference between the largest counter-current.
When the plate heat exchanger import and export of the fluid temperature difference between the two △ t1 and the difference between △ t2 not available when arithmetic average temperature (△ t1 + △ t2) / 2, General △ t1 / △ t2 less than 1.5, May be, if △ t / △ t2 for 3:00, the error is about 10 percent.
1.2 the number of transfer units
In the heat transfer unit of the introduction of a few dimensionless parameters NTU, known as the number of transfer units, it said plate heat exchanger of the total thermal conductivity (heat exchanger heat resistance of the countdown) and the ratio of fluid heat capacity NTU = KA / MC, it said in relation to heat fluid flow, heat transfer capacity of the heat exchanger of the size of the heat exchanger that is, non-dimensional "heat transfer capability." The plate heat exchanger for, KA / MC = △ t / △ tm, where △ t / △ tm known as the temperature difference than, on the right side of the process used NTUp that left the conditions of heat transfer equipment used NTUE said. NTUp is fluid temperature changes in temperature and the average ratio that is used 1 ℃ △ tm of several changes in the value of fluid temperature changes, when △ tm large, NTUp is small when △ tm hours, it has become bigger The tendency. On the contrary, in NTUp larger in the process, △ tm of the larger temperature changes, NTUp smaller, its △ tm small changes in temperature (see table 1).
Table 1 △ tm, NTUp relations
△tm large
△tm small
NTUp small
NTUp large
NTUp large
NTUp small
△tm large changes in temperature
△tm small changes in temperature
Plate heat exchanger, the optimal design, is known NTUE temperature difference than the conditions, to determine a reasonable model, processes and heat transfer area, equivalent to NTUp NTUE.
1.3 heat transfer process and the NTU
Heating and air-conditioning related to the heat transfer process if the show are as follows:
⑴ steam heating water ⑵ water - water heat exchanger
a. steam 133 → 133 ℃ c. a water 65 → 60 ℃
Water 5 → 65 ℃ (hot water) Secondary water 45 ← 40 ℃ (heating)
b. Steam 133 → 133 ℃ d. a water 14 → 9 ℃
Water 55 → 65 ℃ (heating) secondary water 13 ← 7 ℃ (refrigeration)
e. a water 29 → 24 ℃
Secondary water 26 ← 21 ℃ (refrigerator cooling)
More than five cases of the process NTUp (see table 2)
Table 2 heating air-conditioning process of NTUp
process
△tm
NTUp
a
133→133℃
5→65℃
94.86
(65-5)/94.86=0.632
b
133→133℃
55→65℃
72.88
(65-55)/72.88=0.13
c
65→60℃
45←40℃
20.00
(45-40)/20=0.25
d
14→9℃
13←7℃
1.44
(13-7)/1.44=4.17
e
29→24℃
26←21℃
3.00
(26-21)/3=1.67
1.4 plate heat exchanger and NTUE
NTUE plate heat exchanger that the capacity of heat exchanger is the size of a certain length of the heat and the combination of heat transfer units, the total length of heat transfer process is the length and number of units of the product. When the total number of NTUE is, if the number of processes for every 1 NTUe, then NTUE = n ? NTUe (where n is the number of processes).
When NTUe = NTUE = NTUp, the heat exchanger for one-way. If NTUe
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