Ben Sandoval ICE Preliminary Design 1 The Preliminary Design of an I-4, 4-Stroke Engine Executive Summary The following contains the mathematical analysis of a four stroke, inline, four cylinder engine with 1.9 Liters of displacement capable of producing 124hp at 5,600RPM. Other performance characteristics are listed in greater detail in further sections. The main parameters that were mathematically determined are the bore, stroke, and rough engine dimensions. These were: Bore = 3.23inches, Stroke = 3.54 inches, the engine length is roughly 15.51inches, and the spacing between the cylinders is 3.88 inches. As well, the torque, brake mean effective pressure, mechanical efficiency and base specific fuel consumption are a major concern. These were mathematically determined to be roughly T = 1395 in-lbs, BMEP = 151.25psi, nm= 77.3% and the BSFC was 0.4428 lbm/hp-hr. In addition, many of the performance characteristics were compared with the BMW M44. Finally, a rough sketch of the analyzed engine is located in the Conceptual Engine Design section, and located in the Appendix is all of the mathematical code used to perform the analysis.
Ben Sandoval ICE Preliminary Design 2 Introduction The purpose of this paper is to determine some basic dimensions and parameters of an engine described in the problem statement below. Some initial dimensions of the engine are defined using the displacement volume in combination with the engine speed and the piston velocity. More detailed characteristics are then established such as the torque and base mean effective pressure, based off of the engine speed and the power output. An indicated and brake thermal efficiency can be estimated using the compression ratio, and the ratio of specific heats, which is assumed. For a more accurate efficiencies and parameters, an Applet, provided by Wiley (Figure 1), uses an iterative method to obtain results and in turn calculate things such as base specific fuel consumption. Problem Statement: Prepare the preliminary design of a 4-stroke, I-4, DOHC, 1.9L passenger car engine that has a compression ratio of 9.5:1, multi-port fuel injection and a maximum brake power of 124 hp at 5,600 rpm. Note: in the USA, automobile engines are rated without air filter or muffler. Engines are rated at 14.7 psia and 60 deg F. Assume the fuel is gasoline with a heating value of 19,020 Btu/lbm, combustion efficiency is 95%, and the average piston speed is 3300 ft/min. Determine: 1. Bore, stroke and rough engine dimensions 2. At max power: torque, bmep, mechanical efficiency and bsfc. Approach In order to successfully determine the characteristics above, as mentioned in the introduction, some rough mathematical estimates are necessary including torque, stroke, bore, and brake mean effective pressure. There are some assumptions made to obtain these, however. Upon calculating the parameters necessary, the Wiley iterative applet (also using assumptions) can be used to define a few parameters more accurately such as the ideal thermal efficiency, the indicated mean effective pressure, and the volumetric efficiency. From the parameters found using mathematical analysis in combination with those found using the applet, the brake specific fuel consumption and mechanical efficiency can be determined. When seeking a similar engine to compare with, the displacement volume and layout (I-4) were the main parameters in the search.
Ben Sandoval ICE Preliminary Design 3 Analysis Nomenclature: Note: The parameters listed below are necessary in describing the basic specifications of the engine that was characterized. The parameters listed in bold are those that were found based upon parameters that are preceded by an asterisk (*), in addition to parameters that are underlined, meaning the values were based upon assumptions. *V d = Displacement volume *W b = Max brake power *Stroke = Strokes per engine cycle *r C = Compression ratio *Q hv = Heating Value of gasoline *N = Engine speed *U p = Average piston speed *n c = combustion efficiency *P i = Inlet pressure at which engine was rated *T i = Inlet temperature at which engine was rated *N c = Number of cylinders n thi = Indicated thermal efficiency n tha = Actual indicated thermal efficiency n b = Brake thermal efficiency n v = Volumetric efficiency A p = Piston area imep = Indicated mean effective pressure k = Specific heat ratio = 1.4 Φ = Equivalence Ratio = 1 τ = Torque S = Stroke length B = Bore diameter bmep = Brake mean effective pressure
Ben Sandoval ICE Preliminary Design 4 bsfc = Brake specific fuel consumption n m = Mechanical efficiency Lblock = Length of block SCyl = Spacing of the cylinder The following describes the steps and equations used during the analysis. The mathematical code used to find all of these values is located in the appendix and was run using MATLAB. Original copies of the *.m file are available upon request. The main assumptions of this analysis are as follows: 1) The engine was rated at sea level at a temperature of 60F and 14.7psi. 2) The engine is rated without an air filter or a muffler. 3) The Engine is assumed to be fuel injected, meaning that no carburetor is used, and therefore the Taylor estimates from carburetor to inlet for temperature and pressure ratio will not be used in this analysis. In addition, the change in pressure decreases with increasing engine speed (and thus flow velocity), meaning that the temperature drop can be considered negligible. First, it was necessary to find the Stroke Length in inches. Eq. 1, relates the average piston speed to the engine speed and stroke length. The result based upon the given parameters was first in feet and was multiplied by 12in/ft in order to obtain the result in inches. U! = 2SN (Eq. 1) S = 3.5357 inches After finding the Stroke Length, Eq. 2, which relates the Bore with the displacement volume and Stroke Length could then be manipulated and applied to obtain the Bore. It was first necessary to convert the displacement volume from Liters to in 3 and divide by N c in order to obtain the displacement volume per cylinder, however. v! /N! =!! B! S (Eq. 2) B = 3.2308 inches In order to find the Torque, Eq. 3 was applied, which relates the Max Brake Power with the Engine Speed. In this case, the Brake Power was converted from HP to ft-lbs/min, and the Engine Speed was divided by 60sec. and the resultant torque was multiplied by 12in/ft in order to obtain the Torque in in-lbs.
Ben Sandoval ICE Preliminary Design 5 τ =!!! π (!!" ) (Eq. 3) τ = 1.3965E3 in lbs The Base Mean Effective Pressure was found using Eq. 4, which relates the bmep, Torque, and the Engine Displacement Volume. τ =!"#$!! (Eq. 4)!! bmep = 151.2532 psi The indicated efficiency was found using Eq. 5, which assumes a constant specific heat value of k = 1.35 and uses the compression ratio as the main factor. In practice, it is understood that the specific heat ratio changes with the condition of the air, but the assumed value holds relatively true because it is the average at which most engines operate at. n!!! = 1 (!!! )!!! (Eq. 5) The next step in the analysis process called for the use of the Four Stroke Fuel-Air Otto Cycle Applet (inputs and results shown below in Figure 1) that was developed and provided by Wiley. A link to this applet is located in the References section. This applet called for the five variables in metric units. Pi = 14.7psi = 101.3kPa, Ti = 60F = 288K, The exhaust pressure is assumed to be slightly higher than the atmospheric pressure and was assumed to be Pe = 105kPa. The compression ratio was given, and the equivalence ratio was assumed to be 1, which is a good balance between power and efficiency, and is usually the standard for four stroke engines.
Ben Sandoval ICE Preliminary Design 6 Figure 1. The above is an Applet developed by Wiley to provide an estimate of various operating parameters based off of the five input variables located at the top. The results obtained are listed at the bottom of the applet. From the Wiley applet, the volumetric efficiency, the net imep, and the ideal thermal efficiency were obtained. The net imep and thermal efficiency obtained were then multiplied by a factor of %85 percent in order to gain a more realistic estimate of the actual indicated mean effective pressure and the indicated thermal efficiency. The value obtained was finally converted into psi. Using this value for imep, Eq. 6 was applied to find the mechanical efficiency. n! =!"#$!"#! (Eq. 6) n! = 77.28% Finally, the base specific fuel consumption was obtained using Eq. 7 which the thermal efficiency (obtained by multiplying the indicated net thermal efficiency from Wiley by 85%) with the heating value of gasoline. bsfc =!!!!!! (Eq. 7) bsfc = 0.4428lb-m/HP-hr
Ben Sandoval ICE Preliminary Design 7 Conceptual Engine Design Below is a simple sketch of an engine block that would achieve something similar to the performance characteristics described in the problem statement. For the real engine itself, the dual overhead camshafts as well as the valves would be located at the top of the cylinders. Original Solidworks drawing available upon request. Figure 2. A basic sketch of an engine block capable of achieving the performance characteristics determined in the analysis. Comparison with an Existing Engine From 1996 2001, BMW manufactured the successor to their M42 engine called the M44 B19. This engine had a dual length intake manifold (BMW coined the acronym DLIM ) as well as fuel injection. The displacement was a few cubic centimeters under 1.9L, measuring in at 1896cc, and it was build in the DOHC, Inline Four Configuration. The table below (Table 1) summarizes a few key similarities and differences between the two engines.
Ben Sandoval ICE Preliminary Design 8 Table 1. This table is a comparison between some performance characteristics and specifications of the engine that was analyzed and BMWs M44B19 engine. [2], [3] Specification Engine Analyzed BMWs M44B19 4 Stroke Yes Yes DOHC Yes Yes Displacement 1900cc 1896cc Fuel Injection Yes Yes BHP 124 @ 5600RPM 138 @ 6000RPM Torque 116 lb-ft 133lb-ft Compression Ratio 9.5:1 10:1 Bore 3.2308 inches 3.346 inches Stroke 3.5357 inches 3.287 inches It can be seen that these engines are remarkably similar in performance, however the BMW engine is clearly outputs more Torque and Power. This is likely due to the higher compression ratio, along with the tests performed at a higher RPM, although there are likely many factors that aren t necessarily quantifiable characteristics such as the quality of the machining, seals, etc that play a role. The ratio of Bore/Stroke is also much closer to 1 in the BWM engine, possibly accounting for the increased performance. Below in Figure 3 is an image of an inline four that is very similar to the M44, the M43, shown with the cylinder head removed. Figure 3. A photo of an Inline four M43 engine with the cylinder head removed. [4]
Ben Sandoval ICE Preliminary Design 9 References [1]Wiley Four Stroke Fuel-Air Otto Cycle Applet http://www.wiley.com/college/mechs/ferguson356174/apps/cycle/cycle.html [2]http://en.wikipedia.org/wiki/BMW_M44 [3]http://www.bmwheaven.com/database/engine.php?type=M44#/90 [4]http://www.bmwsyndikat.de/bmwsyndikatforum/topic98129_Problem_Oelverlust_M43_Mot or_kettenkasten_3er_bmw_-_e36.html Appendix (Next Page for Matlab Code)
Ben Sandoval ICE Preliminary Design 10 Engine Design Specifications Statement % Problem Statement: Prepare the preliminary design of a 4-stroke, I-4, % DOHC, 1.9L passenger car engine that has a compression ratio of % 9.5:1, multi-port fuel injection and a maximum brake power of % 124 hp at 5,600 rpm. Note: in the USA, automobile engines are % rated without air filter or muffler. Engines are rated at % 14.7 psia and 60 deg F. Assume the fuel is gasoline with a % heating value of 19,020 Btu/lbm, combustion efficiency is % 95%, and the average piston speed is 3300 ft/min. % As a minimum, determine the following: % 1. Bore, stroke and rough engine dimensions % 2. At max power: torque, bmep, mechanical efficiency and bsfc. format compact % Initial Values Given Vd = 1.9; %Liters Nc = 4; %Number of Cylinders str = 4; %4stroke engine rc = 9.5; %compression ratio Wdot_b = 124; %Brake Power [HP] N = 5600; %Revs Per Minute Pi = 14.7; %Engine rated at [psi] T = 60; %[F] Qhv = 19020; %[Btu/lbm] nc =.95; %Combustion Efficiency Up = 3300; %ft/min k = 1.35; %cp/cv, specific heat ratio phi = 1; %Equivalence ratio, selected at 1 b/c good balance P vs Eff. TK = 288.706; %Temperature in [K] = 60F Qhve = Qhv/2545; %btu to [HP-hr] % Stroke, Bore (Eq. 1), (Eq. 2) S = Up/(2*N); %Stroke [ft] Sin = S*12 %Stroke [in] Vdc = Vd/Nc; %Displacement Per Cylinder Vdin = Vdc*61.024; % Liters to inches [in3] B = sqrt((4*vdin)/(pi*sin)) %Bore [in] % Torque(Eq. 3) %Wdot_b = 2*pi*(rpm/60)*T Wdot_be = Wdot_b*550; %Convert HP to [ft-lbs/min] (e nglish) Torque = Wdot_be/(2*pi*(N/60)); %[ft-lbs] Tin = Torque*12 % [in-lbs] % Base Mean Effective Pressure (Eq. 4) %T = (bmep*vd)/(4*pi) bmep = (Tin*4*pi)/(Vdin*4) %Base Mean Effective Pressure [psi] % Indicated Thermal Efficiency (Eq. 5) nind = 1-rc^(1-k); %Indicated Efficiency nb =.5*nind; %Break efficiency
Ben Sandoval ICE Preliminary Design 11 % Results Obtained from Four Stroke Fuel-Air Otto Cycle Applet netimep = 1587.55; %Net Indicated Mean Effective Pressure[kPa] netn_th =.46; %Net Thermal Efficiency nv =.989; %Volumetric Efficiency %(n/n_otto)i =.8 to.9 ni =.85*netn_th; PePi = 105/101.3; %Pexhaust/Pinlet Pressure Ratio % Indicated Mean Effective Pressure IMEP_net = netimep*.85; %IMEP [kpa] IMEPnet = IMEP_net * 0.145037738; %IMEP [psi] % Frictional Mean Effective Pressure, From Taylor fmep = 45 +.5*(105-101.3)+.025*(176-100); %[psi] From Taylor Chart imep = bmep +fmep % Piston Area Ap = (pi/4)*b^2; % Length of a 4cylinder block, Cylinder Spacing Lblock = 1.2*B*4 SCyl = 1.2*B % Mechanical, Thermal Efficiency (Eq. 6) nm = bmep/imepnet nth = nm*ni; %Brake Specific Fuel Consumption (Eq. 7) bsfc = 1/(Qhve*nth)% [lbm/hp-hr]