Abstract:
A computer-implemented method for evaluating cooling performance of equipment in a data center. In one aspect, the method comprises receiving data related to equipment in the data center, determining first parameters related to airflow and temperature in the data center at a first period in time, receiving a description of a transient event affecting one of airflow and temperature in the data center at a second time, breaking a second time period subsequent to the second time into a plurality of time intervals, determining second parameters related to airflow in the data center during one of the time intervals, determining the parameters related to temperature in the data center at each of the time intervals based on the second parameters related to airflow, and storing, on a storage device, a representation of the parameters related to temperature in the data center during the second time period.

Description:
BACKGROUND 
       [0001]    1. Field of the Invention 
         [0002]    At least one embodiment in accordance with the present invention relates generally to systems and methods for data center management and design, and more specifically, to systems and methods for predicting cooling performance within a data center upon the occurrence of one or more transient events related to cooling suppliers or cooling consumers. 
         [0003]    2. Discussion of Related Art 
         [0004]    In response to the increasing demands of information-based economies, information technology networks continue to proliferate across the globe. One manifestation of this growth is the centralized network data center. A centralized network data center typically consists of various information technology equipment, collocated in a structure that provides network connectivity, electrical power and cooling capacity. Often the equipment is housed in specialized enclosures termed “racks” which integrate these connectivity, power and cooling elements. In some data center configurations, these rows are organized into hot and cold aisles to decrease the cost associated with cooling the information technology equipment. A raised floor having an air plenum beneath the floor is typically used for providing cooling air to the racks. Cool air is distributed from the air plenum to the racks through perforated tiles having open areas. 
         [0005]    Various processes and software applications, such as the data center management systems available from American Power Conversion (APC) Corporation of West Kingston, RI, have been developed to aid data center personnel in designing and maintaining efficient and effective data center configurations. These tools often guide data center personnel through activities such as designing the data center structure, positioning equipment within the data center prior to installation and repositioning equipment after construction and installation are complete. Thus, conventional tool sets provide data center personnel with a standardized and predictable design methodology. 
       SUMMARY OF THE INVENTION 
       [0006]    A first aspect of the invention is directed to a computer-implemented method for evaluating cooling performance of equipment in a data center, the equipment including a plurality of equipment racks and at least one cooling provider. The method includes receiving data related to types of equipment and an arrangement of equipment in the data center, determining first parameters related to airflow and parameters related to temperature in at least a portion of the data center at a first period in time, receiving a description of a transient event affecting one of airflow and temperature in the at least a portion of the data center and occurring at a second time, subsequent to the first time period, breaking a second time period subsequent to the second time into a plurality of time intervals, determining second parameters related to airflow in the at least a portion of the data center during one of the plurality of time intervals, determining the parameters related to temperature in the portion of the data center at each of the plurality of time intervals based on the second parameters related to airflow, and storing, on a storage device, a representation of the parameters related to temperature in the portion of the data center during the second time period. 
         [0007]    In accordance with some embodiments, receiving the description of the transient event comprises receiving a description of a period of time over which the transient event affects one of the airflow and the temperature in the at least a portion of the data center. 
         [0008]    In accordance with some embodiments, the method further comprises determining a temperature of inlet air of each of the plurality of equipment racks during each of the plurality of time intervals of the second time period. 
         [0009]    In accordance with some embodiments, the method further comprises providing an indication of whether any of the plurality of equipment racks achieves an unacceptable temperature during a user selectable time period subsequent to the second time. 
         [0010]    In accordance with some embodiments, the method further comprises providing an indication of a time period subsequent to the second time during which an equipment rack of the plurality of equipment racks receives inlet air a temperature below a user defined acceptable temperature. 
         [0011]    In accordance with some embodiments, one of the first parameters related to airflow and the second parameters related to airflow are determined using one of a CFD process and a potential flow model analysis. 
         [0012]    In accordance with some embodiments, determining the parameters related to temperature includes computationally dividing the at least a portion of the data center into a plurality of cells and for each cell of the plurality of cells determining a temperature of the cell by calculating heat transfer into the cell from any adjacent cells. 
         [0013]    In accordance with some embodiments, a temperature of one of an exhaust of each of the plurality of equipment racks and a supply of the at least one cooling provider during each of the plurality of time intervals of the second time period is calculated using an internal thermal mass method. 
         [0014]    In accordance with some embodiments, the method further comprises providing an indication of a change in temperature of at least one the inlet air and an exhaust of the plurality of equipment racks during the second time period. 
         [0015]    In accordance with some embodiments, one of the first parameters related to airflow and the second parameters related to airflow in the portion of the data center are determined using a computational method independent of a different computational method used to determine the parameters related to temperature in the portion of the data center. 
         [0016]    Another aspect of the invention is directed to a system for evaluating equipment in a data center, the equipment including a plurality of equipment racks, and at least one cooling provider. The system includes an interface and a controller coupled to the interface. The controller is configured to receive data related to types of equipment and an arrangement of equipment in the data center, determine first parameters related to airflow and parameters related to temperature in at least a portion of the data center at a first period in time, receive a description of a transient event affecting one of airflow and temperature in the at least a portion of the data center and occurring at a second time, subsequent to the first time period, break a second time period subsequent to the second time into a plurality of time intervals, determine second parameters related to airflow in the at least a portion of the data center during one of the plurality of time intervals, determine the parameters related to temperature in the portion of the data center at each of the plurality of time intervals based on the second parameters related to airflow, and store, on a storage device, a representation of the parameters related to temperature in the portion of the data center during the second time period. 
         [0017]    In accordance with some embodiments, the controller is further configured to determine a temperature of inlet air of each of the plurality of equipment racks during each of the plurality of time intervals of the second time period. 
         [0018]    In accordance with some embodiments, the controller is further configured to determine the temperature of the inlet air of each of the plurality of equipment racks during each of the plurality of time intervals of the second time period using an internal thermal mass method. 
         [0019]    In accordance with some embodiments, the controller is configured to determine one of the first parameters related to airflow and the second parameters related to airflow in the portion of the data center using an algebraic model and to determine the parameters related to temperature in the portion of the data center using a Temperature Model. 
         [0020]    In accordance with some embodiments, the controller is configured to determine one of the first parameters related to airflow and the second parameters related to airflow using one of a CFD process and a potential flow model analysis. 
         [0021]    Another aspect of the invention is directed to a computer readable medium having stored thereon sequences of instruction including instructions that will cause a processor to receive data related to types of equipment and an arrangement of equipment in the data center, determine first parameters related to airflow and parameters related to temperature in at least a portion of the data center at a first period in time, receive a description of a transient event affecting one of airflow and temperature in the at least a portion of the data center and occurring at a second time, subsequent to the first time period, break a second time period subsequent to the second time into a plurality of time intervals, determine second parameters related to airflow in the at least a portion of the data center during one of the plurality of time intervals, determine the parameters related to temperature in the portion of the data center at each of the plurality of time intervals based on the second parameters related to airflow, and store, on a storage device, a representation of the parameters related to temperature in the portion of the data center during the second time period. 
         [0022]    In accordance with some embodiments, the sequences of instructions further include instructions that will cause the processor to determine a temperature of air received by an inlet of each of the plurality of equipment racks during each of the plurality of time intervals of the second time period. 
         [0023]    In accordance with some embodiments, the sequences of instructions further include instructions that will cause the processor to provide an indication of whether any of the plurality of equipment racks achieves an unacceptable temperature during a user selectable time period subsequent to the second time. 
         [0024]    In accordance with some embodiments, the sequences of instructions further include instructions that will cause the processor to provide an indication a cooling runtime subsequent to the second time of the plurality of equipment racks. 
         [0025]    In accordance with some embodiments, the sequences of instructions further include instructions that will cause the processor to provide an indication of a change in temperature of at least one of inlet air and an exhaust of the plurality of equipment racks during the second time period. 
         [0026]    In accordance with some embodiments, the sequences of instructions further include instructions that will cause the processor to determine the temperature of inlet air of each of the plurality of equipment racks during each of the plurality of time intervals of the second time period using an internal thermal mass method. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0027]    The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. In the drawings: 
           [0028]      FIG. 1  is a block diagram of one example of a computer system with which various aspects in accord with the present invention may be implemented; 
           [0029]      FIG. 2  a schematic of one example of a distributed system including a data center management system; 
           [0030]      FIG. 3  is a flowchart of a process in accordance with one example; 
           [0031]      FIG. 4  is a schematic illustration of a small data center populated with one rack, one cooler, and one heated block; 
           [0032]      FIG. 5  demonstrates the use of grid cells in accordance with at least one example; 
           [0033]      FIG. 6  is an interface of a software tool in accordance with one example; 
           [0034]      FIG. 7  is a schematic diagram of a data center in accordance with on example; 
           [0035]      FIG. 8A  is a schematic diagram of the data center of  FIG. 7  at a first time period after the failure of a cooler; 
           [0036]      FIG. 8B  is a schematic diagram of the data center of  FIG. 7  at a second time period after the failure of a cooler; 
           [0037]      FIG. 9  is a schematic diagram of the data center of  FIG. 7  indicating cooling runtime after failure of a cooler; 
           [0038]      FIG. 10  is an example of an illustration of temperature vs. time for racks in the data center of  FIG. 7  after failure of a cooler; 
           [0039]      FIG. 11A  is an example of an illustration of temperature distribution in a data center at a specific time after a cooling system event; and 
           [0040]      FIG. 11B  is an example of an illustration of temperature over time for a rack in a data center after a cooling system event. 
       
    
    
     DETAILED DESCRIPTION 
       [0041]    At least some embodiments in accordance with the present invention relate to systems and processes through which a user may design and analyze data center configurations. These systems and processes may facilitate this design and analysis activity by allowing the user to create models of data center configurations from which performance metrics may be determined Both the systems and the user may employ these performance metrics to determine alternative data center configurations that meet various design objectives. Further, in at least one embodiment, a system provides modeling and prediction of airflow for a proposed layout of a data center equipment and also provides prediction of cooling performance for an installed or planned data center which incorporates the effect of transient events such as enablement or a failure of a portion of a cooling system or enablement or disablement of a heat producing piece of equipment. 
         [0042]    As described in U.S. Pat. No. 7,991,592, titled “System and Method for Evaluating Equipment Rack Cooling,” issued Aug. 2, 2011 (referred to herein as “the &#39;592 patent”), in U.S. patent application Ser. No. 11/342,300, titled “Methods and Systems for Managing Facility Power and Cooling,” filed Jan. 27, 2006 (referred to herein as “the &#39;300 application”), in U.S. patent application Ser. No. 12/884,832, titled “System and Method for Predicting Perforated Tile Airflow in a Data Center,” filed Sep. 17, 2010 (referred to herein as “the &#39;832 Application”), and U.S. patent application Ser. No. 12/795,862, titled “System and Method for Predicting Temperature Values in a Data Center,” filed Jun. 8, 2010 (referred to herein as “the &#39;862 application”), each of which are assigned to the assignee of the present application, and each of which is hereby incorporated herein by reference in its entirety for all purposes, typical equipment racks in modem data centers draw cooling air into the front of the rack and exhaust air out of the rear of the rack. The equipment racks and in-row coolers are typically arranged in rows in an alternating front/back arrangement creating alternating hot and cool aisles in a data center with the front of each row of racks facing the cool aisle and the rear of each row of racks facing the hot aisle. Adjacent rows of equipment racks separated by a cool aisle may be referred to as a cool aisle cluster, and adjacent rows of equipment racks separated by a hot aisle may be referred to as a hot aisle cluster. Further, single rows of equipment may also be considered to form both a cold and a hot aisle cluster by themselves. A row of equipment racks may be part of multiple hot aisle clusters and multiple cool aisle clusters. In descriptions and claims herein, equipment in racks, the racks themselves, or other heat producing equipment may be referred to as cooling consumers, and in-row cooling units, computer room air conditioners (CRACs), computer room air handlers (CRAHs), and/or other forms of cooling equipment may be referred to as cooling providers. In the referenced applications, tools are provided for analyzing the cooling performance of a cluster of racks in a data center. In these tools, multiple analyses may be performed on different layouts to attempt to optimize the cooling performance of the data center. 
         [0043]    In at least one embodiment, a method is provided for performing, in real-time, an analysis on a layout of equipment in a data center for providing predictions of air temperatures within and at inlets and exhausts of equipments racks and cooling providers and the flow rate and temperature of air at various locations in a data center. The air temperature predictions may incorporate predictions of the change in airflow rate and/or temperature over time upon the occurrence of a change in the performance of at least part of a cooling system and/or a cooling consumer. Aspects disclosed herein in accordance with the present embodiments, are not limited in their application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. These aspects are capable of assuming other embodiments and of being practiced or of being carried out in various ways. Examples of specific implementations are provided herein for illustrative purposes only and are not intended to be limiting. In particular, acts, elements and features discussed in connection with any one or more embodiments are not intended to be excluded from a similar role in any other embodiments. 
         [0044]    For example, according to one embodiment of the present invention, a computer system is configured to perform any of the functions described herein, including but not limited to, configuring, modeling, and presenting information regarding specific data center configurations. Further, computer systems in embodiments may be used to automatically measure environmental parameters in a data center, and control equipment, such as chillers or coolers to optimize performance. Moreover, the systems described herein may be configured to include or exclude any of the functions discussed herein. Thus, the embodiments are not limited to a specific function or set of functions. Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use herein of “including,” “comprising,” “having,” “containing,” “involving,” and variations thereof is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. 
       Computer System 
       [0045]    Various aspects and functions described herein in accordance with the present embodiments may be implemented as hardware or software on one or more computer systems. There are many examples of computer systems currently in use. These examples include, among others, network appliances, personal computers, workstations, mainframes, networked clients, servers, media servers, application servers, database servers, and web servers. Other examples of computer systems may include mobile computing devices, such as cellular phones and personal digital assistants, and network equipment, such as load balancers, routers and switches. Further, aspects in accordance with the present embodiments may be located on a single computer system or may be distributed among a plurality of computer systems connected to one or more communications networks. 
         [0046]    For example, various aspects and functions may be distributed among one or more computer systems configured to provide a service to one or more client computers, or to perform an overall task as part of a distributed system. Additionally, aspects may be performed on a client-server or multi-tier system that includes components distributed among one or more server systems that perform various functions. Thus, the embodiments are not limited to executing on any particular system or group of systems. Further, aspects may be implemented in software, hardware or firmware, or any combination thereof. Thus, aspects in accordance with the present embodiments may be implemented within methods, acts, systems, system elements and components using a variety of hardware and software configurations, and the embodiments are not limited to any particular distributed architecture, network, or communication protocol. 
         [0047]      FIG. 1  shows a block diagram of a distributed computer system  100 , in which various aspects and functions in accord with the present embodiments may be practiced. Distributed computer system  100  may include one more computer systems. For example, as illustrated, distributed computer system  100  includes computer systems  102 ,  104 , and  106 . As shown, computer systems  102 ,  104 , and  106  are interconnected by, and may exchange data through, communication network  108 . Network  108  may include any communication network through which computer systems may exchange data. To exchange data using network  108 , computer systems  102 ,  104 , and  106  and network  108  may use various methods, protocols and standards, including, among others, token ring, Ethernet, wireless Ethernet, Bluetooth, TCP/IP, UDP, Http, FTP, SNMP, SMS, MMS, SS7, Json, Soap, and Corba. To ensure data transfer is secure, computer systems  102 ,  104 , and  106  may transmit data via network  108  using a variety of security measures including TLS, SSL or VPN among other security techniques. While distributed computer system  100  illustrates three networked computer systems, distributed computer system  100  may include any number of computer systems and computing devices, networked using any medium and communication protocol. 
         [0048]    Various aspects and functions in accordance with the present embodiments may be implemented as specialized hardware or software executing in one or more computer systems including computer system  102  shown in  FIG. 1 . As depicted, computer system  102  includes processor  110 , memory  112 , bus  114 , interface  116 , and storage  118 . Processor  110  may perform a series of instructions that result in manipulated data. Processor  110  may be a commercially available processor such as an Intel Pentium, Motorola PowerPC, SGI MIPS, Sun UltraSPARC, or Hewlett-Packard PA-RISC processor, but may be any type of processor, multi-processor, microprocessor or controller as many other processors and controllers are available. Processor  110  is connected to other system elements, including one or more memory devices  112 , by bus  114 . 
         [0049]    Memory  112  may be used for storing programs and data during operation of computer system  102 . Thus, memory  112  may be a relatively high performance, volatile, random access memory such as a dynamic random access memory (DRAM) or static memory (SRAM). However, memory  112  may include any device for storing data, such as a disk drive or other non-volatile, non-transitory, storage device. Various embodiments in accordance with the present invention may organize memory  112  into particularized and, in some cases, unique structures to perform the aspects and functions disclosed herein. 
         [0050]    Components of computer system  102  may be coupled by an interconnection element such as bus  114 . Bus  114  may include one or more physical busses, for example, busses between components that are integrated within a same machine, but may include any communication coupling between system elements including specialized or standard computing bus technologies such as IDE, SCSI, PCI, and InfiniB and. Thus, bus  114  enables communications, for example, data and instructions, to be exchanged between system components of computer system  102 . 
         [0051]    Computer system  102  also includes one or more interface devices  116  such as input devices, output devices, and combination input/output devices. Interface devices may receive input or provide output. More particularly, output devices may render information for external presentation. Input devices may accept information from external sources. Examples of interface devices include keyboards, mouse devices, trackballs, microphones, touch screens, printing devices, display screens, speakers, network interface cards, etc. Interface devices allow computer system  102  to exchange information and communicate with external entities, such as users and other systems. 
         [0052]    Storage system  118  may include a computer readable and writeable, nonvolatile, non-transitory, storage medium in which instructions are stored that define a program to be executed by the processor. Storage system  118  also may include information that is recorded, on or in, the medium, and this information may be processed by the program. More specifically, the information may be stored in one or more data structures specifically configured to conserve storage space or increase data exchange performance. The instructions may be persistently stored as encoded signals, and the instructions may cause a processor to perform any of the functions described herein. The medium may, for example, be optical disk, magnetic disk, or flash memory, among others. In operation, the processor or some other controller may cause data to be read from the nonvolatile recording medium into another memory, such as memory  112 , that allows for faster access to the information by the processor than does the storage medium included in storage system  118 . The memory may be located in storage system  118  or in memory  112 , however, processor  110  may manipulate the data within the memory  112 , and then may copy the data to the medium associated with storage system  118  after processing is completed. A variety of components may manage data movement between the medium and integrated circuit memory element and the presently described embodiments are not limited thereto. Further, the embodiments are not limited to a particular memory system or data storage system. 
         [0053]    Although computer system  102  is shown by way of example as one type of computer system upon which various aspects and functions in accordance with the present embodiments may be practiced, any aspects of the presently disclosed embodiments are not limited to being implemented on the computer system as shown in  FIG. 1 . Various aspects and functions in accord with the presently disclosed embodiments may be practiced on one or more computers having a different architectures or components than that shown in  FIG. 1 . For instance, computer system  102  may include specially-programmed, special-purpose hardware, such as for example, an application-specific integrated circuit (ASIC) tailored to perform a particular operation disclosed herein. While another embodiment may perform the same function using several general-purpose computing devices running MAC OS System X with Motorola PowerPC processors and several specialized computing devices running proprietary hardware and operating systems. 
         [0054]    Computer system  102  may be a computer system including an operating system that manages at least a portion of the hardware elements included in computer system  102 . Usually, a processor or controller, such as processor  110 , executes an operating system which may be, for example, a Windows-based operating system such as Windows NT, Windows 2000 (Windows ME), Windows XP, or Windows Vista operating systems, available from the Microsoft Corporation, a MAC OS System X operating system available from Apple Computer, one of many Linux-based operating system distributions, for example, the Enterprise Linux operating system available from Red Hat Inc., a Solaris operating system available from Sun Microsystems, or a UNIX operating system available from various sources. Many other operating systems may be used, and embodiments are not limited to any particular implementation. 
         [0055]    The processor and operating system together define a computer platform for which application programs in high-level programming languages may be written. These component applications may be executable, intermediate, for example, C−, bytecode or interpreted code which communicates over a communication network, for example, the Internet, using a communication protocol, for example, TCP/IP. Similarly, aspects in accord with the presently disclosed embodiments may be implemented using an object-oriented programming language, such as .Net, SmallTalk, Java, C++, Ada, or C# (C-Sharp). Other object-oriented programming languages may also be used. Alternatively, functional, scripting, or logical programming languages may be used. 
         [0056]    Additionally, various aspects and functions in accordance with the presently disclosed embodiments may be implemented in a non-programmed environment, for example, documents created in HTML, XML, or other format that, when viewed in a window of a browser program, render aspects of a graphical-user interface or perform other functions. Further, various embodiments in accord with the present invention may be implemented as programmed or non-programmed elements, or any combination thereof. For example, a web page may be implemented using HTML while a data object called from within the web page may be written in C++. Thus, the presently disclosed embodiments are not limited to a specific programming language and any suitable programming language could also be used. 
         [0057]    A computer system included within an embodiment may perform additional functions outside the scope of the presently disclosed embodiments. For instance, aspects of the system may be implemented using an existing commercial product, such as, for example, Database Management Systems such as SQL Server available from Microsoft of Seattle Wash., Oracle Database from Oracle of Redwood Shores, Calif., and MySQL from MySQL AB, a subsidiary of Oracle or integration software such as Web Sphere middleware from IBM of Armonk, N.Y. However, a computer system running, for example, SQL Server may be able to support both aspects in accord with the presently disclosed embodiments and databases for sundry applications. 
       Example System Architecture 
       [0058]      FIG. 2  presents a context diagram including physical and logical elements of distributed system  200 . As shown, distributed system  200  is specially configured in accordance with the presently disclosed embodiments. The system structure and content recited with regard to  FIG. 2  is for exemplary purposes only and is not intended to limit the embodiments to the specific structure shown in  FIG. 2 . As will be apparent to one of ordinary skill in the art, many variant system structures can be architected without deviating from the scope of the presently disclosed embodiments. The particular arrangement presented in  FIG. 2  was chosen to promote clarity. 
         [0059]    Information may flow between the elements, components, and subsystems depicted in  FIG. 2  using any technique. Such techniques include, for example, passing the information over the network via TCP/IP, passing the information between modules in memory and passing the information by writing to a file, database, or some other non-volatile storage device. Other techniques and protocols may be used without departing from the scope of the presently disclosed embodiments. 
         [0060]    Referring to  FIG. 2 , system  200  includes user  202 , interface  204 , data center design and management system  206 , communications network  208 , and data center database  210 . System  200  may allow user  202 , such as a data center architect or other data center personnel, to interact with interface  204  to create or modify a model of one or more data center configurations. According to one embodiment, interface  204  may include aspects of the floor editor and the rack editor as disclosed in Patent Cooperation Treaty Application No. PCT/US08/63675, titled “Methods and Systems for Managing Facility Power and Cooling,” filed on May 15, 2008, which is incorporated herein by reference in its entirety and is hereinafter referred to as PCT/US08/63675. In other embodiments, interface  204  may be implemented with specialized facilities that enable user  202  to design, in a drag and drop fashion, a model that includes a representation of the physical layout of a data center or any subset thereof. This layout may include representations of data center structural components as well as data center equipment. The features of interface  204 , as may be found in various embodiments in accordance with the present invention, are discussed further below. In at least one embodiment, information regarding a data center is entered into system  200  through the interface, and assessments and recommendations for the data center are provided to the user. Further, in at least one embodiment, optimization processes may be performed to optimize cooling performance and energy usage of the data center. 
         [0061]    As shown in  FIG. 2 , data center design and management system  206  presents data design interface  204  to user  202 . According to one embodiment, data center design and management system  206  may include the data center design and management system as disclosed in PCT/US08/63675. In this embodiment, design interface  204  may incorporate functionality of the input module, the display module and the builder module included in PCT/US08/63675 and may use the database module to store and retrieve data. 
         [0062]    As illustrated, data center design and management system  206  may exchange information with data center database  210  via network  208 . This information may include any information needed to support the features and functions of data center design and management system  206 . For example, in one embodiment, data center database  210  may include at least some portion of the data stored in the data center equipment database described in PCT/US08/63675. In another embodiment, this information may include any information needed to support interface  204 , such as, among other data, the physical layout of one or more data center model configurations, the production and distribution characteristics of the cooling providers included in the model configurations, the consumption characteristics of the cooling consumers in the model configurations, and a listing of equipment racks and cooling providers to be included in a cluster. 
         [0063]    In one embodiment, data center database  210  may store types of cooling providers, the amount of cool air provided by each type of cooling provider, and a temperature of cool air provided by the cooling provider. Thus, for example, data center database  210  includes records of a particular type of CRAC unit that is rated to deliver airflow at the rate of 5,600 cubic feet per minute (cfm) at a temperature of 68 degrees Fahrenheit. In addition, the data center database  210  may store one or more cooling metrics, such as inlet and outlet temperatures of the CRACs and inlet and exhaust temperatures of one or more equipment racks. The temperatures may be periodically measured and input into the system, or in other embodiments, the temperatures may be continuously monitored using devices coupled to the system  200 . 
         [0064]    Data center database  210  may take the form of any logical construction capable of storing information on a computer readable medium including, among other structures, flat files, indexed files, hierarchical databases, relational databases or object oriented databases. The data may be modeled using unique and foreign key relationships and indexes. The unique and foreign key relationships and indexes may be established between the various fields and tables to ensure both data integrity and data interchange performance. 
         [0065]    The computer systems shown in  FIG. 2 , which include data center design and management system  206 , network  208  and data center equipment database  210 , each may include one or more computer systems. As discussed above with regard to  FIG. 1 , computer systems may have one or more processors or controllers, memory and interface devices. The particular configuration of system  200  depicted in  FIG. 2  is used for illustration purposes only and embodiments of the invention may be practiced in other contexts. Thus, embodiments of the invention are not limited to a specific number of users or systems. 
       Data Center Airflow and Temperature Prediction Tool 
       [0066]    Aspects and embodiments of a Potential Flow Model (PFM) to predict airflow patterns, pressures, air temperatures, and capture indices for data center applications was described in U.S. patent application Ser. No. 12/970,605, titled “System and Methods for Rack Cooling Analysis,” filed Dec. 16, 2010 (referred to herein as “the &#39;605 application”), which is assigned to the assignee of the present application, and which is hereby incorporated herein by reference in its entirety for all purposes. In some data center configurations incorporating equipment racks and coolers, the ability to predict how temperatures vary over time in a data center may be important when considering scenarios such as the loss of power. For example, a data center operator may like to know how long it takes each rack in a data center to reach some maximum acceptable temperature subject to a specific cooling-failure event. 
         [0067]    One method for predicting the transient cooling performance of a data center includes a model which assumes that all the air in the data center is at a well-mixed, average temperature. Another method includes performing a full Computational Fluid Dynamics (CFD) analysis on the data center for a time period before, including, and after a specific transient event related to a cooling consumer and/or provider. The former method can be too simplistic and may cause the user to miss important local details or unnecessarily overdesign the cooling infrastructure. CFD can, in theory, provide a desired level of detail but it is typically extremely slow, expensive, and doesn&#39;t always converge to a consistent result. 
         [0068]    Aspects and embodiments of the present invention provide a method by which localized or object-level transient predictions can be made without the need for a full CFD analysis. In some embodiments the airflow and temperature predictions may be computationally separated so that only a limited number of steady-state airflow patterns are calculated and transient calculations are performed primarily for temperatures. A variety of techniques can be used for computing airflows and temperatures, one combination of which is to use algebraic models for airflow prediction and then a temperature model which focuses on the primary airflow streams of interest in the data center—those associated with the inlet and outlet of each rack and cooler. Aspects and embodiments of the invention also include a novel method for accounting for the “internal” thermal mass of objects like racks and coolers which is more computationally efficient and physically realistic than some “external” heat transfer models presently employed. Methods to visualize results by coloring or otherwise visually differentiating representations of racks by “cooling runtime” or by temperature—which may include a slider bar or other adjustment mechanism for selecting a particular time—are also presented. 
         [0069]    In the discussion and examples which follow, the term “cooler” is used generically to mean all types of cooling units including chilled-water and refrigerant-based equipment such as row-based coolers, CRACs, and CRAHs. Additionally, aspects and embodiments of the invention are described with the aid of simple two-dimensional (2D) examples and example equation formulations for specific scenarios. Aspects and embodiments of the invention can be extended to more general data center layouts and three-dimensional (3D) applications without loss of generality. 
       General Airflow and Temperature Calculation Method 
       [0070]    In copending Patent Cooperation Treaty Application No. PCT/US11/66776, titled “System and Method for Prediction of Temperature Values in an Electronics System,” filed Dec. 22, 2011, which is herein incorporate by reference in its entirety for all purposes, a method is presented for coupling a Potential Flow Model (PFM) fluid-flow analysis with a solid-temperature-conduction analysis. While this approach can be used for transient data center cooling predictions and is, indeed, a subset of some embodiments of the present invention, some aspects and embodiments of the present invention cover a broader, general approach which may be employed utilizing several alternative techniques for computing airflow and temperatures. Further, aspects and embodiments of the present invention include several novel aspects unique to data center transient applications. 
         [0071]    The general solution technique of various embodiments of a method in accordance with the present invention is shown in  FIG. 3 , indicated generally at  300 . At act  310 , geometric, airflow, and thermal data for the facility are acquired and, based on user-specified transient events (e.g., cooler fans being turned off or a rack suddenly dissipating more heat), the time period to be analyzed is determined and broken down into a number of discrete periods between events. Next, at act  320 , airflow patterns and temperatures are determined for the starting conditions (e.g., steady-state conditions before a power failure at t=0). Then, the airflow patterns and temperatures are computed for each time period to be analyzed as required (acts  340 - 390 ). The airflow patterns may be updated each time there is a change of airflow boundary conditions, e.g., a cooler or rack is turned “on” or “off” while temperatures may be computed continuously over all time periods until the end of the overall analysis period. The airflow patterns may be assumed to maintain a steady state between the occurrence of transient events. 
       Airflow Pattern Predictions 
       [0072]    Airflow patterns may be determined from algebraic models, PFM, CFD, or other techniques as discussed further below. In some aspects and embodiments, either the “fundamental airflows” or the “full flow field” is determined 
       Fundamental Airflows 
       [0073]    The fundamental airflows are the airflow streams entering and exiting each rack and cooler consistent with the definitions of f ij  and g ij  discussed in the &#39;862 application. These definitions are reviewed here for completeness. f ij  is the fraction of airflow from rack i which is captured by cooling source j and, similarly, g ij  is the fraction of rack i&#39;s inlet airflow which originated from cooling source j. Together, and g ij  may characterize the airflow patterns of greatest importance to the cooling performance of the facility. 
         [0074]    Although, f ij  and g ij  may characterize data center airflow sufficiently by themselves for various aspects and embodiments of the present invention, they may also be used as the building blocks for determining Hot-Aisle Capture Indices (HACIs) and Cold-Aisle Capture Indices (CACIs): 
         [0000]    
       
         
           
             
               
                 
                   
                     HACI 
                     i 
                   
                   = 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                         
                     
                      
                     
                       f 
                       ij 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     CACI 
                     i 
                   
                   = 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                         
                     
                      
                     
                       g 
                       ij 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where N is the number of cooling sources. In the HACI calculation, N may include all local cooling extracts (cooler returns, local exhaust grilles, etc.) and, in the CACI calculation, N may include all local cooling supplies. 
         [0075]    In summary, f ij  and g ij  are the fundamental building blocks of HACI and CACI, respectively, and they may completely characterize the fundamental airflow details with which a data center designer or operator should be concerned. During a power failure or other event in which airflow boundary conditions change, and g ij  may be recalculated. An example of such an event is when some or all coolers are temporarily turned off. 
         [0076]    Full Flow Field 
         [0077]    The traditional approach to predicting data center airflow is to use CFD to determine airflow velocities at essentially all locations in the data center. This is an example of the Full Flow Field technique. This technique may provide greater solution resolution and possibly greater accuracy than the Fundamental Airflows technique. The PFM approach is another example of a Full Flow Field technique. 
         [0078]    Algebraic Model 
         [0079]    As discussed in the &#39;592 patent and the &#39;862 application, algebraic models have been developed to predict both cold and hot-aisle Capture Indexes (CIs) for racks in various configurations. An advantage of the algebraic calculators is that calculations are essentially instantaneous and they are guaranteed to produce a result that, at least, trends in the right direction. The f ij  and g ij  fundamental-airflow building blocks can be extracted directly from the algebraic calculators and, for various aspects and embodiments of the present transient-temperature-prediction application, Capture Indices may not be explicitly required. 
         [0080]    Algebraic models have been developed for essentially all practical groupings of equipment found in a data center so that, with proper recognition of groups and multiple applications of the calculators, all f ij s and g ij s can be determined 
         [0081]    Potential Flow Model (PFM) 
         [0082]    Airflow patterns can also be determined from a PFM analysis as described in the &#39;605 application. PFM analysis may provide more local detail than algebraic models and may work reasonably well for any general application whereas algebraic models may work best for data centers that can be broken down into well-defined equipment clusters bounding common cold or hot aisles. PFM can be solved quickly (perhaps a few seconds for each airflow pattern update) and always converges to a result. PFM analysis can be used as a flow-only model to compute f ij  and g ij  values to be used subsequently for the air temperature calculations or air temperatures may be computed directly in the PFM analysis. In the latter case, one temperature is predicted for every computational grid cell, providing additional resolution. 
         [0083]    Computational Fluid Dynamics (CFD) Model 
         [0084]    CFD in the context of various aspects and embodiments of the present invention may mean using CFD to solve only the required number of discrete airflow patterns over the course of the transient analysis—not using CFD to solve the full transient problem in which the evolution of airflow patterns is rigorously updated at each time step. The latter may be much too slow (perhaps days of computation time) for practical applications. The former approach may still be much slower (perhaps hours) than PFM but offers current CFD practitioners (who may not have access to the algebraic or PFM tools) a way to perform an analysis which would otherwise be impossible. Furthermore, CFD may offer a high degree of prediction accuracy. As with PFM, CFD can be used as a flow-only model to compute f ij  and g ij  values to be used subsequently for air temperature calculations or air temperatures may be computed directly in the CFD analysis. The former approach may further reduce the solution time. 
       Air Temperature Predictions 
       [0085]    Temperature Model 
         [0086]    Once airflow patterns are characterized by f ij s and g ij s, it is possible to estimate all of the temperatures of interest (rack and cooler inlet and outlet temperatures plus one ambient temperature), as discussed in the &#39;862 application. This process will be referred to here as the “Temperature Model.” A basic assumption in this model is that there exists one well-mixed temperature for the airflow stream entering and exiting each rack and cooler. The airflow from each local cooler supply to each rack inlet is tracked as is the airflow from each rack exhaust to each local cooler return. Other airflow interactions are assumed to take place with the surrounding well-mixed ambient environment of the data center. Rack-to-rack and cooler-to-cooler interactions could be modeled directly, but, in this example, un-captured rack exhaust heats the ambient environment which in turn increases the inlet temperature of other racks. Traditional CRAC units remotely located from racks are assumed to draw airflow directly from the ambient. The Temperature Model is a physics-based technique; temperatures are rigorously computed based on the principles of conservation of mass and energy applied to a model of a known flow field. The Temperature Model itself does not employ any additional empiricism. 
         [0087]      FIG. 4  schematically shows an example of a small data center populated with one rack R i , one cooler C j , and one heated block B k  which has a power dissipation of P k . The dashed line is a control volume around the data center ambient air; rack-cooler airflow interactions take place outside the control volume while airflow interactions between solids, such as equipment and walls, and the ambient air occur across the control volume boundaries. 
         [0088]    Balancing the transient energy flow across the control volume boundaries of  FIG. 4  and generalizing to n racks, N c  local cooling returns, and m heated blocks leads to: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ρ 
                        
                       
                           
                       
                        
                       
                         c 
                         p 
                       
                        
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           n 
                         
                          
                         
                             
                         
                          
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     1 
                                   
                                   
                                     N 
                                     c 
                                   
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   f 
                                   ij 
                                 
                               
                             
                             ) 
                           
                            
                           
                             Q 
                             i 
                             R 
                           
                            
                           
                             T 
                             i 
                             RE 
                           
                         
                       
                     
                     + 
                     
                       ρ 
                        
                       
                           
                       
                        
                       
                         c 
                         p 
                       
                        
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           N 
                         
                          
                         
                             
                         
                          
                         
                           
                             ( 
                             
                               
                                 Q 
                                 j 
                                 C 
                               
                               - 
                               
                                 
                                   ∑ 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   n 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     g 
                                     ij 
                                   
                                    
                                   
                                     Q 
                                     i 
                                     R 
                                   
                                 
                               
                             
                             ) 
                           
                            
                           
                             T 
                             j 
                             CS 
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         m 
                       
                        
                       
                           
                       
                        
                       
                         P 
                         k 
                       
                     
                     + 
                     
                       ρ 
                        
                       
                           
                       
                        
                       
                         c 
                         p 
                       
                        
                       
                         Q 
                         l 
                       
                        
                       
                         T 
                         l 
                       
                     
                   
                   = 
                   
                     
                       ρ 
                        
                       
                           
                       
                        
                       
                         c 
                         p 
                       
                        
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           
                             N 
                             c 
                           
                         
                          
                         
                             
                         
                          
                         
                           
                             ( 
                             
                               
                                 Q 
                                 j 
                                 C 
                               
                               - 
                               
                                 
                                   ∑ 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   n 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     f 
                                     ij 
                                   
                                    
                                   
                                     Q 
                                     i 
                                     R 
                                   
                                 
                               
                             
                             ) 
                           
                            
                           
                             T 
                             amb 
                           
                         
                       
                     
                     + 
                     
                       ρ 
                        
                       
                           
                       
                        
                       
                         c 
                         p 
                       
                        
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           n 
                         
                          
                         
                             
                         
                          
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     1 
                                   
                                   N 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   g 
                                   ij 
                                 
                               
                             
                             ) 
                           
                            
                           
                             Q 
                             i 
                             R 
                           
                            
                           
                             T 
                             amb 
                           
                         
                       
                     
                     + 
                     
                       ρ 
                        
                       
                           
                       
                        
                       
                         c 
                         p 
                       
                        
                       
                         Q 
                         CRAC 
                       
                        
                       
                         T 
                         amb 
                       
                     
                     + 
                     
                       
                         h 
                         W 
                       
                        
                       
                         
                           A 
                           W 
                         
                          
                         
                           ( 
                           
                             
                               T 
                               amb 
                             
                             - 
                             
                               T 
                               W 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       ρ 
                        
                       
                           
                       
                        
                       
                         c 
                         p 
                       
                        
                       
                         v 
                         R 
                       
                        
                       
                         
                            
                           
                             T 
                             amb 
                           
                         
                         
                            
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0089]    where Q i   R , Q j   C  are the airflow rates of rack i and cooling source j respectively. Q l  and Q CRAC  are the total leakage and total CRAC airflow rates respectively. T i   RE , T j   CS , and T l  are the exhaust temperature of rack i, the supply temperature of cooler j, and the leakage airflow temperature. T amb  and T W  are the ambient data center room temperature and the average wall temperature, respectively. The product of the density and specific heat of air, ρc p , can be taken as a constant equal to 1196 J/kg° C. The heat transfer coefficient h W  is an average value for all wall surfaces and A W  is the total wall surface area. v R  is the volume of air in the data center room excluding the volume of equipment and the volume of air occupied by the fundamental airflow streams characterized by f ij s and g ij s. In practice, the latter can be estimated as the volume confined in the hot and cold aisles. Note that the heated blocks have no temperature associated with them; they simply add heat (P k ) to the room which increases the ambient temperature. 
         [0090]    The transient term in Equation (3) can be approximated by a linear equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                      
                     
                         
                     
                      
                     
                       c 
                       p 
                     
                      
                     
                       v 
                       R 
                     
                      
                     
                       
                          
                         
                           T 
                           amb 
                         
                       
                       
                          
                         t 
                       
                     
                   
                   ≈ 
                   
                     ρ 
                      
                     
                         
                     
                      
                     
                       c 
                       p 
                     
                      
                     
                       v 
                       R 
                     
                      
                     
                       
                         
                            
                           
                             T 
                             amb 
                           
                         
                         - 
                         
                           T 
                           amb 
                           - 
                         
                       
                       
                         
                            
                           Δ 
                         
                          
                         
                             
                         
                          
                         t 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0091]    where T amb  is the ambient temperature computed from the previous time step. 
         [0092]    Other equations, as described in the &#39;862 application, model the mixing of airflow streams entering and exiting each rack and cooler and allow all inlet and outlet temperatures to be calculated. The rack exhaust and cooler supply temperature predictions depend on the technique used to model the thermal mass of the object as explained further below. 
         [0093]    The temperature model forms a coupled set of equations which, when solved at each time step, may provide the inlet and exhaust temperatures of all racks, the return and supply temperatures of all coolers, and the single well-mixed ambient temperature. 
         [0094]    Discretization Methods—PFM and CFD 
         [0095]    With PFM and CFD, the data center air volume is divided into a discrete number of grid cells. Once airflows (and, therefore, the velocities at all cell faces) are known, the temperature of each grid cell can be determined from an energy balance on each cell. A Finite-Difference or Finite-Volume approach may be used for both PFM and CFD. Finite Element or other approaches can also be used. The PCT/US11/66776 application discusses this approach in detail in the context of a coupled PFM-conduction solver application. As discussed above, the temperature portion of the problem can be solved separately from the airflow portion, even with CFD. In this case, following embodiments of the present invention, the airflow pattern may only need be computed a limited number of times and only when airflow boundary conditions change. 
       Modeling Thermal Mass of Racks and Coolers 
       [0096]    The air and all solid objects inside or bounding the data center have “thermal mass,” meaning that it takes a certain amount of heat transfer, e.g., W, to change the temperature of the air or object by a specified amount, e.g., ° C. It is the thermal mass of (a pre-cooled) data center that allows temperatures to remain within acceptable limits for brief periods of time without cooling. Two techniques that may be utilized for modeling the thermal mass of solid objects include the External Thermal Mass Method (ETMM) and the Internal Thermal Mass Method (ITMM). 
         [0097]    External Thermal Mass Method 
         [0098]    With the approach referred to here as the External Thermal Mass Method (ETMM), the rack exhaust temperature may be computed as follows: 
         [0000]        T   i   RE   =T   i   RI   +ΔT   R   (5)
 
         [0099]    where ΔT R  is the temperature rise across each rack j resulting from the addition of a known rack power to a known airflow rate. T i   RE  is the rack exhaust temperature and T i   RI  the rack inlet temperature for a given rack i. In ETMM the thermal mass of the racks is modeled by explicitly modeling conduction heat transfer in the solid object which represents the rack. The rack&#39;s ability to store heat is then modeled by this mass and heat transfer to/from this mass occurs only at fluid-solid interfaces. 
         [0100]    In a similar fashion, transient heat transfer associated with coolers and all other solid objects takes place at the fluid-solid interfaces external to the cooler. In one scenario, cooler fans may continue to operate during a power failure but the circulation of chilled water to the cooler coils may have stopped. With the ETMM, the cooler supply temperature is equal to the cooler return temperature immediately following the power failure and the thermal mass of the cooler does not affect the temperature of the air flowing through the inside of the cooler. However, in reality, the cold coil and other internal cooler components would cause the supply temperature to rise gradually, not abruptly, following a power failure. 
         [0101]    Referring to  FIG. 5 , energy flows into and out of fluid cell i due to the known velocities through three sides and through convection at the fluid-solid interface. Additionally, the fluid volume may heat up or cool down over time. This transient effect is modeled as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     the 
                      
                     
                         
                     
                      
                     rate 
                      
                     
                         
                     
                      
                     of 
                      
                     
                         
                     
                      
                     change 
                      
                     
                         
                     
                      
                     of 
                      
                     
                         
                     
                      
                     stored 
                      
                     
                         
                     
                      
                     energy 
                   
                   = 
                   
                     
                       
                         ρ 
                         f 
                       
                        
                       
                         c 
                         p 
                         f 
                       
                        
                       
                         v 
                         f 
                       
                        
                       
                         
                            
                           
                             T 
                             i 
                             f 
                           
                         
                         
                            
                           t 
                         
                       
                     
                     ≈ 
                     
                       
                         ρ 
                         f 
                       
                        
                       
                         c 
                         p 
                         f 
                       
                        
                       
                         v 
                         f 
                       
                        
                       
                         
                           
                             T 
                             i 
                             
                               f 
                               + 
                             
                           
                           - 
                           
                             T 
                             i 
                             f 
                           
                         
                         
                           Δ 
                            
                           
                               
                           
                            
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0102]    where T i   f+  is the temperature of fluid cell i after a time step of Δt, ρ f  is the density of the fluid, c p   f  is the specific heat of the fluid, and v f =Δx 3  is the fluid cell volume. Including this term in an energy balance for grid cell i leads to the following expression for the temperature of the fluid cell at a future time: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     i 
                     
                       f 
                       + 
                     
                   
                   = 
                   
                     
                       T 
                       i 
                       f 
                     
                     + 
                     
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           t 
                         
                         
                           Δ 
                            
                           
                               
                           
                            
                           x 
                         
                       
                       [ 
                       
                         
                           
                             V 
                             W 
                           
                            
                           
                             ( 
                             
                               
                                 T 
                                 W 
                                 f 
                               
                               - 
                               
                                 T 
                                 i 
                                 f 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             h 
                             
                               
                                 ρ 
                                 f 
                               
                                
                               
                                 c 
                                 p 
                                 f 
                               
                             
                           
                            
                           
                             ( 
                             
                               
                                 T 
                                 i 
                                 s 
                               
                               - 
                               
                                 T 
                                 i 
                                 f 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0103]    where, for this case, V E , V N , and V W  are velocities across the east, north, and west cell faces respectively and V E +V N =V W  as required by conservation of mass. 
         [0104]    Similarly, an energy balance including transient heating or cooling of the solid cell of  FIG. 5  leads to: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     i 
                     
                       s 
                       + 
                     
                   
                   = 
                   
                     
                       T 
                       i 
                       s 
                     
                     + 
                     
                       
                         
                           h 
                            
                           
                               
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           t 
                         
                         
                           Δ 
                            
                           
                               
                           
                            
                           x 
                            
                           
                               
                           
                            
                           
                             ρ 
                             s 
                           
                            
                           
                             c 
                             p 
                             s 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             T 
                             i 
                             f 
                           
                           - 
                           
                             T 
                             i 
                             s 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         
                           k 
                            
                           
                               
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           t 
                         
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             x 
                             2 
                           
                            
                           
                             ρ 
                             s 
                           
                            
                           
                             c 
                             p 
                             s 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             T 
                             E 
                             s 
                           
                           + 
                           
                             T 
                             W 
                             s 
                           
                           + 
                           
                             T 
                             S 
                             s 
                           
                           - 
                           
                             3 
                              
                             
                                 
                             
                              
                             
                               T 
                               i 
                               s 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0105]    where the superscript “s” denotes “solid.” Equations (7) and (8) are “explicit” representations of the temperature in the fluid and solid cells respectively at a future time. With this approach, the temperature over all cells can be computed sequentially at a given time step. Then, these temperatures are used on the right-hand side of Equations (7) and (8) to compute temperatures at the next time step. This process continues until the desired transient period has been covered. This very straightforward solution procedure is possible due to the fact that, in Equations (7) and (8), the temperatures of all neighboring cells in Equations (7) and (8) are evaluated at the current time. It is also possible to represent the temperatures of all neighboring cells at the future time and this is called an “implicit” approach because the temperature at cell i cannot be isolated as in Equations (7) and (8). In the “implicit” approach, the temperature of all cells (T i   f+  or T i   s+ ) may be solved for simultaneously using a solver, e.g., Gauss-Seidel iteration, at each time step. The explicit approach has the advantage of great simplicity; however, it may only converge to a sensible result if sufficiently small time steps are used. The implicit method has the advantage that it will converge regardless of time-step size and therefore, since larger time steps can be used, the total solution time may be less. 
         [0106]    Internal Thermal Mass Method 
         [0107]    The Internal Thermal Mass Method (ITMM) may include the thermal mass of racks and coolers in the transient analysis while not incurring any substantial solution-time penalty above and beyond the airflow and air temperature calculations. Additionally, this method may be physically more realistic than the ETMM because most of the “access” to the bulk of thermal mass of racks and coolers is via internal airflow, not the skin (typically thin metal panels) of the object. Finally, the effective transient thermal characteristics of the rack or cooler which may be used for this method may be easier to estimate (e.g., from experiment or detailed CH)) than the equivalent characteristics in the ETMM. 
         [0108]    Equations used to apply the ITMM to a rack are as follows. Coolers and other flow objects can be modeled in an analogous manner. A transient energy balance on the entire rack yields: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           m 
                           . 
                         
                         i 
                       
                        
                       
                         c 
                         p 
                       
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                     + 
                     
                       
                         q 
                         . 
                       
                       i 
                       IT 
                     
                   
                   = 
                   
                     
                       
                         
                           m 
                           . 
                         
                         i 
                       
                        
                       
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                         p 
                       
                        
                       
                         T 
                         i 
                         RE 
                       
                     
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                           ( 
                           
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                             p 
                           
                           ) 
                         
                         i 
                         eff 
                       
                        
                       
                         
                            
                           
                             T 
                             i 
                             eff 
                           
                         
                         
                            
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0109]    where (Mc p ) i   eff  is the effective thermal mass (the product of the mass and specific heat) of the rack and {dot over (q)} i   rr  is the total power dissipated by the IT load inside the rack. T i   eff  is the effective temperature of the lumped rack mass. {dot over (m)} i  is the mass airflow rate through rack i. Assuming that all heat transfer to the rack mass occurs through some effective area with an effective heat transfer coefficient (hA) i   eff , the following equation may be obtained: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           Mc 
                           p 
                         
                         ) 
                       
                       i 
                       eff 
                     
                      
                     
                       
                          
                         
                           T 
                           i 
                           eff 
                         
                       
                       
                          
                         t 
                       
                     
                   
                   = 
                   
                     
                       
                         ( 
                         hA 
                         ) 
                       
                       i 
                       eff 
                     
                      
                     
                       ( 
                       
                         
                           T 
                           i 
                           RI 
                         
                         - 
                         
                           T 
                           i 
                           eff 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Equations (9) and (10) can be solved simultaneously to provide explicit representations of T i   eff  and T i   RE : 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     i 
                     eff 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             τ 
                             i 
                           
                           
                             
                               τ 
                               i 
                             
                             + 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               t 
                             
                           
                         
                         ) 
                       
                        
                       
                         T 
                         i 
                         
                           eff 
                           old 
                         
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             Δ 
                              
                             
                                 
                             
                              
                             t 
                           
                           
                             
                               τ 
                               i 
                             
                             + 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               t 
                             
                           
                         
                         ) 
                       
                        
                       
                         T 
                         i 
                         RI 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       T 
                       i 
                       RE 
                     
                     = 
                     
                       
                         T 
                         i 
                         RI 
                       
                       + 
                       
                         
                           
                             q 
                             . 
                           
                           i 
                           IT 
                         
                         
                           
                             
                               m 
                               . 
                             
                             i 
                           
                            
                           
                             c 
                             p 
                           
                         
                       
                       + 
                       
                         
                           ( 
                           
                             
                               τ 
                               i 
                             
                             
                               
                                 τ 
                                 i 
                               
                               + 
                               
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                             
                           
                           ) 
                         
                          
                         
                           
                             
                               ( 
                               hA 
                               ) 
                             
                             i 
                             eff 
                           
                           
                             
                               
                                 m 
                                 . 
                               
                               i 
                             
                              
                             
                               c 
                               p 
                             
                           
                         
                          
                         
                           ( 
                           
                             
                               T 
                               i 
                               
                                 eff 
                                 old 
                               
                             
                             - 
                             
                               T 
                               i 
                               RI 
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       τ 
                       i 
                     
                     ≡ 
                     
                       Rack 
                        
                       
                           
                       
                        
                       Thermal 
                        
                       
                           
                       
                        
                       Time 
                        
                       
                           
                       
                        
                       Constant 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           Mc 
                           p 
                         
                         ) 
                       
                       i 
                       eff 
                     
                     
                       
                         ( 
                         hA 
                         ) 
                       
                       i 
                       eff 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0110]    and T i   eff old  is the temperature of lumped rack mass in the previous time period. 
         [0111]    Equations (11)-(13) may then be used to estimate the rack&#39;s effective and exhaust temperature at each time step in the analysis. The rack thermal time constant which emerges from the above analysis characterizes the time scale over which transient heating or cooling of the rack takes place. For example, a large time constant implies a very large thermal mass or slow heat exchange with the airstream and the effective rack temperature will change very slowly over time. As the rack thermal time constant approaches zero, the rack exhaust temperature is the inlet temperature plus 
         [0000]    
       
         
           
             
               Δ 
                
               
                   
               
                
               
                 T 
                 i 
                 R 
               
             
             = 
             
               
                 
                   
                     q 
                     . 
                   
                   i 
                   IT 
                 
                 
                   
                     
                       m 
                       . 
                     
                     i 
                   
                    
                   
                     c 
                     p 
                   
                 
               
               . 
             
           
         
       
     
         [0112]    Coolers are modeled in an analogous fashion. There is no internal power dissipation and the heat transfer is typically in the direction from the inlet air to the effective internal surfaces of the cooler at T eff . Additionally, if the coolers continue to circulate cooling water (but perhaps at an ever increasing temperature before the chiller is returned to service), embodiments of the invention may include this effect in Equations (9) and (10). 
       Example Embodiments of the Invention 
       [0113]    Table 1 below illustrates various combinations of airflow and temperature prediction methods which may utilized in various embodiments of the present invention. As illustrated in Table 1, if only the fundamental airflows are to be calculated, the Algebraic Calculator coupled with the Temperature Model and Internal Thermal Mass Method (ITMM) for air and solid temperatures respectively may be preferred. PFM or CFD could be used to predict the fundamental airflows if solution accuracy were deemed more important than solution time, cost, stability, etc. With full field airflow calculations, PFM coupled with discretized air temperature calculations and the ITMM may be preferred. Again, CFD could be used in some embodiments for airflow predictions, if solution accuracy were deemed the most important consideration. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Fundamental 
                 Full-Field 
               
               
                   
                 Airflows 
                 Calculations 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Airflow Pattern 
                 Algebraic 
                 PFM 
               
               
                   
                 Calculation 
                 Calculator 
                 CFD 
               
               
                   
                   
                 PFM 
               
               
                   
                   
                 CFD 
               
               
                   
                 Air Temperature 
                 Temperature 
                 Discretization 
               
               
                   
                 Calculation 
                 Model 
                 Method 
               
               
                   
                 Models for Thermal 
                 ITMM 
                 ITMM 
               
               
                   
                 Mass of Racks and 
                   
                 ETMM 
               
               
                   
                 Coolers 
               
               
                   
                   
               
             
          
         
       
     
       Transient Analysis Example Input Scenarios 
       [0114]    In accordance with some embodiments, there is provided a method by which software users can specify the overall nature of a transient analysis they wish to investigate. Such an investigation may involve, for example, predicting the effect of a power failure on various temperatures in the data center. An example of an interface which a user may utilize to specify a particular scenario is illustrated in  FIG. 6 . This interface may be included in a software tool and may be presented on a display of a computer. As indicated by the checked boxes in  FIG. 6 , the user has specified that major cooling equipment excluding chillers are connected to an Uninterruptable Power Supply (UPS). Since the UPS runtime (10 min) is greater than the generator start time, the cooler fans and chilled water pumps will be able to run for an indefinite period of time (so long as the generators continue to run). The chiller, however, is not connected to a UPS (as may be the case because of its large power requirements) so the chilled water in the piping system and emergency reservoir (if applicable) will continue to circulate and heat up until the chiller is back on line. The details of such scenarios are provided in the &#39;592 patent. This example will illustrate the prediction of rack and other specific temperatures throughout the data center. For the example scenario indicated in  FIG. 6 , only one airflow pattern is predicted as racks and cooler airflow patterns are unchanged throughout the transient analysis. However, three distinct time periods exist between transient events during which air and solid-object temperatures may be analyzed:
       1. The initial steady-state period   2. The period after the power failure until the chiller re-starts   3. The period after the chiller re-starts until temperatures return to steady-state values       
 
       Algebraic Airflow 
     Temperature Model Example 
       [0118]    In the following example, the algebraic model is used to calculate airflow patterns before and after a failure event and the Temperature Model is used to compute the transient air temperature changes over time. The example assumes a data center including ten equipment racks and four coolers arranged as illustrated in  FIG. 7 , where the power utilization and airflow of each of the racks and the airflow of each of the coolers is as indicated. For convenience, the thermal mass of solid objects is not included in the example, but, in practice, the Internal Thermal Mass Method may be used with the Algebraic Airflow method and Temperature Model with almost no additional computation time. The Algebraic Airflow—Temperature Model combination allows transient scenarios to be analyzed in real time even for large, practical facilities. In this approach temperatures may be computed for the inlet and outlet of all racks and coolers—plus one well-mixed ambient temperature. In some embodiments, air temperatures everywhere in the data center may not be available for display. 
         [0119]    It is assumed that the upper-right cooler in  FIG. 7  fails at time t=0. Two airflow patterns are computed: the steady-state airflow pattern that existed prior to t=0 with all coolers running and the one after t=0 with one cooler failed. Calculations may be performed essentially instantaneously using the algebraic airflow models and the Temperature Model. 
         [0120]      FIGS. 8A and 8B  show racks patterned based on inlet temperature; a slider-bar allows the user to inspect the results at any instant in time. The temperature levels here are based on the ASHRAE Thermal Guidelines (ASHRAE. 2008. Thermal Guidelines for Data Processing Environments. Atlanta: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.,) with racks with temperatures in a recommended temperature range being indicated without patterning, and racks with temperatures in an allowable temperature range being indicated with hash marks. Racks  1 ,  4 , and  5  are within the recommended range at t=25 seconds (see  FIG. 8A ), but are above the recommended temperature threshold 45 seconds after the cooler failure (see  FIG. 8B  where these racks are illustrated with hash marks). 
         [0121]    Cooling runtime may be defined as the time it takes for a rack inlet temperature to reach its maximum allowable temperature. If the rack inlet temperature never reaches the threshold, then the cooling runtime is taken as infinity.  FIG. 9  shows how cooling runtime may be presented to the user. All times are in seconds and racks may be patterned as indicated in the legend in  FIG. 9  based on user-specified limits. In the illustrations in  FIGS. 8A ,  8 B, and  9 , it should be understood that in other embodiments, other indicators of a particular temperature range or time until a particular temperature is reached, for example, by color coding, may be used. 
         [0122]    In some embodiments, users can also view the temperature changes of each rack versus time as shown in  FIG. 10 . For this example, racks in the row opposite the cooler failure (Racks  6  and  9 , shown in  FIG. 7 ) never exceed the allowable temperature. 
       PFM Airflow 
     Discretized PFM Temperatures Example 
       [0123]    In another example, the PFM approach for computing both airflow and temperatures is used in the 2D data center layout shown in  FIG. 11A . The External Thermal Mass Method is used to model heat exchange with the cooler and rack, but, for simplicity, the cooler, rack, and all bounding walls are maintained at a temperature of 20° C. throughout the transient analysis. This assumption is equivalent to assuming that all solid objects have a very large thermal mass compared to the thermal mass of the air. This assumption could be used accurately in the very early stages of a transient analysis but may be inappropriate over a time period sufficiently long such that the temperatures of solid objects changed appreciably. In that case, if the ETMM is to be used, the solid objects would also be discretized and solid cell temperatures would be computed using equations similar to Equation (8). 
         [0124]    Prior to t=0, the cooler is operating and airflow is supplied in front of the rack through a perforated tile located immediately to the right of the rack in  FIG. 11A . At t=0, the cooler fails and the airflow pattern is subsequently driven only by the rack airflow. Two airflow patterns are computed by PFM: the initial steady-state airflow pattern including the functioning cooler and the airflow pattern after t=0 in which there is no cooler-return airflow or perforated-tile supply airflow.  FIG. 11A  shows example temperatures throughout the space at t=12 seconds.  FIG. 11B  shows the rack inlet and ambient temperatures (in this example, ambient temperature is the cell-based average room temperature) through a two minute period. Note that an important aspect of the PFM approach is that it allows the full temperature distribution in the data center to be displayed to the user at any desired time during the transient analysis. 
         [0125]    In embodiments above, processes and systems are provided that can determine relevant temperatures in a data center, and model the effect of transient disruptions in cooling system operations on these temperatures. The systems and methods can be used to provide optimized design of a data center by using results of the systems and methods to change the actual layout and/or capacity of equipment or the proposed layout and/or capacity of equipment. In processes described above, values related to data center cooling, including airflows and temperatures may be determined. In at least some embodiments, the values determined are predictions for actual values that will occur in a data center having the parameters modeled. In methods of at least one embodiment of the invention, after successful modeling of a cluster in a data center, the results of the model may be used as part of a system to order equipment, ship equipment and install equipment in a data center as per the designed layout. 
         [0126]    In at least some embodiments described herein, airflow in a plenum is described as being generated by a CRAC. Systems and methods described herein can be used with other types of sources of air in plenums, including other types of cooling devices and fans. In at least some embodiments, methods are described as determining specific airflows and the change in these airflows resulting from a disruption in the operation of a cooling system. In at least some embodiments, the determination is a prediction or estimation of actual airflows. 
         [0127]    In at least some embodiments of the invention discussed herein, the performance of assessments and calculations in real-time refers to processes that are completed in a matter of a few seconds or less rather than several minutes or longer as can happen with complex calculations, such as those involving typical CFD calculations. 
         [0128]    In at least some embodiments described above, the design of a data center and/or actual parameters in a data center are altered based on predicted temperature and/or airflow and/or the change in temperature and/or airflow upon the occurrence of a cooling system failure in a data center. For example, a user of the data center design and management system may change the location of coolers or the types of coolers that are used in the actual layout of equipment or the proposed layout of equipment in the data center. These alterations may be implemented to improve the cooling performance and/or may be implemented to provide cost and/or power savings when the performance is found to be within predetermined specifications. Further, based on determined airflow values, a data management system in accordance with one embodiment, may control one or more CRACs to adjust the airflow, and in addition, one or more equipment racks can be controlled to reduce power if the airflow is not adequate to provide sufficient cooling. 
         [0129]    In at least some embodiments described above, tools and processes are provided for determining temperatures and airflows in a data center. In other embodiments, the tools and processes may be used in other types of facilities, and may also be used in mobile applications, including mobile data centers. Further, processes and systems in accordance with embodiments described herein may be used in overhead air plenums, and other types of air plenums. 
         [0130]    Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description and drawings are by way of example only.