$INCLUDE Moody.lib { }

Size: px

Start display at page:

Download "$INCLUDE Moody.lib { }"

Jeffery Dennis
5 years ago
Views:

1 File:F:\Thermal Systems Design\Design Problem 3 attempt 2.EES 11/12/2012 4:14:34 PM Page 1 $INCLUDE Moody.lib {Problem Statement} {In industrial applications, steam is often used as a heating medium. There are companies, however, who manufacture and market what they refer to as heat transfer fluids, that work as effectively as steam and at a lower cost. On such liquid is called Therminol which is available in many different chemical formulas. Consider an application where a Therminol liquid is being used to heat acetone in a shell and tube heat exchanger. The acetone (an organic liquid) flows at 176,000 lbm/hr and needs to be heated from 50 F to 86 F. The acetone can be a few degrees warmer than 86 F, but it cannot drop below 86 F. Heated Therminol (also an organic liquid) is available at 215 F with a flow rate of 220,000 lbm/hr. Select a Therminol fluid for this application and design a shell and tube heat exchanger for this service. When specifying the tubes, keep them at standard lengths of 8, 12, or 16 ft. As you develop your solution, keep the shell and tube heat exchanger design considerations in mind that we discussed in class (and in Section 9.5 of the text). } {Find} {(a) The Therminol fluid selected for this application with a brief explanation of why this fluid was selected (b) Hot and cold fluid outlet temperatures for clean and fouled conditions (c) Pressure drop of the hot and cold fluids (d) Fluid placement (which fluid is in the shell, which fluid is in the tubes) (e) Shell diameter (f) Number of shell and tube passes (g) BWG tube specification (h) Length of the tubes (i) Number of tubes in the heat exchanger (j) Pitch of the tubes (k) Number of baffles in the heat exchanger (l) Baffle spacing (m) The LMTD correction factor F. This tells you how close your HX is performing to a counter flow HX} {Assumptions} {In order to make the problem converge, an outlet temperature of 90[F] was assumed (initially)} {The 90[F] outlet temperature met the requirements of the problem (86[F] or above)} {Assuming Turbulent Flow Through Tubes (more effective heat transfer in turbulent flow)} {Copper Tubes Were Assumed To Be used In The HX} {Assuming incompressible fluid model/ effectiveness NTU model} {The inlet temperature of the available cold fluid (acetone) was 50[F], and we assumed an outlet temperature of 90[F] because it met the requirements of the problem statement. After getting the problem to converge at a given outlet temperature, we were able to update our guesses and iterate the problem using EES. We used an initial number of loops of 1 in order to set up initial guesses for the fluid properties and NTU values.} {The following block of code calculates the properties of the cold fluid (acetone)} {Solution} {Fluid Properties} {Properties of Acetone (Cold Fluid)} P = 20[psia] T_c_i = 50[F] T_c_avg = (T_c_i + T_c_o[1])/2 {Acetone} rho_c=density(acetone,t=t_c_avg,p=p) mu_c=viscosity(acetone,t=t_c_avg,p=p) k_c=conductivity(acetone,t=t_c_avg,p=p) {Assumed Pressure Cold Side} {Temperature of Cold Fluid In} {Average Temperature Cold Side}

2 File:F:\Thermal Systems Design\Design Problem 3 attempt 2.EES 11/12/2012 4:14:34 PM Page 2 C_p_c=Cp(Acetone,T=T_c_i,P=P) Pr_c=Prandtl(Acetone,T=T_c_avg,P=P) nu_c = mu_c/rho_c {We included all therminol options in our code so that we could analyze each fluid side by side. It was more difficult to run everything in loops, but we looked at it as though it would save time in the long run. We ran each block of code as it was set up to make sure units were correct and our actual code was performing correctly. With the four fluids side-by-side, we were able to pick the fluid that met all of our given criteria.} {Properties of Hot Fluid (Type of Therminol)} T_h_i = 215[F] {Fluid Option 1} rho[1]=rho_ ('Therminol_59', T_h_i) mu[1]=mu_ ('Therminol_59', T_h_avg[1]) {THERMINOL 59} k[1]=k_ ('Therminol_59', T_h_avg[1]) C_p[1]=c_ ('Therminol_59', T_h_i) Pr_[1] = C_p[1]*mu[1]/k[1] nu[1] = mu[1]/rho[1] {Fluid Option 2} rho[2]=rho_ ('Therminol_66', T_h_i) mu[2]=mu_ ('Therminol_66', T_h_avg[2]) {Therminol 66} k[2]=k_ ('Therminol_66', T_h_avg[2]) C_p[2]=c_ ('Therminol_66', T_h_i) Pr_[2] = C_p[2]*mu[2]/k[2] nu[2] = mu[2]/rho[2] {Fluid Option 3} rho[3]=rho_ ('Therminol_VP1', T_h_i) mu[3]=mu_ ('Therminol_VP1', T_h_avg[3]) {Therminol VP1} k[3]=k_ ('Therminol_VP1', T_h_avg[3]) C_p[3]=c_ ('Therminol_VP1', T_h_i) Pr_[3] = C_p[3]*mu[3]/k[3] nu[3] = mu[3]/rho[3] {Fluid Option 4} rho[4]=rho_ ('Therminol_XP', T_h_i) mu[4]=mu_ ('Therminol_XP', T_h_avg[4]) {Therminol_XP} k[4]=k_ ('Therminol_XP', T_h_avg[4]) C_p[4]=c_ ('Therminol_XP', T_h_i) Pr_[4] = C_p[4]*mu[4]/k[4] nu[4] = mu[4]/rho[4] {Heat Transfer Variable List} {m_dot_c = mass flow rate through cold side (acetone)} {C_dot_c = Capacitance rate through cold side (acetone)} {C_dot_h[i] = Capacitance rate through hot side (therminol)} {m_dot_h = mass flow rate of therminol (hot side)} {rho[i] = rho values for each therminol fluid} {nu[i] = kinematic viscosity for each therminol fluid} {k[i] = thermal conductivity of each therminol fluid} {Pr[i] = Prandtl number for each therminol fluid} {V_dot_h[i] = Volumetric flow rate for each therminol fluid} {A_h = hot side area (cross sectional)} {C_r[i] = Ratio of C_dot min to C_dot_max for fluids} {NTU[i] = Number of transfer units between hot, cold fluids} {UA[i] = UA product between fluids} {Q_dot[i] = heat transfer between fluids (changes based on therminol)} {Q_dot_max[i] = maximum heat transfer based on fluids} {Epsilon[i] = Effectiveness of heat exchanger} {P[i],R[i] = Necessary Inputs for LMTD "F" Function} {F[i] = Correction Factor For Each Fluid} {U_o_dirty[i], U_o_clean[i] = Fouled and Dirty U Factors of HX}

3 File:F:\Thermal Systems Design\Design Problem 3 attempt 2.EES 11/12/2012 4:14:34 PM Page 3 {T_h_avg[i] = Average temperature of each hot fluid} {Flow Information} {Cold Fluid} m_dot_c = [lb_m/hr] m_dot_c = rho_c*v_dot_c C_dot_c = m_dot_c*c_p_c {Mass Flow Rate Cold Fluid} {Solved For Cold Volumetric Flow} {Capacitance Rate Cold Side} {The following block of code solves for the hot fluid properties based on temperatures. This block also sets the shell fluid equal to the hot fluid for the last loop of code. The last loop of code is further down the page and is specified using "shell" eqations.} {Hot Fluid(s)} m_dot_h = [lb_m/hr] Duplicate i = 1,4 m_dot_h = rho[i]*v_dot_h[i] rho[i]=rho_s[i] nu[i]=nu_s[i] k[i] = k_s[i] Pr_[i] = Pr_s[i] V_dot_h[i] = A_h*V_h[i] C_dot_h[i] = C_p[i]*m_dot_h {Mass Flow Rate Hot Fluid} {Solves For Volumetric Flow Hot FLuids} {Sets shell, hot fluid densities equal} {Sets shell, hot fluid viscosities equal} {Sets shell, hot fluid cond. values equal} {Sets Shell, hot fluid prandtl equal} {Solves For Hot Side Velocities} {Solves For hot side capacitance rates} {We set up a loop that solved for C_r, epsilon, NTU, etc. values for all of the fluids. It took a little bit of time to get everything to converge for the first time, but we were able to set up initial guess values piece-by-piece and everything worked.} {Heat Transfer Model} C_r[i] = C_dot_c/C_dot_h[i] {Ratio Of C_dot min to C_dot_max} NTU[i] = UA[i]/C_dot_c {Number of Transfer Units} UA[i] = U_o_dirty[i]*A_o {UA Product} Q_dot[i] = C_dot_h[i]*(T_h_i - T_h_o[i]) {Heat Transfer Equation} Q_dot[i] = C_dot_c*(T_c_o[i] - T_c_i) {Heat Transfer Equation} Q_dot_max[i] = C_dot_c*(T_h_i - T_c_i) {Maximum Heat Transfer} epsilon[i] = 2*(1+C_r[i]+((1+exp(-NTU[i]*(1+C_r[i]^2)^(1/2)))/(1-exp(-NTU[i]*(1+C_r[i]^2)^(1/2))))*(1+C_r[i]^2)^(1/2))^(-1) epsilon[i] = Q_dot[i]/Q_dot_max[i] {Effectiveness Of HX} P[i] = (T_c_o[i]-T_c_i)/(T_h_i-T_c_i) {Constant for "F" function} R[i] = (T_h_i-T_h_o[i])/(T_c_o[i]-T_c_i) {Constant for "F" Function} F[i]=LMTD_CF('shell&tube_4N',P[i],R[i]) {Correction Factor} U_o_dirty[i] =1/( 1/U_o_clean[i] + R_dprime_f_h +R_dprime_f_c) {Actual U_o Value (Fouled)} U_o_clean[i] = 1/(1/h_o[i] + (1/h_i)*(OD_t/ID_t)) {Clean U_o_Value} T_h_avg[i] = (T_h_i + T_h_o[i])/2 {Average Temperature Hot Side} End {Now that the fluid properties were evaluated, we were able to move on to the shell and tube analysis. Several assumptions were initially made in order to reach solutions (with the intent of later adjusting these assuptions to create a reasonable heat exchanger).} {Shell And Tube Analysis} {Shell and Tube Variable List} {D_e[1] = equivalent diameter assuming square pitch of tubes} {D_e[2] = equivalent diameter assuming triangular pitch of tubes} {OD_t = outside diameter of tubes in HX} {P_t = center to center distance between tubes} {Nus_t = Nusselt number inside HX tubes} {h_i = "h" coefficient of heat transfer inside tubes}

4 File:F:\Thermal Systems Design\Design Problem 3 attempt 2.EES 11/12/2012 4:14:34 PM Page 4 {f = friction factor inside tubes} {ID_t = Inside diameter of tubes in HX} {Pr_t = Prandtl Number Inside tubes in HX} {k_t = thermal conductivity of fluid inside HX} {Re_t = Reynolds Number HX tubes} {m_dot_t = mass flow rate through HX tubes} {mu_t = viscosity of fluid in HX tubes} {Nus_s = Nusselt Number Through Shell Side} {Re_s = Reynolds Number Through Shell Side} {Pr_s = Prandtl Number Through Shell Side} {k_s = Thermal Conductivity through shell side} {h_o = "h" coefficient of heat transfer outside tubes} {V_s = Velocity Through Shell Side} {V_st = Velocity Through Shell Side (converted to ft/s)} {nu_s = kinematic viscosity through shell side} {rho_s = density of fluid moving through shell} {A_s = shell area} {D_s = Diameter of Shell} {C = Tube Clearance} {B=Baffle Spacing} {L = Length of Heat Exchanger} {N_b = Number of Baffles} {N_t = Number of Tubes (find Max number from book)} {N_p = Number of Passes} {DELTAP_t = Pressure Drop Through Tubes} {DELTAP_s = Pressure Drop Through Shell} {f_s = friction factor shell side} {f_c = friction factor tube side} {In building a heat exchanger that met all of the provided parameters, we adjusted the following lengths, diameters, etc. to provide the necessary output temperature, pressure drops, and economic velocities. Because all four fluids were built into one code, we were able to analyze the effect on the system using each fluid. We had to be careful adjusting the number of baffles because the pressure drop in the shell side was increased with each baffle. We had to be careful in adjusting our tube diameters because this affected the pressure drops and velocities in the tubes. We decided to use #10 BWG tubing and adjusted the number of tubes to meet our needs.} {Tubing Used} {#10 BWG --> OD = 3/4", ID =.482"} {Baffles Used} {N_b = 8 --> 8 baffles, pressure drop in shell was minimal, spacing requirements were met.} {Length of HX} {L=8[ft] --> We wanted to keep material costs down, 8 ft was smallest size, friction minimalized.} {Number of Tubes} {N_t = > We pluged 23 tubes (178 max) with given arrangement, met required T_out.} {Tubing Pitch} {P_t = 1" --> We decided on using a 1 inch triangular pitch to maximize heat transfer.} {Shell Diameter} {D_s = 17.25" --> We used the minimum diameter with the given arrangement to meet requirements.} {Shell/ Tube Fluid} {Acetone moves through tubes, Therminol travels through shell} {Note: ALL SHELL SIDE INPUTS CAN BE FOUND IN THE FOLLOWING CODE!!} {Assumed Lengths, Diameters, etc} N_p = 4 {Assumed Number of Passes} N_b = 8 {Assumed Number of Baffles} L = 8[ft] {Assumed Length of H} ID_t =.482*convert(in,ft) {Assumed Inside Diameter of tubes} OD_t = (3/4)*convert(in,ft) {Assumed Outside Diameter of Tubes} D_s = 17.25*convert(in,ft) {Assumed Outside Diameter of Shell pg.448} P_t = (1)*convert(in,ft) {Assumed 1 inch square Pitch} N_t = 155 {Max Amt. Tubes 1 in, square pitch}

5 File:F:\Thermal Systems Design\Design Problem 3 attempt 2.EES 11/12/2012 4:14:34 PM Page 5 C = P_t - OD_t B = L/(N_b+1) m_dot_s = m_dot_h mu_t = mu_c nu_t = nu_c rho_t = rho_c Pr_t = Pr_c k_t = k_c epsilon_t = [ft] D_e[1] = ((4*P_t^2)/(pi*OD_t))-OD_t D_e[2] = ((2*sqrt(3)*(P_t^2))/(pi*OD_t))-OD_t R_dprime_f_h =.001[ft^2-hr-R/Btu] R_dprime_f_c =.001[ft^2-hr-R/Btu] g_c = 32.17[lb_m-ft/lbf-s^2] {Tube Clearance} {Baffle Spacing} {Fluid In Shell Is Hot Fluid} {Roughness Factor of Copper} {Equivalent Diameter Square Pitch} {Equivalent Diameter Triangular Pitch} {Therminol Assumed To Be Organic Liq.} {Acetone, Organic Liquid} {Gravitational Constant} {The following equations were all related to areas. By keeping the areas/ mass flow rate per tube separated, they were easy to find in the code when verification was necessary.} {Area Equations} A_s = A_h A_s = (D_s*C*B)/(P_t) A_c = ((pi*id_t^2)/4)*(n_t/n_p) A_t = (pi/4)*id_t^2 A_o = N_t*pi*OD_t*L m_dot_c/n_t = m_dot_t m_dot_t*convert(lb_m/hr,lb_m/s) = rho_t*a_t*v_t {Hot Fluid Is On Outside, Cold In Tubes} {Area Of Shell} {Area Of Cold Tubes} {Area Of EACH Cold Tube} {Outside Area Of Tubes} {Mass Flow Rate Through Each Tube} {Find Velocity Through Each Tube} {The following block of code calculate the nusselt/ friction/ reynolds number on the code side of the heat exchanger. Any underscore with a "c" represents cold side fluid. Since the cold side required no iterations, loops weren't necessary, and we were able to separate these variables from the later loops.} {Nusselt/ Reynolds Correlations Through Tubes} f_c=fricfac('churchill',re_t,epsilon_t/id_t) {Friction Factor Tube Side (Cold Fluid)} Nus_t = h_i*id_t/k_t {Nusselt Number Through Tubes} Nus_t = ((f_c/8)*(re_t-1000)*pr_t)/(1+12.7*(f_c/8)^(1/2)*(pr_t^(2/3)-1)) Re_t = (V_t*convert(ft/s,ft/hr)*ID_t)/(nu_t) {Reynolds Number Tube Side} {The following loop calculates the nusselt numbers, reynolds numbers, velocities, friction factors, and pressure drops based on the therminol fluid used. We initially intended on using the therminol fluid with the highest heat transfer, but we ended up comparing fluids and making our decision based on the actual outlet temperatures, pressure drops, etc.} {Nusselt/ Reynolds Correlations Through Shell} Duplicate k=1,4 Nus_s[k] =.36*Re_s[k]^(.55)*Pr_s[k]^(1/3) {Nusselt Number Through Shell Side} Nus_s[k] = h_o[k]*d_e[2]/k_s[k] {Solves For Outside "h" Coefficient} Re_s[k] = V_s[k]*D_e[2]/nu_s[k] {Reynolds Number Shell Side} V_s[k] = m_dot_s/(rho_s[k]*a_s) {Velocity of Fluid Through Shell} V_st[k] = V_s[k]*convert(ft/hr,ft/s) {Converts Velocities To Ft/s Form} f_s[k] = exp( *ln(re_s[k])) {Friction Factors Shell Side} DELTAP_s[k] = f_s[k]*(n_b+1)*(d_s/d_e[2])*((rho_s[k]*v_st[k]^2)/(2*g_c))*convert(psf,psi) End {Since the pressure drop through the tube was based solely on the number of passes and the cold-side friction factor, only one pressure drop equation was needed for the cold side. } {Pressure Drop Tube Side}

6 File:F:\Thermal Systems Design\Design Problem 3 attempt 2.EES 11/12/2012 4:14:34 PM Page 6 DELTAP_t = (N_p*(f_c*(L/ID_t)+4)*((rho_t*V_t^2)/(2*g_c)))*convert(psf,psi) {The final block of code simply calls values from the arrays table. Since we needed these chosen values in our "key variables" table, we wrote this block} {Displays Necessary Outputs} F_corr = F[1] V_st[1] = V_s T_h_o[1] = T_h_o T_c_o[1] = T_c_o DELTAP_s[1] = DELTAP_s Material = pi*d_s*l {Correction Factor For Chosen Fluid} {Velocity of Shell Fluid} {Hot Temperature Of Chosen Fluid} {Cold Temperature of Chosen Fluid} {Pressure Drop Through Shell Chosen FLuid} {Inner Surface Area Of Shell} SOLUTION Unit Settings: Eng F psia mass deg Ac = [ft 2 ] Ah = [ft 2 ] Ao = [ft 2 ] As = [ft 2 ] At = [ft 2 ] B = [ft] C = [ft] Cc = [Btu/R-hr] Cp,c = [Btu/lbm-R] Ps = [psi] Pt = [psi] Ds = [ft] εt = [ft] fc = Fcorr = gc = [lb m -ft/lbf-s 2 ] hi = [Btu/hr-ft 2 -R] IDt = [ft] kc = [Btu/hr-ft-R] kt = [Btu/hr-ft-R] L = 8 [ft] Material = [ft 2 ] µc = [lb m /ft-hr] µt = [lb m /ft-hr] mc = [lb m /hr] mh = [lb m /hr] ms = [lb m /hr] mt = 1135 [lb m /hr] Nust = νc = [ft 2 /hr] νt = [ft 2 /hr] Nb = 8 Np = 4 Nt = 155 ODt = [ft] P = 20 [psia] Prc = Prt = Pt = [ft] Ret = ρc = [lb m /ft 3 ] ρt = [lb m /ft 3 ] Rdprime,f,c = [ft 2 -hr-r/btu] Rdprime,f,h = [ft 2 -hr-r/btu] Tc,avg = [F] Tc,i = 50 [F] Tc,o = [F] Th,i = 215 [F] Th,o = [F] vc = 3568 [ft 3 /hr] Vs = 3.35 [ft/s] Vt = [ft/s] No unit problems were detected. KEY VARIABLES Tc,o = [F] Th,o = [F] Pt = [psi] Ps = [psi] Ds = [ft] Np = 4 Cold Fluid Outlet Temp (b) Hot Fluid Outlet Temp (b) Pressure Drop Through Tubes (cold fluid) (c) Pressure Drop Through Shell (c) Fluid In Shell --> Therminol (d) Fluid In Tubes --> Acetone (d) Diameter of Shell 17.25" (e) Number of Tube Passes (f) Number of shell passes --> 1 (f) Tube Size --> BWG 10 (g)

7 File:F:\Thermal Systems Design\Design Problem 3 attempt 2.EES 11/12/2012 4:14:34 PM Page 7 L = 8 [ft] Nt = 155 Pt = [ft] Nb = 8 B = [ft] Fcorr = Vt = [ft/s] Vs = 3.35 [ft/s] Material = [ft 2 ] Length of HX (h) Number of Tubes (23 plugged off of max) (i) Pitch of Tubes 1" (j) Number of Baffles in HX (k) Baffle Spacing (l) LMTD Correction Factor (m) Velocity of Acetone --> Meets Ec. Velocity Velocity Through Shell Surface Area of Shell Material, Used In Design

Introduction to Heat and Mass Transfer

Introduction to Heat and Mass Transfer Week 16 Merry X mas! Happy New Year 2019! Final Exam When? Thursday, January 10th What time? 3:10-5 pm Where? 91203 What? Lecture materials from Week 1 to 16 (before