COMPUTER AIDED DESIGN AND CASE STUDY OF CRYOGENIC STORAGE VESSEL

Transcription

1 Proceedings of the National Conference on COMPUTER AIDED DESIGN AND CASE STUDY OF CRYOGENIC STORAGE VESSEL Sachin D. Daxini 1 and Jagdish S. Talpada 2 1 Department of Mechanical Engg., A. D. Patel Institute of Tech., New V.V.Nagar , Gujarat, India. 2 Department of Mechanical Engg., A. D. Patel Institute of Tech., New V.V.Nagar , Gujarat, India. 1,2 Phone: , , Fax: , 1 sachin_daxini@rediffmail.com Abstract The paper presents the details of different design parameters of cryogenic storage vessels such as cryogenic liquid to be stored, temperature, pressure, shape and size of vessel, volume of liquid to be stored etc. It reports especially the parameters and their effects on design aspects with a successful computer program to make it more users friendly, precise, quick and faultless. While designing the cryogenic storage vessel the other important factor is material selection, which also includes insulating material its thickness its desirable properties at specified cryogenic temperatures with consideration for mechanical properties at such a lower temperature range and heat leak in a practical case study is taken and solved with a developed computer program. The cryogenic storage vessel taken here is cylindrical vessel for liquid nitrogen, Selected vessel material is stainless steel, and Volume to be stored is 25 liters, type of weld joint selected is butt joints with complete penetration etc. It has been observed that the design and the co-related program have been found successful in operation and the results obtained are quite satisfactory. This program can be universal tool for commercial design and testing of cryo vessels. KeyWords: Cryocontainer, Computerized Design 1.0 Introduction Cryogenic Vessels have been commonly used for more than 40 years for the storage and transportation of industrial and medical gases. Cryogenic containers come under the category of Pressure vessel. 1 A pressure vessel is a closed container of limited length, the wall of which are subjected to net differential pressure i.e. internal pressure, external pressure or both. The utility of a pressure vessel is to contain the storage media under specified pressure or temperature or both. Thus, cryogenic storage vessels are pressure vessels store liquefied gases whose temperature can be as low as 4K. 5 In modern day technology cryogenic liquid storage container has progressed rapidly as a result of growing use of cryogenic fluids in many areas, and so as to handle cryogenic fluids Cryocans are used Design Considerations Cryogenic containers are manufactured in various shapes, sizes and that hold different cryogenic liquids. Two basic configurations for cryocans are: 1. Cylindrical 2. Spherical One of the most economical configurations is the cylindrical container with, dished, elliptical and hemispherical heads, while spherical vessels are most efficient so far as heat leakage is concerned. Here, we will restrict ourselves to only cylindrical shape vessels. All cryogenic storage vessels consist of a uniformly thick inner vessel concentrically enveloped by a uniform thick outer vessel. The inner vessel holds the cryogenic liquid to be stored but not to its full capacity. A small percent of volume usually, around 8 to 10%, is left in the inner vessel above the liquid to be stored to allow for the liquid to evaporate due to heat inleak so that excess pressure is not built up. This space is called ullage space. The space between inner and outer vessel is provided with vacuum to provide means of insulation. 2.1 Selection of material for vessel 2,4 In the usual applications for storage, the outer vessel is usually at the temperature and pressure of the surroundings, while the inner vessel must withstand the design internal pressure and temperature, the weight of the fluid within the vessel, the bending stresses as a result of bending action. Thus, materials for the fabrication of cryogenic storage vessel should withstand external as well as thermal loads and stresses, which are usually dynamic in nature. Materials and properties of materials are taken from standard tables available in journals. Since all the cryogenic 1

2 fluids are in the gaseous state at room temperature, they have to be liquefied to cryogenic temperature below their boiling point first and purified to desired level and then they will be ready for storage and transfer. The challenge of design for cryogenic container is to use such materials that do not loose their desirable properties at such low temperatures but still should not contribute to the heat inleak from outside into the liquid in the inner vessel. Many materials exposed to low temperature lose their toughness and ductility. Thus, one of the most desirable property for the material of vessel is low temperature toughness. As temperature goes down material tends to become brittle and it may cause brittle fracture. Another possible cause of the vessel failure is fatigue. This is caused by cyclic conditions of temperature or mechanical load. Repeated refilling of vessels with cryogen can build in unanticipated stresses, strains and excessive thermal gradients leading to failure. This mode of failure is very severe especially when the material shows a transition from ductile to brittle properties under the working conditions. This is because the failure can be very sudden and almost undetectable since crack initiation and propagation occurs very fast. Possible recommendations can be carbon steels for outer vessel material, while for low weight applications use aluminum grades. Possible benefits and drawbacks must be analyzed for different application for different materials. Without going into much detail regarding configurations of vessels we will focus our attention to design aspect of vessels. 2.2 Computer aided design Design problems have no unique answers; a good answer today is poor answer tomorrow. As such design is highly iterative process and thus time consuming and considerable effort is required. The use of a computer can greatly reduce this effort and time, provided it use can be extended for future modifications and extensions with case. Design of cryogenic vessel is not an exception in this. Design parameters and governing equations: a) Design pressure: design pressure is the pressure used to determine the minimum required thickness of each vessel shell component. It includes a suitable margin above the operating pressure. b) Required thickness of vessel: it is the minimum vessel thickness as computed from code formula, it will not include corrosion allowance. While design thickness is including corrosion allowance. c) Nominal stress on vessel: the nominal stress in any part of the vessel is computed from the code and standard engineering formulas. d) Design temperature: for most standard vessels the design temperature is the maximum temperature of the operating fluid plus 10 deg. Centigrade as a safety margin. The design procedure adopted is to find out dimensions of inner vessel first, then dimensions of outer vessel then finding heat transfer rate and boil off rate. Same is followed in the computer program, while design of stiffening rings and insulation is not taken into consideration. 2.3 Design of inner vessel The inner vessel must withstand the design internal pressure, the bending force acting on the vessel as beam and the weight of the fluid within the container. To reduce cool down losses and time to cool down and also to avoid the possibility of thermal stresses being induced, the thickness of inner vessel is taken as thin as practicable. It will reduce cost. According to the ASME CODE pressure vessels selection, the minimum thickness of the inner shell for a cylindrical vessel determined with the help of details below: P D t = i i (1) 2( Sanw 0.6P i ) Similarly, thickness of conical head can be determined from: P D t i i h = (2) 2( S a n w 0.6P i ) cosα 2.4 Design of outer vessel Outer vessel is not exposed to cryogenic temperature and has only atmospheric pressure acting on it. The outer shell does not fail because of examine stress but it would fail from the stand point of elastic instability i.e., collapsing or buckling. Failure by elastic instability is covered by the ASME code in which design charts are present for the cylinders subjected to external pressure. According to ASME code critical pressure is given by: 2

3 P c = 5P a For thickness of outer shell in case of external pressure, from ASME code we have, Proceedings of the National Conference on 5 t E D o 2 P = t c 0.45 (4) 3 D o L 1 v 2 4 D o It is also mentioned in the ASME code that in case of apex angle near about 30, thickness of conical head shall be same as required thickness of cylindrical shell subjected to external pressure. In both cases, inner and outer vessel, to find out weight of vessel formulas are available and same is used in program for calculation. After calculating major and important parameters for both vessels, heat transfer rate and boil off rate are required to be determined. Here, heat transfer is considered by radiation between two concentric surfaces. Then find out boil off rate by taking ratio of total energy transfer to container during a day to energy required to evaporate container contents. The procedure and formula just discussed is used in developing a very interactive and simple C program which calculates each and every required parameter, at the same time some values for vessels are assumed i.e. inner and outer diameter, neck height in both cases, atmospheric pressure, apex angle etc. They are clearly specified in the program. (3) Nomenclature S Density P Pressure (Subscripts:C Critical, I inside, A atmospheric) Dni Neck diameter Lni Head height t Shell thickness e Emissivity of surface T Temperature Br Boil off rate Q Heat transfer rate n w Weld joint efficiency S a Allowable stress E Young s modulus 3.0 Program of Design of Cryogenic Container #define dgnpr #define di 300 #define dni 50 #define lni 80 #define ln2 15 #define pi #define do 400 #define dno 55 #define lo 475 #define sigma 5.67*pow(10,-14) #define alpha 33 #include<stdio.h> #include<math.h> #include<conio.h> void main() int c,den,str,den1,str1,t1,t2; float mu,ym,mu1,ym1,cap,t,th,deno,num,li,wi,pc,num1,deno1,to,x1,a3; float r1,num2,sub,pc1,wo,a1,a2,e1,e2,q,ed,et,nbp,hfg,br,q1; clrscr(); printf("\n Shape selected for vessel is cylindrical : \n"); printf("\n Unit system is SI: \n"); printf("\n Weld joint efficiency is taken 100% \n"); printf("\n Enter the capacity of the container in liters :\n"); 3

4 scanf("%f",&cap); /* Material selection for vessels */ printf("\n Select material for inner vessel :\n"); printf("\n Enter choice for material for vessel: \n"); printf("\n Enter 1 for stainless steel, 2 for low alloy steel, 3 for carbon steel \n"); scanf("%d",&c); if(c==1) den = 7900; str = 130; mu = 0.27; ym = 2.07*pow(10,5); else if(c==2) den = 7830; str = 145; mu = 0.27; ym = 2*pow(10,5); else if(c==3) den = 7720; str = 95; mu = 0.27; ym = 2*pow(10,5); printf("\n Properties of material for vessel are:\n density-%d\n stress-%d\n poission's ratio-%f\n young's modulus-%f \n ",den,str,mu,ym); /* Design of inner container */ printf("\n Design of inner container : \n"); /* Length of cylindrical part of inner vessel : */ deno = (pi/4)*di*di; num = (1/3)*(pi/4)*lni*di*di - pi*(ln2/4)*dni*dni; li = (cap*pow(10,6) - num) / deno; li = (int)(li+5.5); printf("\n Length of cylindrical part of inner vessel is : %f mm \n",li); /* Shell thickness for inner vessel */ t = (dgnpr*di)/(2*(str-0.6*dgnpr)); t = (int)(t+1.5); printf("\n shell thickness of inner vessel is : %f mm \n",t); /* Head thickness of conical head */ a1 = (pi/180)*alpha; th = (dgnpr*di)/( 2*cos(a3)*(str-0.6*dgnpr)); th = (int)(th+1.5); printf("\n Head thickness of conical head is : %f mm \n",th); /* Weight of inner container */ wi = den*pow(10,-9)*pi*((di+t)*t*li +(di+th)*(di+th)*th); printf("\n Weight of the inner vessel is: %f kg \n",wi); /* Design of outer container */ printf("\n Design of outer container :\n"); printf("\n Select material for outer vessel :\n"); printf("\n Enter choice for material for vessel: \n"); printf("\n Enter 1 for stainless steel, 2 for low alloy steel, 3 for carbon steel \n"); scanf("%d",&c); switch(c) case 1: den1 = 7900; 4

5 Proceedings of the National Conference on str1 = 130; mu1 = 0.27; ym1 = 2.07*pow(10,5); break; case 2: den1 = 7830; str1 = 145; mu1 = 0.27; ym1 = 2*pow(10,5); break; case 3: den1 = 7720; str1 = 95; mu1 = 0.27; ym1 = 2*pow(10,5); break; printf("\n For choice equal to %d: \n",c); printf("\n Properties of material are:\n density-%d\n stress-%d\n poission's ratio-%f\n young's modulus-%f \n ",den1,str1,mu1,ym1); pc=5*dgnpr; printf("\n Critical pressure is: %f \n",pc); /* Thickness of outer shell */ num1 = pc*(1-mu1*mu1)*(lo/do); deno1 = 2.42*ym1; x1 = num1/deno1; to =pow(x1,0.4)*do; to =(int)(to+0.5); printf("\n Thickness of the outer shell is: %f \n",to); /* Checking critical pressure for safe design */ r1 = to/do; num2 = 2.42*ym1*pow(r1,2.5)/(pow((1-mu1*mu1),0.75)*(lo/do)); sub = 0.45*pow(r1,0.5); pc1 = num2-sub; printf("\n Critical pressure from the formulae: %f \n",pc1); if(pc1<=pc) printf("\n Redefine parameters for outer container or change the material: \n"); printf("\n As pc1>critical pressure, design is safe \n"); /* Weight of the outer shell */ wo = den*pow(10,-9)*pi*((do+to)*to*lo+(pi/4)*(do+to)*(do+to)*to); printf("\n Weight of the outer container is: %f kg \n",wo); /* Calculating Heat transfer and Boil off rate */ printf("\n Heat transfer is taken between two cylinders by radiation : \n"); a1 = pi*di*li; a2 = pi*do*lo; printf("\n Enter e1 :\n"); scanf("%f",&e1); printf("\n Enter e2 :\n"); scanf("%f",&e2); printf("\n Enter temperature T1 :\n"); scanf("%d",&t1); printf("\n Enter temperature T2 :\n"); scanf("%d",&t2); q = (sigma*a1*(pow(t1,4)-pow(t2,4)))/(1/e1 + (a1/a2)*(1/e2-1)); printf("\n Heat trnasfer by radiation is: %f \n",q); /* Calculating Boil off rate */ 5

6 printf("\n Allowable static evaporation loss is: 8.33 cc/hr.\n"); printf("\n 1 watt heat load causes evaporation of 22.5 cc/hr. \n"); q1 = 8.33/22.5 ; printf("\n So heat required for evaporation of static evaporation loss: %f \n",q1); printf("\n Ed is total energy transfer to container in a day : \n"); printf("\n Et is total energy required to evaporate container contains : \n"); ed = q1*3.6*24; printf("\n Total energy transfer to container in a day, ed is: %f \n",ed); printf("\n Enter normal boiling point of the liquid : \n "); scanf("%f",&nbp); printf("\n Enter hfg of the liquid : \n"); scanf("%f",&hfg); et = nbp*hfg*cap; br = (ed/et)*100; printf("\n Boil off rate is: %f per day \n",br); getch(); 4.0 Output Of The Program Shape selected for vessel is cylindrical: Unit system is SI: Weld joint efficiency is taken 100% Enter the capacity of the container in liters: 25 Select material for inner vessel: Enter choice for material for vessel: Enter 1 for stainless steel, 2 for low alloy steel, 3 for carbon steel 1 Properties of material for vessel are: Density-7900 kg/m3 Stress-130 N/mm2 Poisson s ratio Young s modulus N/mm2 Design of inner container: Length of cylindrical part of inner vessel is: mm Shell thickness of inner vessel is : mm Head thickness of conical head is: mm Weight of the inner vessel is: kg Design of outer container: Select material for outer vessel: Enter choice for material for vessel: Enter 1 for stainless steel, 2 for low alloy steel, 3 for carbon steel 3 For choice equal to 3: Properties of material are: Density-7720 kg/mm3 Stress-95 N/mm2 Poisson s ratio Young s modulus N/mm2 Critical pressure is: N/mm2 Thickness of the outer shell is: mm Critical pressure from the formulae, pc1: N/mm2 As pc1>critical pressure, design is safe Weight of the outer container is: kg Heat transfer is taken between two cylinders by radiation: Enter emissivity e1:.02 Enter emissivity e2:.05 Enter outside temperature T1 in kelvin: 300 Enter inside temperature T2 in kelvin: 77 Heat transfer by radiation is: watt Allowable static evaporation loss is 8.33 cc/hr. 1 watt heat load causes evaporation of 22.5cc/hr. So heat required for evaporation of static evaporation loss: watt Ed is total energy transfer to container in a day: Et is total energy required to evaporate container contains: Total energy transfer to container in a day, ed is: KJ/day Enter normal boiling point of the liquid: Enter hfg of the liquid:.809 Total energy required to evaporate container content, et is : KJ Boil off rate is: per day 5.0 Conclusion Thus, the paper describes various design parameters such as cryogenic liquid to be stored, temperature, pressure, shape and size of vessel, volume of liquid to be stored and its significance in overall design of the Cryogenic storage vessel. Also the design procedure adopted here takes care of material selection for inner and outer vessels, which is very crucial parameter in design of cylindrical cryogenic storage vessel. Presented C program is comprehensible and spotless. 6

7 Proceedings of the National Conference on References 1. HERVÉ BARTHÉLEMY, Cryogenic vessels for the storage and transportation of compressed gases in liquid form, ISO/TC 220, Cryogenic vessels, WG 1, Design and construction. 2. JOHN F. HARVEY, 2001, Theory and Design of Pressure vessels (CBS Publishers and Distributors). 3. PATRICK KELLY, Application of Cryogenic Technology, Vol PETER KITTEL, Advances in Cryogenic Engineering, Vol. 43, Part B, NASA Research Center. 5. S.M. ACEVES, J.M. MARTINEZ-FRIAS, O.GARCIA-VILLAZANA, Evaluation of Insulated Pressure Vessels for Cryogenic Hydrogen Storage, ASME Int. J. Mech. Congress and Exposition Nashville, TM. 7